From 74ea4422621d70b313f60f78c80a29abe506d6b4 Mon Sep 17 00:00:00 2001
From: Karine Deschinkel <kdeschin@grappa.iut-bm.univ-fcomte.fr>
Date: Fri, 5 Jun 2015 16:18:31 +0200
Subject: [PATCH 1/1] super modifs

---
 PeCO-EO/articleeo.log  |   54 +-
 PeCO-EO/articleeo.pdf  |  Bin 734629 -> 734558 bytes
 PeCO-EO/articleeo.tex  |   74 +-
 PeCO-EO/articleeo.tex~ | 1733 ++++++++++++++++++++--------------------
 PeCO-EO/reponse.tex    |   87 +-
 5 files changed, 972 insertions(+), 976 deletions(-)

diff --git a/PeCO-EO/articleeo.log b/PeCO-EO/articleeo.log
index f0d9217..7e6f3a7 100644
--- a/PeCO-EO/articleeo.log
+++ b/PeCO-EO/articleeo.log
@@ -1,4 +1,4 @@
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+This is pdfTeX, Version 3.1415926-2.4-1.40.13 (TeX Live 2012/Debian) (format=pdflatex 2013.9.3)  15 MAY 2015 13:26
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-(epstopdf)                    date: 2015-05-08 17:47:31
+(epstopdf)                    date: 2015-02-20 10:11:12
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-(epstopdf)                    date: 2015-05-09 17:25:26
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@@ -522,10 +522,10 @@ File: figure1a-eps-converted-to.pdf Graphic file (type pdf)
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 Package epstopdf Info: Source file: <figure1b.eps>
-(epstopdf)                    date: 2015-05-08 17:47:31
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 (epstopdf)                    size: 241675 bytes
 (epstopdf)             Output file: <figure1b-eps-converted-to.pdf>
-(epstopdf)                    date: 2015-05-09 17:25:27
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-(epstopdf)                    date: 2015-05-08 17:47:31
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 (epstopdf)                    size: 508784 bytes
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-(epstopdf)                    date: 2015-05-08 17:47:31
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  [6 <./figure2-eps-converted-to.pdf> <./figure3-eps-converted-to.pdf>]
 Package epstopdf Info: Source file: <figure4.eps>
-(epstopdf)                    date: 2015-05-08 17:47:31
+(epstopdf)                    date: 2015-02-20 10:11:12
 (epstopdf)                    size: 428048 bytes
 (epstopdf)             Output file: <figure4-eps-converted-to.pdf>
-(epstopdf)                    date: 2015-05-09 17:25:29
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 (epstopdf)                    size: 24136 bytes
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-(epstopdf)                    date: 2015-05-09 17:25:30
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  [13 <./figure6-eps-converted-to.pdf>]
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diff --git a/PeCO-EO/articleeo.pdf b/PeCO-EO/articleeo.pdf
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diff --git a/PeCO-EO/articleeo.tex b/PeCO-EO/articleeo.tex
index 40af2f4..1dbc9e0 100644
--- a/PeCO-EO/articleeo.tex
+++ b/PeCO-EO/articleeo.tex
@@ -27,7 +27,7 @@ as long as  possible. Among  known  available approaches  that can  be used  to
 improve  power  management,  lifetime coverage  optimization  provides  activity
 scheduling which ensures sensing coverage while minimizing the energy cost. We propose such an approach called Perimeter-based Coverage Optimization
 protocol (PeCO). It is a  hybrid of centralized and distributed methods: the
-region of interest is first subdivided into subregions and our protocol is then
+region of interest is first subdivided into subregions and the protocol is then
 distributed among sensor nodes in each  subregion.
 The novelty of our approach lies essentially in the formulation of a new
 mathematical optimization  model based on the  perimeter coverage level  to schedule
@@ -100,8 +100,8 @@ This paper makes the following contributions.
 
 
 
-The rest  of the paper is  organized as follows.  In the next section  we review
-some related work in the  field. Section~\ref{sec:The PeCO Protocol Description}
+The rest  of the paper is  organized as follows.  In the next section
+some related work in the  field is reviewed. Section~\ref{sec:The PeCO Protocol Description}
 is devoted to the PeCO protocol  description and Section~\ref{cp} focuses on the
 coverage model  formulation which is used  to schedule the activation  of sensor
 nodes.  Section~\ref{sec:Simulation  Results and Analysis}  presents simulations
@@ -112,9 +112,9 @@ Section~\ref{sec:Conclusion and Future Works}.
 \section{Related Literature}
 \label{sec:Literature Review}
 
-In  this section,  we  summarize  some  related works  regarding  the
-coverage problem and  distinguish our PeCO protocol from the  works presented in
-the literature.
+In  this section, some  related works  regarding  the
+coverage problem is summarized, and specific aspects of the PeCO protocol from the  works presented in
+the literature are presented.
 
 The most  discussed coverage problems in  literature can be classified  in three
 categories~\citep{li2013survey}   according   to  their   respective   monitoring
@@ -129,8 +129,8 @@ nodes    or   between    disk   of    sensor   nodes    and   boundaries.     In
 \citep{Huang:2003:CPW:941350.941367}  authors prove  that  if  the perimeters  of
 sensors are sufficiently  covered it will be  the case for the  whole area. They
 provide an algorithm in $O(nd~log~d)$  time to compute the perimeter-coverage of
-each  sensor,  where  $d$  denotes  the  maximum  number  of  sensors  that  are
-neighbors  to  a  sensor and  $n$  is  the  total  number of  sensors  in  the
+each  sensor. $d$  denotes  the  maximum  number  of  sensors  that  are
+neighbors  to  a  sensor, and  $n$  is  the  total  number of  sensors  in  the
 network. {\it In PeCO protocol, instead  of determining the level of coverage of
   a set  of discrete  points, our  optimization model is  based on  checking the
   perimeter-coverage of each sensor to activate a minimal number of sensors.}
@@ -200,8 +200,8 @@ used~\citep{castano2013column,doi:10.1080/0305215X.2012.687732,deschinkel2012col
 \section{ The P{\scshape e}CO Protocol Description}
 \label{sec:The PeCO Protocol Description}
 
-In  this  section,  we  describe in  details  our Perimeter-based  Coverage
-Optimization protocol.  First we present the  assumptions we made and the models
+In  this  section,  the Perimeter-based  Coverage
+Optimization protocol is decribed in details.  First we present the  assumptions we made and the models
 we considered (in particular the perimeter coverage one), second we describe the
 background idea of our protocol, and third  we give the outline of the algorithm
 executed by each node.
@@ -217,11 +217,7 @@ of interest.  We  assume that all the  sensor nodes are homogeneous  in terms of
 communication,  sensing,  and  processing capabilities  and  heterogeneous  from
 the energy provision  point of  view.  The  location information  is available  to a
 sensor node either  through hardware such as embedded GPS  or location discovery
-algorithms.   We  assume  that  each  sensor  node  can  directly  transmit  its
-measurements to  a mobile  sink node.  For  example, a sink  can be  an unmanned
-aerial  vehicle  (UAV)  flying  regularly  over  the  sensor  field  to  collect
-measurements from sensor nodes. A mobile sink node collects the measurements and
-transmits them to the base station.   We consider a Boolean disk coverage model,
+algorithms. We consider a Boolean disk coverage model,
 which is the most  widely used sensor coverage model in  the literature, and all
 sensor nodes  have a constant sensing  range $R_s$.  Thus, all  the space points
 within a disk centered at a sensor with  a radius equal to the sensing range are
@@ -232,11 +228,11 @@ complete coverage of a convex area implies connectivity among active nodes.
 
 The PeCO protocol  uses the  same perimeter-coverage  model as \citet{huang2005coverage}. It  can be expressed as follows:  a sensor is
 said to be perimeter  covered if all the points on its  perimeter are covered by
-at least  one sensor  other than  itself.  They  proved that  a network  area is
-$k$-covered if and only if each sensor in the network is $k$-perimeter-covered (perimeter covered by at least $k$ sensors).
+at least  one sensor  other than  itself. Authors \citet{huang2005coverage}  proved that  a network  area is
+$k$-covered (every point in the area covered by at least k sensors) if and only if each sensor in the network is $k$-perimeter-covered (perimeter covered by at least $k$ sensors). 
  
 Figure~\ref{figure1}(a)  shows  the coverage  of  sensor  node~$0$. On  this
-figure, we can  see that sensor~$0$ has  nine neighbors and we  have reported on
+figure, sensor~$0$ has  nine neighbors and we  have reported on
 its  perimeter (the  perimeter  of the  disk  covered by  the  sensor) for  each
 neighbor  the  two  points  resulting  from the intersection  of  the  two  sensing
 areas. These points are denoted for  neighbor~$i$ by $iL$ and $iR$, respectively
@@ -259,8 +255,8 @@ Figure~\ref{figure1}(b) describes the geometric information used to find the
 locations of the  left and right points of  an arc on the perimeter  of a sensor
 node~$u$ covered by a sensor node~$v$. Node~$v$ is supposed to be located on the
 west  side of  sensor~$u$,  with  the following  respective  coordinates in  the
-sensing area~: $(v_x,v_y)$ and $(u_x,u_y)$. From the previous coordinates we can
-compute the euclidean distance between nodes~$u$ and $v$: $Dist(u,v)=\sqrt{\vert
+sensing area~: $(v_x,v_y)$ and $(u_x,u_y)$. From the previous coordinates 
+the euclidean distance between nodes~$u$ and $v$ is computed: $Dist(u,v)=\sqrt{\vert
   u_x  - v_x  \vert^2 +  \vert u_y-v_y  \vert^2}$, while  the angle~$\alpha$  is
 obtained through  the formula:
  \[
@@ -274,7 +270,7 @@ Every couple of intersection points is placed on the angular interval $[0,2\pi)$
 in  a  counterclockwise manner,  leading  to  a  partitioning of  the  interval.
 Figure~\ref{figure1}(a)  illustrates  the arcs  for  the  nine neighbors  of
 sensor $0$ and  Figure~\ref{figure2} gives the position of  the corresponding arcs
-in  the interval  $[0,2\pi)$. More  precisely, we  can see  that the  points are
+in  the interval  $[0,2\pi)$. More  precisely, the  points are
 ordered according  to the  measures of  the angles  defined by  their respective
 positions. The intersection points are  then visited one after another, starting
 from the first  intersection point  after  point~zero,  and  the maximum  level  of
@@ -471,10 +467,10 @@ construct the set of active sensors in the sensing stage.
 \section{Perimeter-based Coverage Problem Formulation}
 \label{cp}
 
-In this  section, the coverage model is  mathematically formulated. We
-start  with a  description of the notations that will  be used  throughout the
+In this  section, the coverage model is  mathematically formulated. The following
+notations are used  throughout the
 section.\\
-First, we have the following sets:
+First, the following sets:
 \begin{itemize}
 \item $S$ represents the set of WSN sensor nodes;
 \item $A \subseteq S $ is the subset of alive sensors;
@@ -495,7 +491,7 @@ a^j_{ik} = \left \{
 \end{equation}
 Note that $a^k_{ik}=1$ by definition of the interval.
 
-Second,  we define  several binary  and integer  variables.  Hence,  each binary
+Second, several binary  and integer  variables are defined.  Hence,  each binary
 variable $X_{k}$  determines the activation of  sensor $k$ in the  sensing phase
 ($X_k=1$ if  the sensor $k$  is active or 0  otherwise).  $M^j_i$ is  an integer
 variable  which  measures  the  undercoverage  for  the  coverage  interval  $i$
@@ -510,7 +506,7 @@ sensor $j$  is given by  $\sum_{k \in A} a^j_{ik}  X_k$.  To extend  the network
 lifetime,  the objective  is to  activate a  minimal number  of sensors  in each
 period to  ensure the  desired coverage  level. As the  number of  alive sensors
 decreases, it becomes impossible to reach  the desired level of coverage for all
-coverage intervals. Therefore we use variables  $M^j_i$ and $V^j_i$ as a measure
+coverage intervals. Therefore  variables  $M^j_i$ and $V^j_i$ are introduced as a measure
 of the  deviation between  the desired  number of active  sensors in  a coverage
 interval and  the effective  number. And  we try  to minimize  these deviations,
 first to  force the  activation of  a minimal  number of  sensors to  ensure the
@@ -527,8 +523,8 @@ Our coverage optimization problem can then be mathematically expressed as follow
 \begin{array}{ll}
 \min \sum_{j \in S} \sum_{i \in I_j} (\alpha^j_i ~ M^j_i + \beta^j_i ~ V^j_i )&\\
 \textrm{subject to :}&\\
-\sum_{k \in A} ( a^j_{ik} ~ X_{k}) + M^j_i  \geq l \quad \forall i \in I_j, \forall j \in S\\
-\sum_{k \in A} ( a^j_{ik} ~ X_{k}) - V^j_i  \leq l \quad \forall i \in I_j, \forall j \in S\\
+\sum_{k \in A} ( a^j_{ik} ~ X_{k}) + M^j_i  = l \quad \forall i \in I_j, \forall j \in S\\
+\sum_{k \in A} ( a^j_{ik} ~ X_{k}) - V^j_i  = l \quad \forall i \in I_j, \forall j \in S\\
 X_{k} \in \{0,1\}, \forall k \in A
 \end{array}
 \right.
@@ -544,9 +540,9 @@ brachytherapy treatment planning  for optimizing dose  distribution
 each subregion at the beginning of  each sensing phase, whenever the environment
 has  changed (new  leader,  death of  some  sensors). Note  that  the number  of
 constraints in the model is constant  (constraints of coverage expressed for all
-sensors), whereas the number of variables $X_k$ decreases over periods, since we
-consider only alive  sensors (sensors with enough energy to  be alive during one
-sensing phase) in the model.
+sensors), whereas the number of variables $X_k$ decreases over periods, since 
+only alive  sensors (sensors with enough energy to  be alive during one
+sensing phase) are considered in the model.
 
 \section{Performance Evaluation and Analysis}  
 \label{sec:Simulation Results and Analysis}
@@ -580,7 +576,7 @@ Initial energy  & in range 500-700~Joules  \\
 Sensing period & duration of 60 minutes \\
 $E_{th}$ & 36~Joules\\
 $R_s$ & 5~m   \\     
-
+$R_c$ & 10~m   \\   
 $\alpha^j_i$ & 0.6   \\
 
 $\beta^j_i$ & 0.4
@@ -604,14 +600,14 @@ pre-sensing phases.  According  to the interval of initial energy,  a sensor may
 be active during at most 20 periods.
 
 The values  of $\alpha^j_i$ and  $\beta^j_i$ have been  chosen to ensure  a good
-network coverage and a longer WSN lifetime.  We have given a higher priority to
+network coverage and a longer WSN lifetime.  Higher priority is given to
 the  undercoverage  (by  setting  the  $\alpha^j_i$ with  a  larger  value  than
 $\beta^j_i$)  so as  to prevent  the non-coverage  for the  interval~$i$ of  the
-sensor~$j$.  On the  other hand,  we have assigned to
-$\beta^j_i$ a value which is slightly lower so as to minimize the number of active sensor nodes which contribute
+sensor~$j$.  On the  other hand,  
+$\beta^j_i$ is assigned to a value which is slightly lower so as to minimize the number of active sensor nodes which contribute
 in covering the interval.
 
-We introduce the following performance metrics to evaluate the efficiency of our
+The following performance metrics are used to evaluate the efficiency of the
 approach.
 
 
@@ -625,7 +621,7 @@ approach.
   because without  network connectivity a  sensor may not be  able to send  to a
   base station an event it has sensed.
 \item {\bf  Coverage Ratio (CR)} : it  measures how  well the  WSN is  able to
-  observe the area of interest. In our  case, we discretized the sensor field as
+  observe the area of interest. In our  case, the sensor field is discretized as
   a regular grid, which yields the following equation:
   
 
@@ -637,8 +633,8 @@ approach.
 
   where $n$  is the  number of covered  grid points by  active sensors  of every
   subregions during  the current sensing phase  and $N$ is total  number of grid
-  points in  the sensing  field.  In  our simulations  we have  set a  layout of
-  $N~=~51~\times~26~=~1326$~grid points.
+  points in  the sensing  field.  In  simulations  a  layout of
+  $N~=~51~\times~26~=~1326$~grid points is considered.
 \item {\bf Active Sensors Ratio (ASR)}: a  major objective of our protocol is to
   activate  as few nodes as possible,  in order  to minimize  the communication
   overhead and maximize the WSN lifetime. The active sensors ratio is defined as
diff --git a/PeCO-EO/articleeo.tex~ b/PeCO-EO/articleeo.tex~
index caeaa18..58e1e1d 100644
--- a/PeCO-EO/articleeo.tex~
+++ b/PeCO-EO/articleeo.tex~
@@ -1,867 +1,866 @@
-% gENOguide.tex
-% v4.0 released April 2013
-
-\documentclass{gENO2e}
-%\usepackage[linesnumbered,ruled,vlined,commentsnumbered]{algorithm2e}
-%\renewcommand{\algorithmcfname}{ALGORITHM}
-\begin{document}
-
-%\jvol{00} \jnum{00} \jyear{2013} \jmonth{April}
-
-%\articletype{GUIDE}
-
-\title{{\itshape Perimeter-based Coverage Optimization to Improve Lifetime in Wireless Sensor Networks}}
-
-\author{Ali Kadhum Idrees$^{a}$, Karine Deschinkel$^{a}$$^{\ast}$\thanks{$^\ast$Corresponding author. Email: karine.deschinkel@univ-fcomte.fr}, Michel Salomon$^{a}$ and Rapha\"el Couturier $^{a}$
-$^{a}${\em{FEMTO-ST Institute, UMR 6174 CNRS, University of Franche-Comte,
-          Belfort, France}};}
-
-
-\maketitle
-
-\begin{abstract}
-The most important problem in a Wireless Sensor Network (WSN) is to optimize the
-use of its limited energy provision, so that it can fulfill its monitoring task
-as long as  possible. Among  known  available approaches  that can  be used  to
-improve  power  management,  lifetime coverage  optimization  provides  activity
-scheduling which ensures sensing coverage while minimizing the energy cost. In
-this paper,  we propose such an approach called Perimeter-based Coverage Optimization
-protocol (PeCO). It is a  hybrid of centralized and distributed methods: the
-region of interest is first subdivided into subregions and our protocol is then
-distributed among sensor nodes in each  subregion.
-The novelty of our approach lies essentially in the formulation of a new
-mathematical optimization  model based on the  perimeter coverage level  to schedule
-sensors' activities.  Extensive simulation experiments have been performed using
-OMNeT++, the  discrete event simulator, to  demonstrate that PeCO  can
-offer longer lifetime coverage for WSNs in comparison with some other protocols.
-
-\begin{keywords}Wireless Sensor Networks, Area Coverage, Energy efficiency, Optimization, Scheduling.
-\end{keywords}
-
-\end{abstract}
-
-
-\section{Introduction}
-\label{sec:introduction}
-
-\noindent The continuous progress in Micro Electro-Mechanical Systems (MEMS) and
-wireless communication hardware  has given rise to the opportunity  to use large
-networks    of     tiny    sensors,    called    Wireless     Sensor    Networks
-(WSN)~\citep{akyildiz2002wireless,puccinelli2005wireless}, to  fulfill monitoring
-tasks.   A  WSN  consists  of  small low-powered  sensors  working  together  by
-communicating with one another through multi-hop radio communications. Each node
-can send the data  it collects in its environment, thanks to  its sensor, to the
-user by means of  sink nodes. The features of a WSN made  it suitable for a wide
-range of application  in areas such as business,  environment, health, industry,
-military, and so on~\citep{yick2008wireless}.   Typically, a sensor node contains
-three main components~\citep{anastasi2009energy}: a  sensing unit able to measure
-physical,  chemical, or  biological  phenomena observed  in  the environment;  a
-processing unit which will process and store the collected measurements; a radio
-communication unit for data transmission and receiving.
-
-The energy needed  by an active sensor node to  perform sensing, processing, and
-communication is supplied by a power supply which is a battery. This battery has
-a limited energy provision and it may  be unsuitable or impossible to replace or
-recharge it in  most applications. Therefore it is necessary  to deploy WSN with
-high density in order to increase  reliability and to exploit node redundancy
-thanks to energy-efficient activity  scheduling approaches.  Indeed, the overlap
-of sensing  areas can be exploited  to schedule alternatively some  sensors in a
-low power sleep mode and thus save  energy. Overall, the main question that must
-be answered is: how to extend the lifetime coverage of a WSN as long as possible
-while  ensuring   a  high  level  of   coverage?   These past few years  many
-energy-efficient mechanisms have been suggested  to retain energy and extend the
-lifetime of the WSNs~\citep{rault2014energy}.\\\\
-This paper makes the following contributions.
-\begin{enumerate}
-\item We have devised a framework to schedule nodes to be activated alternatively such
-  that the network lifetime is prolonged  while ensuring that a certain level of
-  coverage is preserved.  A key idea in  our framework is to exploit spatial and
-  temporal subdivision.   On the one hand,  the area of interest  is divided into
-  several smaller subregions and, on the other hand, the time line is divided into
-  periods of equal length. In each subregion the sensor nodes will cooperatively
-  choose a  leader which will schedule  nodes' activities, and this  grouping of
-  sensors is similar to typical cluster architecture.
-\item We have proposed a new mathematical  optimization model.  Instead of  trying to
-  cover a set of specified points/targets as  in most of the methods proposed in
-  the literature, we formulate an integer program based on perimeter coverage of
-  each sensor.  The  model involves integer variables to  capture the deviations
-  between  the actual  level of  coverage and  the required  level.  Hence, an
-  optimal scheduling  will be  obtained by  minimizing a  weighted sum  of these
-  deviations.
-\item We have conducted extensive simulation  experiments, using the  discrete event
-  simulator OMNeT++, to demonstrate the  efficiency of our protocol. We have compared
-  our   PeCO   protocol   to   two   approaches   found   in   the   literature:
-  DESK~\citep{ChinhVu} and  GAF~\citep{xu2001geography}, and also to  our previous
-  work published in~\citep{Idrees2} which is  based on another optimization model
-  for sensor scheduling.
-\end{enumerate}
-
-
-
-
-
-
-The rest  of the paper is  organized as follows.  In the next section  we review
-some related work in the  field. Section~\ref{sec:The PeCO Protocol Description}
-is devoted to the PeCO protocol  description and Section~\ref{cp} focuses on the
-coverage model  formulation which is used  to schedule the activation  of sensor
-nodes.  Section~\ref{sec:Simulation  Results and Analysis}  presents simulations
-results and discusses the comparison  with other approaches. Finally, concluding
-remarks   are  drawn   and  some   suggestions are  given  for   future  works   in
-Section~\ref{sec:Conclusion and Future Works}.
-
-\section{Related Literature}
-\label{sec:Literature Review}
-
-\noindent  In  this section,  we  summarize  some  related works  regarding  the
-coverage problem and  distinguish our PeCO protocol from the  works presented in
-the literature.
-
-The most  discussed coverage problems in  literature can be classified  in three
-categories~\citep{li2013survey}   according   to  their   respective   monitoring
-objective.  Hence,  area coverage \citep{Misra}  means that every point  inside a
-fixed area  must be monitored, while  target coverage~\citep{yang2014novel} refers
-to  the objective  of coverage  for a  finite number  of discrete  points called
-targets,  and  barrier coverage~\citep{HeShibo,kim2013maximum}  focuses  on
-preventing  intruders   from  entering   into  the   region  of   interest.   In
-\citep{Deng2012}  authors  transform the  area  coverage  problem into  the  target
-coverage one taking into account the  intersection points among disks of sensors
-nodes    or   between    disk   of    sensor   nodes    and   boundaries.     In
-\citep{Huang:2003:CPW:941350.941367}  authors prove  that  if  the perimeters  of
-sensors are sufficiently  covered it will be  the case for the  whole area. They
-provide an algorithm in $O(nd~log~d)$  time to compute the perimeter-coverage of
-each  sensor,  where  $d$  denotes  the  maximum  number  of  sensors  that  are
-neighbors  to  a  sensor and  $n$  is  the  total  number of  sensors  in  the
-network. {\it In PeCO protocol, instead  of determining the level of coverage of
-  a set  of discrete  points, our  optimization model is  based on  checking the
-  perimeter-coverage of each sensor to activate a minimal number of sensors.}
-
-The major  approach to extend network  lifetime while preserving coverage  is to
-divide/organize the  sensors into a suitable  number of set covers  (disjoint or
-non-disjoint)\citep{wang2011coverage}, where  each set completely  covers a  region of interest,  and to
-activate these set  covers successively. The network activity can  be planned in
-advance and scheduled  for the entire network lifetime or  organized in periods,
-and the set  of active sensor nodes  is decided at the beginning  of each period
-\citep{ling2009energy}.  Active node selection is determined based on the problem
-requirements (e.g.   area monitoring,  connectivity, or power  efficiency).  For
-instance, \citet{jaggi2006}  address the problem of maximizing
-the lifetime  by dividing sensors  into the  maximum number of  disjoint subsets
-such  that each  subset  can ensure  both coverage  and  connectivity. A  greedy
-algorithm  is applied  once to  solve  this problem  and the  computed sets  are
-activated  in   succession  to  achieve   the  desired  network   lifetime.   
-\citet{chin2007},  \citet{yan2008design}, \citet{pc10},  propose  algorithms
-working in a periodic fashion where a  cover set is computed at the beginning of
-each period.   {\it Motivated by  these works,  PeCO protocol works  in periods,
-  where each  period contains a  preliminary phase for information  exchange and
-  decisions, followed by a sensing phase where one cover set is in charge of the
-  sensing task.}
-
-Various centralized  and distributed approaches, or  even a mixing  of these two
-concepts, have  been proposed  to extend the  network lifetime \citep{zhou2009variable}.   In distributed algorithms~\citep{Tian02,yangnovel,ChinhVu,qu2013distributed} each sensor decides of its
-own activity scheduling  after an information exchange with  its neighbors.  The
-main interest of such an approach is to avoid long range communications and thus
-to reduce the energy dedicated to the communications.  Unfortunately, since each
-node has only information on  its immediate neighbors (usually the one-hop ones)
-it may make a bad decision leading to a global suboptimal solution.  Conversely,
-centralized
-algorithms~\citep{cardei2005improving,zorbas2010solving,pujari2011high}     always
-provide nearly  or close to  optimal solution since  the algorithm has  a global
-view of the whole network. The disadvantage of a centralized method is obviously
-its high  cost in communications needed to  transmit to a single  node, the base
-station which will globally schedule  nodes' activities, data from all the other
-sensor nodes  in the area.  The price  in communications can be  huge since
-long range  communications will be  needed. In fact  the larger the WNS  is, the
-higher the  communication and  thus the energy  cost are.   {\it In order  to be
-  suitable for large-scale  networks, in the PeCO protocol,  the area of interest
-  is divided into several smaller subregions, and in each one, a node called the
-  leader  is  in  charge  of  selecting  the active  sensors  for  the  current
-  period.  Thus our  protocol is  scalable  and is a  globally distributed  method,
-  whereas it is centralized in each subregion.}
-
-Various  coverage scheduling  algorithms have  been developed  these past few years.
-Many of  them, dealing with  the maximization of the  number of cover  sets, are
-heuristics.   These  heuristics involve  the  construction  of  a cover  set  by
-including in priority the sensor nodes  which cover critical targets, that is to
-say   targets   that  are   covered   by   the   smallest  number   of   sensors
-\citep{berman04,zorbas2010solving}.  Other  approaches are based  on mathematical
-programming formulations~\citep{cardei2005energy,5714480,pujari2011high,Yang2014}
-and dedicated techniques (solving with a branch-and-bound algorithm available in
-optimization  solver).  The  problem is  formulated as  an optimization  problem
-(maximization of the lifetime or number of cover sets) under target coverage and
-energy  constraints.   Column  generation   techniques,  well-known  and  widely
-practiced techniques for  solving linear programs with too  many variables, have
-also                                                                        been
-used~\citep{castano2013column,doi:10.1080/0305215X.2012.687732,deschinkel2012column}. {\it  In the PeCO
-  protocol, each  leader, in charge  of a  subregion, solves an  integer program
-  which has a twofold objective: minimize the overcoverage and the undercoverage
-  of the perimeter of each sensor.}
-
-
-
-\section{ The P{\scshape e}CO Protocol Description}
-\label{sec:The PeCO Protocol Description}
-
-\noindent  In  this  section,  we  describe in  details  our Perimeter-based  Coverage
-Optimization protocol.  First we present the  assumptions we made and the models
-we considered (in particular the perimeter coverage one), second we describe the
-background idea of our protocol, and third  we give the outline of the algorithm
-executed by each node.
-
-
-\subsection{Assumptions and Models}
-\label{CI}
-
-\noindent A WSN consisting of $J$ stationary sensor nodes randomly and uniformly
-distributed in  a bounded sensor field  is considered. The wireless  sensors are
-deployed in high density  to ensure initially a high coverage  ratio of the area
-of interest.  We  assume that all the  sensor nodes are homogeneous  in terms of
-communication,  sensing,  and  processing capabilities  and  heterogeneous  from
-the energy provision  point of  view.  The  location information  is available  to a
-sensor node either  through hardware such as embedded GPS  or location discovery
-algorithms.   We  assume  that  each  sensor  node  can  directly  transmit  its
-measurements to  a mobile  sink node.  For  example, a sink  can be  an unmanned
-aerial  vehicle  (UAV)  flying  regularly  over  the  sensor  field  to  collect
-measurements from sensor nodes. A mobile sink node collects the measurements and
-transmits them to the base station.   We consider a Boolean disk coverage model,
-which is the most  widely used sensor coverage model in  the literature, and all
-sensor nodes  have a constant sensing  range $R_s$.  Thus, all  the space points
-within a disk centered at a sensor with  a radius equal to the sensing range are
-said to be covered  by this sensor. We also assume  that the communication range
-$R_c$ satisfies $R_c  \geq 2 \cdot R_s$. In fact,  \citet{Zhang05}
-proved  that if  the  transmission  range fulfills  the  previous hypothesis,  the
-complete coverage of a convex area implies connectivity among active nodes.
-
-The PeCO protocol  uses the  same perimeter-coverage  model as \citet{huang2005coverage}. It  can be expressed as follows:  a sensor is
-said to be perimeter  covered if all the points on its  perimeter are covered by
-at least  one sensor  other than  itself.  They  proved that  a network  area is
-$k$-covered if and only if each sensor in the network is $k$-perimeter-covered (perimeter covered by at least $k$ sensors).
- 
-Figure~\ref{figure1}(a)  shows  the coverage  of  sensor  node~$0$. On  this
-figure, we can  see that sensor~$0$ has  nine neighbors and we  have reported on
-its  perimeter (the  perimeter  of the  disk  covered by  the  sensor) for  each
-neighbor  the  two  points  resulting  from the intersection  of  the  two  sensing
-areas. These points are denoted for  neighbor~$i$ by $iL$ and $iR$, respectively
-for  left and  right from  a neighboing  point of  view.  The  resulting couples  of
-intersection points subdivide  the perimeter of sensor~$0$  into portions called
-arcs.
-
-\begin{figure}[ht!]
-  \centering
-  \begin{tabular}{@{}cr@{}}
-    \includegraphics[width=75mm]{figure1a.eps} & \raisebox{3.25cm}{(a)} \\
-    \includegraphics[width=75mm]{figure1b.eps} & \raisebox{2.75cm}{(b)}
-  \end{tabular}
-  \caption{(a) Perimeter  coverage of sensor node  0 and (b) finding  the arc of
-    $u$'s perimeter covered by $v$.}
-  \label{figure1}
-\end{figure} 
-
-Figure~\ref{figure1}(b) describes the geometric information used to find the
-locations of the  left and right points of  an arc on the perimeter  of a sensor
-node~$u$ covered by a sensor node~$v$. Node~$v$ is supposed to be located on the
-west  side of  sensor~$u$,  with  the following  respective  coordinates in  the
-sensing area~: $(v_x,v_y)$ and $(u_x,u_y)$. From the previous coordinates we can
-compute the euclidean distance between nodes~$u$ and $v$: $Dist(u,v)=\sqrt{\vert
-  u_x  - v_x  \vert^2 +  \vert u_y-v_y  \vert^2}$, while  the angle~$\alpha$  is
-obtained through  the formula:
- \[
-\alpha =  \arccos \left(\frac{Dist(u,v)}{2R_s}
-\right).
-\] 
-The arc on the perimeter of~$u$ defined by the angular interval $[\pi
-  - \alpha,\pi + \alpha]$ is said to be perimeter-covered by sensor~$v$.
-
-Every couple of intersection points is placed on the angular interval $[0,2\pi]$
-in  a  counterclockwise manner,  leading  to  a  partitioning of  the  interval.
-Figure~\ref{figure1}(a)  illustrates  the arcs  for  the  nine neighbors  of
-sensor $0$ and  figure~\ref{figure2} gives the position of  the corresponding arcs
-in  the interval  $[0,2\pi]$. More  precisely, we  can see  that the  points are
-ordered according  to the  measures of  the angles  defined by  their respective
-positions. The intersection points are  then visited one after another, starting
-from the first  intersection point  after  point~zero,  and  the maximum  level  of
-coverage is determined  for each interval defined by two  successive points. The
-maximum  level of  coverage is  equal to  the number  of overlapping  arcs.  For
-example, 
-between~$5L$  and~$6L$ the maximum  level of  coverage is equal  to $3$
-(the value is highlighted in yellow  at the bottom of figure~\ref{figure2}), which
-means that at most 2~neighbors can cover  the perimeter in addition to node $0$. 
-Table~\ref{my-label} summarizes for each coverage  interval the maximum level of
-coverage and  the sensor  nodes covering the  perimeter.  The  example discussed
-above is thus given by the sixth line of the table.
-
-
-\begin{figure*}[t!]
-\centering
-\includegraphics[width=127.5mm]{figure2.eps}  
-\caption{Maximum coverage levels for perimeter of sensor node $0$.}
-\label{figure2}
-\end{figure*} 
-
-
-
-
- \begin{table}
- \tbl{Coverage intervals and contributing sensors for sensor node 0 \label{my-label}}
-{\begin{tabular}{|c|c|c|c|c|c|c|c|c|}
-\hline
-\begin{tabular}[c]{@{}c@{}}Left \\ point \\ angle~$\alpha$ \end{tabular} & \begin{tabular}[c]{@{}c@{}}Interval \\ left \\ point\end{tabular} & \begin{tabular}[c]{@{}c@{}}Interval \\ right \\ point\end{tabular} & \begin{tabular}[c]{@{}c@{}}Maximum \\ coverage\\  level\end{tabular} & \multicolumn{5}{c|}{\begin{tabular}[c]{@{}c@{}}Set of sensors\\ involved \\ in coverage interval\end{tabular}} \\ \hline
-0.0291    & 1L                                                                        & 2L                                                        & 4                                                                     & 0                     & 1                     & 3                    & 4                    &                      \\ \hline
-0.104     & 2L                                                                        & 3R                                                        & 5                                                                     & 0                     & 1                     & 3                    & 4                    & 2                    \\ \hline
-0.3168    & 3R                                                                        & 4R                                                        & 4                                                                     & 0                     & 1                     & 4                    & 2                    &                      \\ \hline
-0.6752    & 4R                                                                        & 1R                                                        & 3                                                                     & 0                     & 1                     & 2                    &                      &                      \\ \hline
-1.8127    & 1R                                                                        & 5L                                                        & 2                                                                     & 0                     & 2                     &                      &                      &                      \\ \hline
-1.9228    & 5L                                                                        & 6L                                                        & 3                                                                     & 0                     & 2                     & 5                    &                      &                      \\ \hline
-2.3959    & 6L                                                                        & 2R                                                        & 4                                                                     & 0                     & 2                     & 5                    & 6                    &                      \\ \hline
-2.4258    & 2R                                                                        & 7L                                                        & 3                                                                     & 0                     & 5                     & 6                    &                      &                      \\ \hline
-2.7868    & 7L                                                                        & 8L                                                        & 4                                                                     & 0                     & 5                     & 6                    & 7                    &                      \\ \hline
-2.8358    & 8L                                                                        & 5R                                                        & 5                                                                     & 0                     & 5                     & 6                    & 7                    & 8                    \\ \hline
-2.9184    & 5R                                                                        & 7R                                                        & 4                                                                     & 0                     & 6                     & 7                    & 8                    &                      \\ \hline
-3.3301    & 7R                                                                        & 9R                                                        & 3                                                                     & 0                     & 6                     & 8                    &                      &                      \\ \hline
-3.9464    & 9R                                                                        & 6R                                                        & 4                                                                     & 0                     & 6                     & 8                    & 9                    &                      \\ \hline
-4.767     & 6R                                                                        & 3L                                                        & 3                                                                     & 0                     & 8                     & 9                    &                      &                      \\ \hline
-4.8425    & 3L                                                                        & 8R                                                        & 4                                                                     & 0                     & 3                     & 8                    & 9                    &                      \\ \hline
-4.9072    & 8R                                                                        & 4L                                                        & 3                                                                     & 0                     & 3                     & 9                    &                      &                      \\ \hline
-5.3804    & 4L                                                                        & 9R                                                        & 4                                                                     & 0                     & 3                     & 4                    & 9                    &                      \\ \hline
-5.9157    & 9R                                                                        & 1L                                                        & 3                                                                     & 0                     & 3                     & 4                    &                      &                      \\ \hline
-\end{tabular}}
-
-
-\end{table}
-
-
-
-
-In the PeCO  protocol, the scheduling of the sensor  nodes' activities is formulated  with an
-integer program  based on  coverage intervals. The  formulation of  the coverage
-optimization problem is  detailed in~section~\ref{cp}.  Note that  when a sensor
-node  has a  part of  its sensing  range outside  the WSN  sensing field,  as in
-figure~\ref{figure3}, the maximum coverage level for  this arc is set to $\infty$
-and  the  corresponding  interval  will  not   be  taken  into  account  by  the
-optimization algorithm.
-
- \newpage
-\begin{figure}[h!]
-\centering
-\includegraphics[width=62.5mm]{figure3.eps}  
-\caption{Sensing range outside the WSN's area of interest.}
-\label{figure3}
-\end{figure} 
-
-
-\subsection{The Main Idea}
-
-\noindent The  WSN area of  interest is, in a  first step, divided  into regular
-homogeneous subregions  using a divide-and-conquer  algorithm. In a  second step
-our  protocol  will  be  executed  in   a  distributed  way  in  each  subregion
-simultaneously to schedule nodes' activities for one sensing period.
-
-As  shown in  figure~\ref{figure4}, node  activity  scheduling is  produced by  our
-protocol in a periodic manner. Each period is divided into 4 stages: Information
-(INFO)  Exchange,  Leader Election,  Decision  (the  result of  an  optimization
-problem),  and  Sensing.   For  each  period there  is  exactly  one  set  cover
-responsible for  the sensing task.  Protocols  based on a periodic  scheme, like
-PeCO, are more  robust against an unexpected  node failure. On the  one hand, if
-a node failure is discovered before  taking the decision, the corresponding sensor
-node will  not be considered  by the optimization  algorithm. On  the other
-hand, if the sensor failure happens after  the decision, the sensing task of the
-network will be temporarily affected: only  during the period of sensing until a
-new period starts, since a new set cover will take charge of the sensing task in
-the next period. The energy consumption and some other constraints can easily be
-taken  into  account since  the  sensors  can  update  and then  exchange  their
-information (including their  residual energy) at the beginning  of each period.
-However, the pre-sensing  phases (INFO Exchange, Leader  Election, and Decision)
-are energy consuming, even for nodes that will not join the set cover to monitor
-the area.
-
-\begin{figure}[t!]
-\centering
-\includegraphics[width=80mm]{figure4.eps}  
-\caption{PeCO protocol.}
-\label{figure4}
-\end{figure} 
-
-We define two types of packets to be used by PeCO protocol:
-
-\begin{itemize} 
-\item INFO  packet: sent  by each  sensor node to  all the  nodes inside  a same
-  subregion for information exchange.
-\item ActiveSleep packet: sent  by the leader to all the  nodes in its subregion
-  to transmit to  them their respective status (stay Active  or go Sleep) during
-  sensing phase.
-\end{itemize}
-
-
-Five status are possible for a sensor node in the network:
-
-\begin{itemize} 
-\item LISTENING: waits for a decision (to be active or not);
-\item COMPUTATION: executes the optimization algorithm as leader to
-  determine the activities scheduling;
-\item ACTIVE: node is sensing;
-\item SLEEP: node is turned off;
-\item COMMUNICATION: transmits or receives packets.
-\end{itemize}
-
-
-\subsection{PeCO Protocol Algorithm}
-
-\noindent The  pseudocode implementing the  protocol on  a node is  given below.
-More  precisely,  Algorithm~\ref{alg:PeCO}  gives  a brief  description  of  the
-protocol applied by a sensor node $s_k$ where $k$ is the node index in the WSN.
-
-
-
-\begin{algorithm}      
- % \KwIn{all the parameters related to information exchange}
-%  \KwOut{$winer-node$ (: the id of the winner sensor node, which is the leader of current round)}
-%  \BlankLine
-  %\emph{Initialize the sensor node and determine it's position and subregion} \; 
-  
-\noindent{\bf If} $RE_k \geq E_{th}$ {\bf then}\\
-\hspace*{0.6cm} \emph{$s_k.status$ = COMMUNICATION;}\\
-\hspace*{0.6cm}  \emph{Send $INFO()$ packet to other nodes in subregion;}\\
-\hspace*{0.6cm}  \emph{Wait $INFO()$ packet from other nodes in subregion;}\\
-\hspace*{0.6cm} \emph{Update K.CurrentSize;}\\
-\hspace*{0.6cm}  \emph{LeaderID = Leader election;}\\
-\hspace*{0.6cm} {\bf If} $ s_k.ID = LeaderID $ {\bf then}\\
-\hspace*{1.2cm}   \emph{$s_k.status$ = COMPUTATION;}\\
-\hspace*{1.2cm}{\bf If} \emph{$ s_k.ID $ is Not previously selected as a Leader} {\bf then}\\
-\hspace*{1.8cm} \emph{ Execute the perimeter coverage model;}\\
-\hspace*{1.2cm} {\bf end}\\
-\hspace*{1.2cm}{\bf If} \emph{($s_k.ID $ is the same Previous Leader)~And~(K.CurrentSize = K.PreviousSize)}\\
-\hspace*{1.8cm} \emph{ Use the same previous cover set for current sensing stage;}\\
-\hspace*{1.2cm}  {\bf end}\\
-\hspace*{1.2cm}  {\bf else}\\
-\hspace*{1.8cm}\emph{Update $a^j_{ik}$; prepare data for IP~Algorithm;}\\
-\hspace*{1.8cm} \emph{$\left\{\left(X_{1},\dots,X_{l},\dots,X_{K}\right)\right\}$ = Execute Integer Program Algorithm($K$);}\\
-\hspace*{1.8cm} \emph{K.PreviousSize = K.CurrentSize;}\\
-\hspace*{1.2cm}  {\bf end}\\
-\hspace*{1.2cm}\emph{$s_k.status$ = COMMUNICATION;}\\
-\hspace*{1.2cm}\emph{Send $ActiveSleep()$ to each node $l$ in subregion;}\\
-\hspace*{1.2cm}\emph{Update $RE_k $;}\\
-\hspace*{0.6cm}  {\bf end}\\
-\hspace*{0.6cm}  {\bf else}\\
-\hspace*{1.2cm}\emph{$s_k.status$ = LISTENING;}\\
-\hspace*{1.2cm}\emph{Wait $ActiveSleep()$ packet from the Leader;}\\
-\hspace*{1.2cm}\emph{Update $RE_k $;}\\
-\hspace*{0.6cm}  {\bf end}\\
-{\bf end}\\
-{\bf else}\\
-\hspace*{0.6cm} \emph{Exclude $s_k$ from entering in the current sensing stage;}\\
-{\bf end}\\
-\label{alg:PeCO}
-\end{algorithm}
-
-
-
-In this  algorithm, K.CurrentSize and K.PreviousSize  respectively represent the
-current number and  the previous number of living nodes in  the subnetwork of the
-subregion.  Initially, the sensor node checks its remaining energy $RE_k$, which
-must be greater than a threshold $E_{th}$ in order to participate in the current
-period.  Each  sensor node  determines its position  and its subregion  using an
-embedded  GPS or a  location discovery  algorithm. After  that, all  the sensors
-collect position coordinates,  remaining energy, sensor node ID,  and the number
-of their  one-hop live  neighbors during the  information exchange.  The sensors
-inside a same region cooperate to elect a leader. The selection criteria for the
-leader, in order of priority,  are: larger numbers of neighbors, larger remaining
-energy, and  then in case  of equality, larger  index.  Once chosen,  the leader
-collects information to formulate and  solve the integer program which allows to
-construct the set of active sensors in the sensing stage.
-
-
-\section{Perimeter-based Coverage Problem Formulation}
-\label{cp}
-
-\noindent In this  section, the coverage model is  mathematically formulated. We
-start  with a  description of the notations that will  be used  throughout the
-section.\\
-First, we have the following sets:
-\begin{itemize}
-\item $S$ represents the set of WSN sensor nodes;
-\item $A \subseteq S $ is the subset of alive sensors;
-\item  $I_j$  designates  the  set  of  coverage  intervals  (CI)  obtained  for
-  sensor~$j$.
-\end{itemize}
-$I_j$ refers to the set of  coverage intervals which have been defined according
-to the  method introduced in  subsection~\ref{CI}. For a coverage  interval $i$,
-let $a^j_{ik}$ denotes  the indicator function of whether  sensor~$k$ is involved
-in coverage interval~$i$ of sensor~$j$, that is:
-\begin{equation}
-a^j_{ik} = \left \{ 
-\begin{array}{lll}
-  1 & \mbox{if sensor $k$ is involved in the } \\
-  	&	\mbox{coverage interval $i$ of sensor $j$}, \\
-  0 & \mbox{otherwise.}\\
-\end{array} \right.
-\end{equation}
-Note that $a^k_{ik}=1$ by definition of the interval.
-
-Second,  we define  several binary  and integer  variables.  Hence,  each binary
-variable $X_{k}$  determines the activation of  sensor $k$ in the  sensing phase
-($X_k=1$ if  the sensor $k$  is active or 0  otherwise).  $M^j_i$ is  an integer
-variable  which  measures  the  undercoverage  for  the  coverage  interval  $i$
-corresponding to  sensor~$j$. In  the same  way, the  overcoverage for  the same
-coverage interval is given by the variable $V^j_i$.
-
-If we decide to sustain a level of coverage equal to $l$ all along the perimeter
-of sensor  $j$, we have  to ensure  that at least  $l$ sensors involved  in each
-coverage  interval $i  \in I_j$  of  sensor $j$  are active.   According to  the
-previous notations, the number of active sensors in the coverage interval $i$ of
-sensor $j$  is given by  $\sum_{k \in A} a^j_{ik}  X_k$.  To extend  the network
-lifetime,  the objective  is to  activate a  minimal number  of sensors  in each
-period to  ensure the  desired coverage  level. As the  number of  alive sensors
-decreases, it becomes impossible to reach  the desired level of coverage for all
-coverage intervals. Therefore we use variables  $M^j_i$ and $V^j_i$ as a measure
-of the  deviation between  the desired  number of active  sensors in  a coverage
-interval and  the effective  number. And  we try  to minimize  these deviations,
-first to  force the  activation of  a minimal  number of  sensors to  ensure the
-desired coverage level, and if the desired level cannot be completely satisfied,
-to reach a coverage level as close as possible to the desired one.
-
-
-
-
-Our coverage optimization problem can then be mathematically expressed as follows: 
-
-\begin{equation} 
-\left \{
-\begin{array}{ll}
-\min \sum_{j \in S} \sum_{i \in I_j} (\alpha^j_i ~ M^j_i + \beta^j_i ~ V^j_i )&\\
-\textrm{subject to :}&\\
-\sum_{k \in A} ( a^j_{ik} ~ X_{k}) + M^j_i  \geq l \quad \forall i \in I_j, \forall j \in S\\
-\sum_{k \in A} ( a^j_{ik} ~ X_{k}) - V^j_i  \leq l \quad \forall i \in I_j, \forall j \in S\\
-X_{k} \in \{0,1\}, \forall k \in A
-\end{array}
-\right.
-\end{equation}
-
-$\alpha^j_i$ and $\beta^j_i$  are nonnegative weights selected  according to the
-relative importance of satisfying the associated level of coverage. For example,
-weights associated with  coverage intervals of a specified part  of a region may
-be  given by a  relatively larger  magnitude than  weights associated  with another
-region. This  kind of integer program  is inspired from the  model developed for
-brachytherapy treatment planning  for optimizing dose  distribution
-\citep{0031-9155-44-1-012}. The integer  program must be solved by  the leader in
-each subregion at the beginning of  each sensing phase, whenever the environment
-has  changed (new  leader,  death of  some  sensors). Note  that  the number  of
-constraints in the model is constant  (constraints of coverage expressed for all
-sensors), whereas the number of variables $X_k$ decreases over periods, since we
-consider only alive  sensors (sensors with enough energy to  be alive during one
-sensing phase) in the model.
-
-\section{Performance Evaluation and Analysis}  
-\label{sec:Simulation Results and Analysis}
-
-
-\subsection{Simulation Settings}
-
-
-The WSN  area of interest is  supposed to be divided  into 16~regular subregions
-and we use the same energy consumption than in our previous work~\citep{Idrees2}.
-Table~\ref{table3} gives the chosen parameters settings.
-
-\begin{table}[ht]
-\tbl{Relevant parameters for network initialization \label{table3}}{
-
-\centering
-
-\begin{tabular}{c|c}
-
-\hline
-Parameter & Value  \\ [0.5ex]
-   
-\hline
-% inserts single horizontal line
-Sensing field & $(50 \times 25)~m^2 $   \\
-
-WSN size &  100, 150, 200, 250, and 300~nodes   \\
-
-Initial energy  & in range 500-700~Joules  \\  
-
-Sensing period & duration of 60 minutes \\
-$E_{th}$ & 36~Joules\\
-$R_s$ & 5~m   \\     
-
-$\alpha^j_i$ & 0.6   \\
-
-$\beta^j_i$ & 0.4
-
-\end{tabular}}
-
-
-\end{table}
-To  obtain  experimental  results  which are  relevant,  simulations  with  five
-different node densities going from  100 to 300~nodes were performed considering
-each time 25~randomly  generated networks. The nodes are deployed  on a field of
-interest of $(50 \times 25)~m^2 $ in such a way that they cover the field with a
-high coverage ratio. Each node has an  initial energy level, in Joules, which is
-randomly drawn in the interval $[500-700]$.   If its energy provision reaches a
-value below  the threshold $E_{th}=36$~Joules,  the minimum energy needed  for a
-node  to stay  active during  one period,  it will  no more  participate in  the
-coverage task. This value corresponds to the energy needed by the sensing phase,
-obtained by multiplying  the energy consumed in active state  (9.72 mW) with the
-time in  seconds for one  period (3600 seconds), and  adding the energy  for the
-pre-sensing phases.  According  to the interval of initial energy,  a sensor may
-be active during at most 20 periods.
-
-The values  of $\alpha^j_i$ and  $\beta^j_i$ have been  chosen to ensure  a good
-network coverage and a longer WSN lifetime.  We have given a higher priority to
-the  undercoverage  (by  setting  the  $\alpha^j_i$ with  a  larger  value  than
-$\beta^j_i$)  so as  to prevent  the non-coverage  for the  interval~$i$ of  the
-sensor~$j$.  On the  other hand,  we have assigned to
-$\beta^j_i$ a value which is slightly lower so as to minimize the number of active sensor nodes which contribute
-in covering the interval.
-
-We introduce the following performance metrics to evaluate the efficiency of our
-approach.
-
-
-\begin{itemize}
-\item {\bf Network Lifetime}: the lifetime  is defined as the time elapsed until
-  the  coverage  ratio  falls  below a  fixed  threshold.   $Lifetime_{95}$  and
-  $Lifetime_{50}$  denote, respectively,  the  amount of  time  during which  is
-  guaranteed a  level of coverage  greater than $95\%$  and $50\%$. The  WSN can
-  fulfill the expected  monitoring task until all its nodes  have depleted their
-  energy or if the network is no  more connected. This last condition is crucial
-  because without  network connectivity a  sensor may not be  able to send  to a
-  base station an event it has sensed.
-\item {\bf  Coverage Ratio (CR)} : it  measures how  well the  WSN is  able to
-  observe the area of interest. In our  case, we discretized the sensor field as
-  a regular grid, which yields the following equation:
-  
-
-\[
-    \scriptsize
-    \mbox{CR}(\%) = \frac{\mbox{$n$}}{\mbox{$N$}} \times 100
-\]
-
-
-  where $n$  is the  number of covered  grid points by  active sensors  of every
-  subregions during  the current sensing phase  and $N$ is total  number of grid
-  points in  the sensing  field.  In  our simulations  we have  set a  layout of
-  $N~=~51~\times~26~=~1326$~grid points.
-\item {\bf Active Sensors Ratio (ASR)}: a  major objective of our protocol is to
-  activate  as few nodes as possible,  in order  to minimize  the communication
-  overhead and maximize the WSN lifetime. The active sensors ratio is defined as
-  follows:
- 
-\[
-    \scriptsize
-    \mbox{ASR}(\%) =  \frac{\sum\limits_{r=1}^R \mbox{$|A_r^p|$}}{\mbox{$|S|$}} \times 100
-\]
-
-  where $|A_r^p|$ is  the number of active  sensors in the subregion  $r$ in the
-  current sensing period~$p$, $|S|$ is the number of sensors in the network, and
-  $R$ is the number of subregions.
-\item {\bf Energy Consumption (EC)}: energy consumption can be seen as the total
-  energy  consumed by  the  sensors during  $Lifetime_{95}$ or  $Lifetime_{50}$,
-  divided by  the number of  periods. The value of  EC is computed  according to
-  this formula:
-
-\[  
-  \scriptsize
-    \mbox{EC} = \frac{\sum\limits_{p=1}^{P} \left( E^{\mbox{com}}_p+E^{\mbox{list}}_p+E^{\mbox{comp}}_p  
-      + E^{a}_p+E^{s}_p \right)}{P},
-\]
- 
-  where $P$ corresponds  to the number of periods. The  total energy consumed by
-  the  sensors  comes  through  taking   into  consideration  four  main  energy
-  factors. The first one, denoted $E^{\scriptsize \mbox{com}}_p$, represents the
-  energy consumption spent  by all the nodes for  wireless communications during
-  period $p$.  $E^{\scriptsize \mbox{list}}_p$,  the next factor, corresponds to
-  the energy  consumed by the sensors  in LISTENING status before  receiving the
-  decision to go active or sleep in period $p$.  $E^{\scriptsize \mbox{comp}}_p$
-  refers to  the energy  needed by  all the  leader nodes  to solve  the integer
-  program during a period.  Finally, $E^a_{p}$ and $E^s_{p}$ indicate the energy
-  consumed by the WSN during the sensing phase (active and sleeping nodes).
-\end{itemize}
-
-
-\subsection{Simulation Results}
-
-In  order  to  assess and  analyze  the  performance  of  our protocol  we  have
-implemented PeCO protocol in  OMNeT++~\citep{varga} simulator.  Besides PeCO, two
-other  protocols,  described  in  the  next paragraph,  will  be  evaluated  for
-comparison purposes.   The simulations were run  on a DELL laptop  with an Intel
-Core~i3~2370~M (1.8~GHz)  processor (2  cores) whose MIPS  (Million Instructions
-Per Second) rate  is equal to 35330. To  be consistent with the use  of a sensor
-node based on  Atmels AVR ATmega103L microcontroller (6~MHz) having  a MIPS rate
-equal to 6,  the original execution time  on the laptop is  multiplied by 2944.2
-$\left(\frac{35330}{2} \times  \frac{1}{6} \right)$.  The modeling  language for
-Mathematical Programming (AMPL)~\citep{AMPL} is  employed to generate the integer
-program instance  in a  standard format, which  is then read  and solved  by the
-optimization solver  GLPK (GNU  linear Programming Kit  available in  the public
-domain) \citep{glpk} through a Branch-and-Bound method.
-
-As said previously, the PeCO is  compared to three other approaches. The first
-one,  called  DESK,  is  a  fully distributed  coverage  algorithm  proposed  by
-\citep{ChinhVu}. The second one,  called GAF~\citep{xu2001geography}, consists in
-dividing  the monitoring  area into  fixed  squares. Then,  during the  decision
-phase, in each square, one sensor is  chosen to remain active during the sensing
-phase. The last  one, the DiLCO protocol~\citep{Idrees2}, is  an improved version
-of a research work we presented in~\citep{idrees2014coverage}. Let us notice that
-PeCO and  DiLCO protocols are  based on the  same framework. In  particular, the
-choice for the simulations of a partitioning in 16~subregions was made because
-it corresponds to the configuration producing  the best results for DiLCO. The
-protocols are distinguished  from one another by the formulation  of the integer
-program providing the set of sensors which  have to be activated in each sensing
-phase. DiLCO protocol tries to satisfy the coverage of a set of primary points,
-whereas the PeCO protocol objective is to reach a desired level of coverage for each
-sensor perimeter. In our experimentations, we chose a level of coverage equal to
-one ($l=1$).
-
-\subsubsection{\bf Coverage Ratio}
-
-Figure~\ref{figure5}  shows the  average coverage  ratio for  200 deployed  nodes
-obtained with the  four protocols. DESK, GAF, and DiLCO  provide a slightly better
-coverage ratio with respectively 99.99\%,  99.91\%, and 99.02\%, compared to the 98.76\%
-produced by  PeCO for the  first periods. This  is due to  the fact that  at the
-beginning the DiLCO protocol  puts to  sleep status  more redundant  sensors (which
-slightly decreases the coverage ratio), while the three other protocols activate
-more sensor  nodes. Later, when the  number of periods is  beyond~70, it clearly
-appears that  PeCO provides a better  coverage ratio and keeps  a coverage ratio
-greater  than 50\%  for  longer periods  (15  more compared  to  DiLCO, 40  more
-compared to DESK). The energy saved by  PeCO in the early periods allows later a
-substantial increase of the coverage performance.
-
-\parskip 0pt    
-\begin{figure}[h!]
-\centering
- \includegraphics[scale=0.5] {figure5.eps} 
-\caption{Coverage ratio for 200 deployed nodes.}
-\label{figure5}
-\end{figure} 
-
-
-
-
-\subsubsection{\bf Active Sensors Ratio}
-
-Having the less active sensor nodes in  each period is essential to minimize the
-energy consumption  and thus to  maximize the network  lifetime.  Figure~\ref{figure6}
-shows the  average active nodes ratio  for 200 deployed nodes.   We observe that
-DESK and  GAF have 30.36  \% and  34.96 \% active  nodes for the  first fourteen
-rounds and  DiLCO and PeCO  protocols compete perfectly  with only 17.92~\% and
-20.16~\% active  nodes during the same  time interval. As the  number of periods
-increases, PeCO protocol  has a lower number of active  nodes in comparison with
-the three other approaches, while keeping a greater coverage ratio as shown in
-figure \ref{figure5}.
-
-\begin{figure}[h!]
-\centering
-\includegraphics[scale=0.5]{figure6.eps}  
-\caption{Active sensors ratio for 200 deployed nodes.}
-\label{figure6}
-\end{figure} 
-
-\subsubsection{\bf Energy Consumption}
-
-We studied the effect of the energy  consumed by the WSN during the communication,
-computation, listening, active, and sleep status for different network densities
-and  compared  it for  the  four  approaches.  Figures~\ref{figure7}(a)  and  (b)
-illustrate  the  energy   consumption  for  different  network   sizes  and  for
-$Lifetime95$ and  $Lifetime50$. The results show  that our PeCO protocol  is the
-most competitive  from the energy  consumption point of  view. As shown  in both
-figures, PeCO consumes much less energy than the three other methods.  One might
-think that the  resolution of the integer  program is too costly  in energy, but
-the  results show  that it  is very  beneficial to  lose a  bit of  time in  the
-selection of  sensors to  activate.  Indeed the  optimization program  allows to
-reduce significantly the number of active  sensors and so the energy consumption
-while keeping a good coverage level.
-
-\begin{figure}[h!]
-  \centering
-  \begin{tabular}{@{}cr@{}}
-    \includegraphics[scale=0.475]{figure7a.eps} & \raisebox{2.75cm}{(a)} \\
-    \includegraphics[scale=0.475]{figure7b.eps} & \raisebox{2.75cm}{(b)}
-  \end{tabular}
-  \caption{Energy consumption per period for (a)~$Lifetime_{95}$ and (b)~$Lifetime_{50}$.}
-  \label{figure7}
-\end{figure} 
-
-
-
-\subsubsection{\bf Network Lifetime}
-
-We observe the superiority of PeCO and DiLCO protocols in comparison with the
-two    other   approaches    in    prolonging   the    network   lifetime.    In
-Figures~\ref{figure8}(a)  and (b),  $Lifetime95$ and  $Lifetime50$ are  shown for
-different  network  sizes.   As  highlighted  by  these  figures,  the  lifetime
-increases with the size  of the network, and it is clearly   largest for DiLCO
-and PeCO  protocols.  For instance,  for a  network of 300~sensors  and coverage
-ratio greater than 50\%, we can  see on figure~\ref{figure8}(b) that the lifetime
-is about twice longer with  PeCO compared to DESK protocol.  The performance
-difference    is    more    obvious   in    figure~\ref{figure8}(b)    than    in
-figure~\ref{figure8}(a) because the gain induced  by our protocols increases with
- time, and the lifetime with a coverage  of 50\% is far  longer than with
-95\%.
-
-\begin{figure}[h!]
-  \centering
-  \begin{tabular}{@{}cr@{}}
-    \includegraphics[scale=0.475]{figure8a.eps} & \raisebox{2.75cm}{(a)} \\  
-    \includegraphics[scale=0.475]{figure8b.eps} & \raisebox{2.75cm}{(b)}
-  \end{tabular}
-  \caption{Network Lifetime for (a)~$Lifetime_{95}$ \\
-    and (b)~$Lifetime_{50}$.}
-  \label{figure8}
-\end{figure} 
-
-
-
-Figure~\ref{figure9}  compares  the  lifetime  coverage of  our  protocols  for
-different coverage  ratios. We denote by  Protocol/50, Protocol/80, Protocol/85,
-Protocol/90, and  Protocol/95 the amount  of time  during which the  network can
-satisfy an area coverage greater than $50\%$, $80\%$, $85\%$, $90\%$, and $95\%$
-respectively, where the term Protocol refers to  DiLCO  or PeCO.  Indeed there  are applications
-that do not require a 100\% coverage of  the area to be monitored. PeCO might be
-an interesting  method since  it achieves  a good balance  between a  high level
-coverage ratio and network lifetime. PeCO always outperforms DiLCO for the three
-lower  coverage  ratios,  moreover  the   improvements  grow  with  the  network
-size. DiLCO is better  for coverage ratios near 100\%, but in  that case PeCO is
-not ineffective for the smallest network sizes.
-
-\begin{figure}[h!]
-\centering \includegraphics[scale=0.5]{figure9.eps}
-\caption{Network lifetime for different coverage ratios.}
-\label{figure9}
-\end{figure} 
-
-
-
-
-\section{Conclusion and Future Works}
-\label{sec:Conclusion and Future Works}
-
-In this paper  we have studied the problem of  Perimeter-based Coverage Optimization in
-WSNs. We have designed  a new protocol, called Perimeter-based  Coverage Optimization, which
-schedules nodes'  activities (wake up  and sleep  stages) with the  objective of
-maintaining a  good coverage ratio  while maximizing the network  lifetime. This
-protocol is  applied in a distributed  way in regular subregions  obtained after
-partitioning the area of interest in a preliminary step. It works in periods and
-is based on the resolution of an integer program to select the subset of sensors
-operating in active status for each period. Our work is original in so far as it
-proposes for  the first  time an  integer program  scheduling the  activation of
-sensors  based on  their perimeter  coverage level,  instead of  using a  set of
-targets/points to be covered.
-
-
-We  have carried out  several simulations  to  evaluate the  proposed protocol.   The
-simulation  results  show   that  PeCO  is  more   energy-efficient  than  other
-approaches, with respect to lifetime,  coverage ratio, active sensors ratio, and
-energy consumption.
-
-We plan to extend our framework so that the schedules are planned for multiple
-sensing periods.
-
-We also want  to improve our integer program to  take into account heterogeneous
-sensors  from both  energy  and node  characteristics point of views.
-
-Finally,  it   would  be   interesting  to  implement   our  protocol   using  a
-sensor-testbed to evaluate it in real world applications.
-
-\bibliographystyle{gENO}
-\bibliography{biblio}
-
-
-\end{document}
+% gENOguide.tex
+% v4.0 released April 2013
+
+\documentclass{gENO2e}
+%\usepackage[linesnumbered,ruled,vlined,commentsnumbered]{algorithm2e}
+%\renewcommand{\algorithmcfname}{ALGORITHM}
+\usepackage{indentfirst}
+\begin{document}
+
+%\jvol{00} \jnum{00} \jyear{2013} \jmonth{April}
+
+%\articletype{GUIDE}
+
+\title{{\itshape Perimeter-based Coverage Optimization to Improve Lifetime in Wireless Sensor Networks}}
+
+\author{Ali Kadhum Idrees$^{a}$, Karine Deschinkel$^{a}$$^{\ast}$\thanks{$^\ast$Corresponding author. Email: karine.deschinkel@univ-fcomte.fr}, Michel Salomon$^{a}$ and Rapha\"el Couturier $^{a}$
+$^{a}${\em{FEMTO-ST Institute, UMR 6174 CNRS, University of Franche-Comte,
+          Belfort, France}};}
+
+
+\maketitle
+
+\begin{abstract}
+The most important problem in a Wireless Sensor Network (WSN) is to optimize the
+use of its limited energy provision, so that it can fulfill its monitoring task
+as long as  possible. Among  known  available approaches  that can  be used  to
+improve  power  management,  lifetime coverage  optimization  provides  activity
+scheduling which ensures sensing coverage while minimizing the energy cost. We propose such an approach called Perimeter-based Coverage Optimization
+protocol (PeCO). It is a  hybrid of centralized and distributed methods: the
+region of interest is first subdivided into subregions and the protocol is then
+distributed among sensor nodes in each  subregion.
+The novelty of our approach lies essentially in the formulation of a new
+mathematical optimization  model based on the  perimeter coverage level  to schedule
+sensors' activities.  Extensive simulation experiments demonstrate that PeCO  can
+offer longer lifetime coverage for WSNs in comparison with some other protocols.
+
+\begin{keywords}Wireless Sensor Networks, Area Coverage, Energy efficiency, Optimization, Scheduling.
+\end{keywords}
+
+\end{abstract}
+
+
+\section{Introduction}
+\label{sec:introduction}
+
+The continuous progress in Micro Electro-Mechanical Systems (MEMS) and
+wireless communication hardware  has given rise to the opportunity  to use large
+networks    of     tiny    sensors,    called    Wireless     Sensor    Networks
+(WSN)~\citep{akyildiz2002wireless,puccinelli2005wireless}, to  fulfill monitoring
+tasks.   A  WSN  consists  of  small low-powered  sensors  working  together  by
+communicating with one another through multi-hop radio communications. Each node
+can send the data  it collects in its environment, thanks to  its sensor, to the
+user by means of  sink nodes. The features of a WSN made  it suitable for a wide
+range of application  in areas such as business,  environment, health, industry,
+military, and so on~\citep{yick2008wireless}.   Typically, a sensor node contains
+three main components~\citep{anastasi2009energy}: a  sensing unit able to measure
+physical,  chemical, or  biological  phenomena observed  in  the environment;  a
+processing unit which will process and store the collected measurements; a radio
+communication unit for data transmission and receiving.
+
+The energy needed  by an active sensor node to  perform sensing, processing, and
+communication is supplied by a power supply which is a battery. This battery has
+a limited energy provision and it may  be unsuitable or impossible to replace or
+recharge it in  most applications. Therefore it is necessary  to deploy WSN with
+high density in order to increase  reliability and to exploit node redundancy
+thanks to energy-efficient activity  scheduling approaches.  Indeed, the overlap
+of sensing  areas can be exploited  to schedule alternatively some  sensors in a
+low power sleep mode and thus save  energy. Overall, the main question that must
+be answered is: how to extend the lifetime coverage of a WSN as long as possible
+while  ensuring   a  high  level  of   coverage?   These past few years  many
+energy-efficient mechanisms have been suggested  to retain energy and extend the
+lifetime of the WSNs~\citep{rault2014energy}.\\\\
+This paper makes the following contributions.
+\begin{enumerate}
+\item We have devised a framework to schedule nodes to be activated alternatively such
+  that the network lifetime is prolonged  while ensuring that a certain level of
+  coverage is preserved.  A key idea in  our framework is to exploit spatial and
+  temporal subdivision.   On the one hand,  the area of interest  is divided into
+  several smaller subregions and, on the other hand, the time line is divided into
+  periods of equal length. In each subregion the sensor nodes will cooperatively
+  choose a  leader which will schedule  nodes' activities, and this  grouping of
+  sensors is similar to typical cluster architecture.
+\item We have proposed a new mathematical  optimization model.  Instead of  trying to
+  cover a set of specified points/targets as  in most of the methods proposed in
+  the literature, we formulate an integer program based on perimeter coverage of
+  each sensor.  The  model involves integer variables to  capture the deviations
+  between  the actual  level of  coverage and  the required  level.  Hence, an
+  optimal schedule  will be  obtained by  minimizing a  weighted sum  of these
+  deviations.
+\item We have conducted extensive simulation  experiments, using the  discrete event
+  simulator OMNeT++, to demonstrate the  efficiency of our protocol. We have compared
+  our   PeCO   protocol   to   two   approaches   found   in   the   literature:
+  DESK~\citep{ChinhVu} and  GAF~\citep{xu2001geography}, and also to  our previous
+  work published in~\citep{Idrees2} which is  based on another optimization model
+  for sensor scheduling.
+\end{enumerate}
+
+
+
+
+
+
+The rest  of the paper is  organized as follows.  In the next section
+some related work in the  field is reviewed. Section~\ref{sec:The PeCO Protocol Description}
+is devoted to the PeCO protocol  description and Section~\ref{cp} focuses on the
+coverage model  formulation which is used  to schedule the activation  of sensor
+nodes.  Section~\ref{sec:Simulation  Results and Analysis}  presents simulations
+results and discusses the comparison  with other approaches. Finally, concluding
+remarks   are  drawn   and  some   suggestions are  given  for   future  works   in
+Section~\ref{sec:Conclusion and Future Works}.
+
+\section{Related Literature}
+\label{sec:Literature Review}
+
+In  this section, some  related works  regarding  the
+coverage problem is summarized, and specific aspects of the PeCO protocol from the  works presented in
+the literature are presented.
+
+The most  discussed coverage problems in  literature can be classified  in three
+categories~\citep{li2013survey}   according   to  their   respective   monitoring
+objective.  Hence,  area coverage \citep{Misra}  means that every point  inside a
+fixed area  must be monitored, while  target coverage~\citep{yang2014novel} refers
+to  the objective  of coverage  for a  finite number  of discrete  points called
+targets,  and  barrier coverage~\citep{HeShibo,kim2013maximum}  focuses  on
+preventing  intruders   from  entering   into  the   region  of   interest.   In
+\citep{Deng2012}  authors  transform the  area  coverage  problem into  the  target
+coverage one taking into account the  intersection points among disks of sensors
+nodes    or   between    disk   of    sensor   nodes    and   boundaries.     In
+\citep{Huang:2003:CPW:941350.941367}  authors prove  that  if  the perimeters  of
+sensors are sufficiently  covered it will be  the case for the  whole area. They
+provide an algorithm in $O(nd~log~d)$  time to compute the perimeter-coverage of
+each  sensor. $d$  denotes  the  maximum  number  of  sensors  that  are
+neighbors  to  a  sensor, and  $n$  is  the  total  number of  sensors  in  the
+network. {\it In PeCO protocol, instead  of determining the level of coverage of
+  a set  of discrete  points, our  optimization model is  based on  checking the
+  perimeter-coverage of each sensor to activate a minimal number of sensors.}
+
+The major  approach to extend network  lifetime while preserving coverage  is to
+divide/organize the  sensors into a suitable  number of set covers  (disjoint or
+non-disjoint)\citep{wang2011coverage}, where  each set completely  covers a  region of interest,  and to
+activate these set  covers successively. The network activity can  be planned in
+advance and scheduled  for the entire network lifetime or  organized in periods,
+and the set  of active sensor nodes  is decided at the beginning  of each period
+\citep{ling2009energy}.  Active node selection is determined based on the problem
+requirements (e.g.   area monitoring,  connectivity, or power  efficiency).  For
+instance, \citet{jaggi2006}  address the problem of maximizing
+the lifetime  by dividing sensors  into the  maximum number of  disjoint subsets
+such  that each  subset  can ensure  both coverage  and  connectivity. A  greedy
+algorithm  is applied  once to  solve  this problem  and the  computed sets  are
+activated  in   succession  to  achieve   the  desired  network   lifetime.   
+\citet{chin2007},  \citet{yan2008design}, \citet{pc10},  propose  algorithms
+working in a periodic fashion where a  cover set is computed at the beginning of
+each period.   {\it Motivated by  these works,  PeCO protocol works  in periods,
+  where each  period contains a  preliminary phase for information  exchange and
+  decisions, followed by a sensing phase where one cover set is in charge of the
+  sensing task.}
+
+Various centralized  and distributed approaches, or  even a mixing  of these two
+concepts, have  been proposed  to extend the  network lifetime \citep{zhou2009variable}.   In distributed algorithms~\citep{Tian02,yangnovel,ChinhVu,qu2013distributed} each sensor decides of its
+own activity scheduling  after an information exchange with  its neighbors.  The
+main interest of such an approach is to avoid long range communications and thus
+to reduce the energy dedicated to the communications.  Unfortunately, since each
+node has only information on  its immediate neighbors (usually the one-hop ones)
+it may make a bad decision leading to a global suboptimal solution.  Conversely,
+centralized
+algorithms~\citep{cardei2005improving,zorbas2010solving,pujari2011high}     always
+provide nearly  or close to  optimal solution since  the algorithm has  a global
+view of the whole network. The disadvantage of a centralized method is obviously
+its high  cost in communications needed to  transmit to a single  node, the base
+station which will globally schedule  nodes' activities, and data from all the other
+sensor nodes  in the area.  The price  in communications can be  huge since
+long range  communications will be  needed. In fact  the larger the WNS  is, the
+higher the  communication and  thus the energy  cost are.   {\it In order  to be
+  suitable for large-scale  networks, in the PeCO protocol,  the area of interest
+  is divided into several smaller subregions, and in each one, a node called the
+  leader  is  in  charge  of  selecting  the active  sensors  for  the  current
+  period.  Thus our  protocol is  scalable  and is a  globally distributed  method,
+  whereas it is centralized in each subregion.}
+
+Various  coverage scheduling  algorithms have  been developed  these past few years.
+Many of  them, dealing with  the maximization of the  number of cover  sets, are
+heuristics.   These  heuristics involve  the  construction  of  a cover  set  by
+including in priority the sensor nodes  which cover critical targets, that is to
+say   targets   that  are   covered   by   the   smallest  number   of   sensors
+\citep{berman04,zorbas2010solving}.  Other  approaches are based  on mathematical
+programming formulations~\citep{cardei2005energy,5714480,pujari2011high,Yang2014}
+and dedicated techniques (solving with a branch-and-bound algorithm available in
+optimization  solver).  The  problem is  formulated as  an optimization  problem
+(maximization of the lifetime or number of cover sets) under target coverage and
+energy  constraints.   Column  generation   techniques,  well-known  and  widely
+practiced techniques for  solving linear programs with too  many variables, have
+also                                                                        been
+used~\citep{castano2013column,doi:10.1080/0305215X.2012.687732,deschinkel2012column}. {\it  In the PeCO
+  protocol, each  leader, in charge  of a  subregion, solves an  integer program
+  which has a twofold objective: minimize the overcoverage and the undercoverage
+  of the perimeter of each sensor.}
+
+
+
+\section{ The P{\scshape e}CO Protocol Description}
+\label{sec:The PeCO Protocol Description}
+
+In  this  section,  the Perimeter-based  Coverage
+Optimization protocol is decribed in details.  First we present the  assumptions we made and the models
+we considered (in particular the perimeter coverage one), second we describe the
+background idea of our protocol, and third  we give the outline of the algorithm
+executed by each node.
+
+
+\subsection{Assumptions and Models}
+\label{CI}
+
+A WSN consisting of $J$ stationary sensor nodes randomly and uniformly
+distributed in  a bounded sensor field  is considered. The wireless  sensors are
+deployed in high density  to ensure initially a high coverage  ratio of the area
+of interest.  We  assume that all the  sensor nodes are homogeneous  in terms of
+communication,  sensing,  and  processing capabilities  and  heterogeneous  from
+the energy provision  point of  view.  The  location information  is available  to a
+sensor node either  through hardware such as embedded GPS  or location discovery
+algorithms.   We  assume  that  each  sensor  node  can  directly  transmit  its
+measurements to  a mobile  sink node.  For  example, a sink  can be  an unmanned
+aerial  vehicle  (UAV)  flying  regularly  over  the  sensor  field  to  collect
+measurements from sensor nodes. A mobile sink node collects the measurements and
+transmits them to the base station.   We consider a Boolean disk coverage model,
+which is the most  widely used sensor coverage model in  the literature, and all
+sensor nodes  have a constant sensing  range $R_s$.  Thus, all  the space points
+within a disk centered at a sensor with  a radius equal to the sensing range are
+said to be covered  by this sensor. We also assume  that the communication range
+$R_c$ satisfies $R_c  \geq 2 \cdot R_s$. In fact,  \citet{Zhang05}
+proved  that if  the  transmission  range fulfills  the  previous hypothesis,  the
+complete coverage of a convex area implies connectivity among active nodes.
+
+The PeCO protocol  uses the  same perimeter-coverage  model as \citet{huang2005coverage}. It  can be expressed as follows:  a sensor is
+said to be perimeter  covered if all the points on its  perimeter are covered by
+at least  one sensor  other than  itself. Authors \citet{huang2005coverage}  proved that  a network  area is
+$k$-covered (every point in the area covered by at least k sensors) if and only if each sensor in the network is $k$-perimeter-covered (perimeter covered by at least $k$ sensors). 
+ 
+Figure~\ref{figure1}(a)  shows  the coverage  of  sensor  node~$0$. On  this
+figure, sensor~$0$ has  nine neighbors and we  have reported on
+its  perimeter (the  perimeter  of the  disk  covered by  the  sensor) for  each
+neighbor  the  two  points  resulting  from the intersection  of  the  two  sensing
+areas. These points are denoted for  neighbor~$i$ by $iL$ and $iR$, respectively
+for  left and  right from  a neighboing  point of  view.  The  resulting couples  of
+intersection points subdivide  the perimeter of sensor~$0$  into portions called
+arcs.
+
+\begin{figure}[ht!]
+  \centering
+  \begin{tabular}{@{}cr@{}}
+    \includegraphics[width=75mm]{figure1a.eps} & \raisebox{3.25cm}{(a)} \\
+    \includegraphics[width=75mm]{figure1b.eps} & \raisebox{2.75cm}{(b)}
+  \end{tabular}
+  \caption{(a) Perimeter  coverage of sensor node  0 and (b) finding  the arc of
+    $u$'s perimeter covered by $v$.}
+  \label{figure1}
+\end{figure} 
+
+Figure~\ref{figure1}(b) describes the geometric information used to find the
+locations of the  left and right points of  an arc on the perimeter  of a sensor
+node~$u$ covered by a sensor node~$v$. Node~$v$ is supposed to be located on the
+west  side of  sensor~$u$,  with  the following  respective  coordinates in  the
+sensing area~: $(v_x,v_y)$ and $(u_x,u_y)$. From the previous coordinates 
+the euclidean distance between nodes~$u$ and $v$ is computed: $Dist(u,v)=\sqrt{\vert
+  u_x  - v_x  \vert^2 +  \vert u_y-v_y  \vert^2}$, while  the angle~$\alpha$  is
+obtained through  the formula:
+ \[
+\alpha =  \arccos \left(\frac{Dist(u,v)}{2R_s}
+\right).
+\] 
+The arc on the perimeter of~$u$ defined by the angular interval $[\pi
+  - \alpha,\pi + \alpha]$ is said to be perimeter-covered by sensor~$v$.
+
+Every couple of intersection points is placed on the angular interval $[0,2\pi)$
+in  a  counterclockwise manner,  leading  to  a  partitioning of  the  interval.
+Figure~\ref{figure1}(a)  illustrates  the arcs  for  the  nine neighbors  of
+sensor $0$ and  Figure~\ref{figure2} gives the position of  the corresponding arcs
+in  the interval  $[0,2\pi)$. More  precisely, the  points are
+ordered according  to the  measures of  the angles  defined by  their respective
+positions. The intersection points are  then visited one after another, starting
+from the first  intersection point  after  point~zero,  and  the maximum  level  of
+coverage is determined  for each interval defined by two  successive points. The
+maximum  level of  coverage is  equal to  the number  of overlapping  arcs.  For
+example, 
+between~$5L$  and~$6L$ the maximum  level of  coverage is equal  to $3$
+(the value is highlighted in yellow  at the bottom of Figure~\ref{figure2}), which
+means that at most 2~neighbors can cover  the perimeter in addition to node $0$. 
+Table~\ref{my-label} summarizes for each coverage  interval the maximum level of
+coverage and  the sensor  nodes covering the  perimeter.  The  example discussed
+above is thus given by the sixth line of the table.
+
+
+\begin{figure*}[t!]
+\centering
+\includegraphics[width=127.5mm]{figure2.eps}  
+\caption{Maximum coverage levels for perimeter of sensor node $0$.}
+\label{figure2}
+\end{figure*} 
+
+
+
+
+ \begin{table}
+ \tbl{Coverage intervals and contributing sensors for sensor node 0 \label{my-label}}
+{\begin{tabular}{|c|c|c|c|c|c|c|c|c|}
+\hline
+\begin{tabular}[c]{@{}c@{}}Left \\ point \\ angle~$\alpha$ \end{tabular} & \begin{tabular}[c]{@{}c@{}}Interval \\ left \\ point\end{tabular} & \begin{tabular}[c]{@{}c@{}}Interval \\ right \\ point\end{tabular} & \begin{tabular}[c]{@{}c@{}}Maximum \\ coverage\\  level\end{tabular} & \multicolumn{5}{c|}{\begin{tabular}[c]{@{}c@{}}Set of sensors\\ involved \\ in coverage interval\end{tabular}} \\ \hline
+0.0291    & 1L                                                                        & 2L                                                        & 4                                                                     & 0                     & 1                     & 3                    & 4                    &                      \\ \hline
+0.104     & 2L                                                                        & 3R                                                        & 5                                                                     & 0                     & 1                     & 3                    & 4                    & 2                    \\ \hline
+0.3168    & 3R                                                                        & 4R                                                        & 4                                                                     & 0                     & 1                     & 4                    & 2                    &                      \\ \hline
+0.6752    & 4R                                                                        & 1R                                                        & 3                                                                     & 0                     & 1                     & 2                    &                      &                      \\ \hline
+1.8127    & 1R                                                                        & 5L                                                        & 2                                                                     & 0                     & 2                     &                      &                      &                      \\ \hline
+1.9228    & 5L                                                                        & 6L                                                        & 3                                                                     & 0                     & 2                     & 5                    &                      &                      \\ \hline
+2.3959    & 6L                                                                        & 2R                                                        & 4                                                                     & 0                     & 2                     & 5                    & 6                    &                      \\ \hline
+2.4258    & 2R                                                                        & 7L                                                        & 3                                                                     & 0                     & 5                     & 6                    &                      &                      \\ \hline
+2.7868    & 7L                                                                        & 8L                                                        & 4                                                                     & 0                     & 5                     & 6                    & 7                    &                      \\ \hline
+2.8358    & 8L                                                                        & 5R                                                        & 5                                                                     & 0                     & 5                     & 6                    & 7                    & 8                    \\ \hline
+2.9184    & 5R                                                                        & 7R                                                        & 4                                                                     & 0                     & 6                     & 7                    & 8                    &                      \\ \hline
+3.3301    & 7R                                                                        & 9R                                                        & 3                                                                     & 0                     & 6                     & 8                    &                      &                      \\ \hline
+3.9464    & 9R                                                                        & 6R                                                        & 4                                                                     & 0                     & 6                     & 8                    & 9                    &                      \\ \hline
+4.767     & 6R                                                                        & 3L                                                        & 3                                                                     & 0                     & 8                     & 9                    &                      &                      \\ \hline
+4.8425    & 3L                                                                        & 8R                                                        & 4                                                                     & 0                     & 3                     & 8                    & 9                    &                      \\ \hline
+4.9072    & 8R                                                                        & 4L                                                        & 3                                                                     & 0                     & 3                     & 9                    &                      &                      \\ \hline
+5.3804    & 4L                                                                        & 9R                                                        & 4                                                                     & 0                     & 3                     & 4                    & 9                    &                      \\ \hline
+5.9157    & 9R                                                                        & 1L                                                        & 3                                                                     & 0                     & 3                     & 4                    &                      &                      \\ \hline
+\end{tabular}}
+
+
+\end{table}
+
+
+
+
+In the PeCO  protocol, the scheduling of the sensor  nodes' activities is formulated  with an
+integer program  based on  coverage intervals. The  formulation of  the coverage
+optimization problem is  detailed in~Section~\ref{cp}.  Note that  when a sensor
+node  has a  part of  its sensing  range outside  the WSN  sensing field,  as in
+Figure~\ref{figure3}, the maximum coverage level for  this arc is set to $\infty$
+and  the  corresponding  interval  will  not   be  taken  into  account  by  the
+optimization algorithm.
+
+ \newpage
+\begin{figure}[h!]
+\centering
+\includegraphics[width=62.5mm]{figure3.eps}  
+\caption{Sensing range outside the WSN's area of interest.}
+\label{figure3}
+\end{figure} 
+
+
+\subsection{The Main Idea}
+
+The  WSN area of  interest is, in a  first step, divided  into regular
+homogeneous subregions  using a divide-and-conquer  algorithm. In a  second step
+our  protocol  will  be  executed  in   a  distributed  way  in  each  subregion
+simultaneously to schedule nodes' activities for one sensing period.
+
+As  shown in  Figure~\ref{figure4}, node  activity  scheduling is  produced by  our
+protocol in a periodic manner. Each period is divided into 4 stages: Information
+(INFO)  Exchange,  Leader Election,  Decision  (the  result of  an  optimization
+problem),  and  Sensing.   For  each  period there  is  exactly  one  set  cover
+responsible for  the sensing task.  Protocols  based on a periodic  scheme, like
+PeCO, are more  robust against an unexpected  node failure. On the  one hand, if
+a node failure is discovered before  taking the decision, the corresponding sensor
+node will  not be considered  by the optimization  algorithm. On  the other
+hand, if the sensor failure happens after  the decision, the sensing task of the
+network will be temporarily affected: only  during the period of sensing until a
+new period starts, since a new set cover will take charge of the sensing task in
+the next period. The energy consumption and some other constraints can easily be
+taken  into  account since  the  sensors  can  update  and then  exchange  their
+information (including their  residual energy) at the beginning  of each period.
+However, the pre-sensing  phases (INFO Exchange, Leader  Election, and Decision)
+are energy consuming, even for nodes that will not join the set cover to monitor
+the area.
+
+\begin{figure}[t!]
+\centering
+\includegraphics[width=80mm]{figure4.eps}  
+\caption{PeCO protocol.}
+\label{figure4}
+\end{figure} 
+
+We define two types of packets to be used by PeCO protocol:
+
+\begin{itemize} 
+\item INFO  packet: sent  by each  sensor node to  all the  nodes inside  a same
+  subregion for information exchange.
+\item ActiveSleep packet: sent  by the leader to all the  nodes in its subregion
+  to transmit to  them their respective status (stay Active  or go Sleep) during
+  sensing phase.
+\end{itemize}
+
+
+Five statuses are possible for a sensor node in the network:
+
+\begin{itemize} 
+\item LISTENING: waits for a decision (to be active or not);
+\item COMPUTATION: executes the optimization algorithm as leader to
+  determine the activities scheduling;
+\item ACTIVE: node is sensing;
+\item SLEEP: node is turned off;
+\item COMMUNICATION: transmits or receives packets.
+\end{itemize}
+
+
+\subsection{PeCO Protocol Algorithm}
+
+The  pseudocode implementing the  protocol on  a node is  given below.
+More  precisely,  Algorithm~\ref{alg:PeCO}  gives  a brief  description  of  the
+protocol applied by a sensor node $s_k$ where $k$ is the node index in the WSN.
+
+
+
+\begin{algorithm}      
+ % \KwIn{all the parameters related to information exchange}
+%  \KwOut{$winer-node$ (: the id of the winner sensor node, which is the leader of current round)}
+%  \BlankLine
+  %\emph{Initialize the sensor node and determine it's position and subregion} \; 
+  
+\noindent{\bf If} $RE_k \geq E_{th}$ {\bf then}\\
+\hspace*{0.6cm} \emph{$s_k.status$ = COMMUNICATION;}\\
+\hspace*{0.6cm}  \emph{Send $INFO()$ packet to other nodes in subregion;}\\
+\hspace*{0.6cm}  \emph{Wait $INFO()$ packet from other nodes in subregion;}\\
+\hspace*{0.6cm} \emph{Update K.CurrentSize;}\\
+\hspace*{0.6cm}  \emph{LeaderID = Leader election;}\\
+\hspace*{0.6cm} {\bf If} $ s_k.ID = LeaderID $ {\bf then}\\
+\hspace*{1.2cm}   \emph{$s_k.status$ = COMPUTATION;}\\
+\hspace*{1.2cm}{\bf If} \emph{$ s_k.ID $ is Not previously selected as a Leader} {\bf then}\\
+\hspace*{1.8cm} \emph{ Execute the perimeter coverage model;}\\
+\hspace*{1.2cm} {\bf end}\\
+\hspace*{1.2cm}{\bf If} \emph{($s_k.ID $ is the same Previous Leader)~And~(K.CurrentSize = K.PreviousSize)}\\
+\hspace*{1.8cm} \emph{ Use the same previous cover set for current sensing stage;}\\
+\hspace*{1.2cm}  {\bf end}\\
+\hspace*{1.2cm}  {\bf else}\\
+\hspace*{1.8cm}\emph{Update $a^j_{ik}$; prepare data for IP~Algorithm;}\\
+\hspace*{1.8cm} \emph{$\left\{\left(X_{1},\dots,X_{l},\dots,X_{K}\right)\right\}$ = Execute Integer Program Algorithm($K$);}\\
+\hspace*{1.8cm} \emph{K.PreviousSize = K.CurrentSize;}\\
+\hspace*{1.2cm}  {\bf end}\\
+\hspace*{1.2cm}\emph{$s_k.status$ = COMMUNICATION;}\\
+\hspace*{1.2cm}\emph{Send $ActiveSleep()$ to each node $l$ in subregion;}\\
+\hspace*{1.2cm}\emph{Update $RE_k $;}\\
+\hspace*{0.6cm}  {\bf end}\\
+\hspace*{0.6cm}  {\bf else}\\
+\hspace*{1.2cm}\emph{$s_k.status$ = LISTENING;}\\
+\hspace*{1.2cm}\emph{Wait $ActiveSleep()$ packet from the Leader;}\\
+\hspace*{1.2cm}\emph{Update $RE_k $;}\\
+\hspace*{0.6cm}  {\bf end}\\
+{\bf end}\\
+{\bf else}\\
+\hspace*{0.6cm} \emph{Exclude $s_k$ from entering in the current sensing stage;}\\
+{\bf end}\\
+\label{alg:PeCO}
+\end{algorithm}
+
+
+
+In this  algorithm, K.CurrentSize and K.PreviousSize  respectively represent the
+current number and  the previous number of living nodes in  the subnetwork of the
+subregion.  Initially, the sensor node checks its remaining energy $RE_k$, which
+must be greater than a threshold $E_{th}$ in order to participate in the current
+period.  Each  sensor node  determines its position  and its subregion  using an
+embedded  GPS or a  location discovery  algorithm. After  that, all  the sensors
+collect position coordinates,  remaining energy, sensor node ID,  and the number
+of their  one-hop live  neighbors during the  information exchange.  The sensors
+inside a same region cooperate to elect a leader. The selection criteria for the
+leader, in order of priority,  are: larger numbers of neighbors, larger remaining
+energy, and  then in case  of equality, larger  index.  Once chosen,  the leader
+collects information to formulate and  solve the integer program which allows to
+construct the set of active sensors in the sensing stage.
+
+
+\section{Perimeter-based Coverage Problem Formulation}
+\label{cp}
+
+In this  section, the coverage model is  mathematically formulated. The following
+notations are used  throughout the
+section.\\
+First, the following sets:
+\begin{itemize}
+\item $S$ represents the set of WSN sensor nodes;
+\item $A \subseteq S $ is the subset of alive sensors;
+\item  $I_j$  designates  the  set  of  coverage  intervals  (CI)  obtained  for
+  sensor~$j$.
+\end{itemize}
+$I_j$ refers to the set of  coverage intervals which have been defined according
+to the  method introduced in  subsection~\ref{CI}. For a coverage  interval $i$,
+let $a^j_{ik}$ denotes  the indicator function of whether  sensor~$k$ is involved
+in coverage interval~$i$ of sensor~$j$, that is:
+\begin{equation}
+a^j_{ik} = \left \{ 
+\begin{array}{lll}
+  1 & \mbox{if sensor $k$ is involved in the } \\
+  	&	\mbox{coverage interval $i$ of sensor $j$}, \\
+  0 & \mbox{otherwise.}\\
+\end{array} \right.
+\end{equation}
+Note that $a^k_{ik}=1$ by definition of the interval.
+
+Second, several binary  and integer  variables are defined.  Hence,  each binary
+variable $X_{k}$  determines the activation of  sensor $k$ in the  sensing phase
+($X_k=1$ if  the sensor $k$  is active or 0  otherwise).  $M^j_i$ is  an integer
+variable  which  measures  the  undercoverage  for  the  coverage  interval  $i$
+corresponding to  sensor~$j$. In  the same  way, the  overcoverage for  the same
+coverage interval is given by the variable $V^j_i$.
+
+If we decide to sustain a level of coverage equal to $l$ all along the perimeter
+of sensor  $j$, we have  to ensure  that at least  $l$ sensors involved  in each
+coverage  interval $i  \in I_j$  of  sensor $j$  are active.   According to  the
+previous notations, the number of active sensors in the coverage interval $i$ of
+sensor $j$  is given by  $\sum_{k \in A} a^j_{ik}  X_k$.  To extend  the network
+lifetime,  the objective  is to  activate a  minimal number  of sensors  in each
+period to  ensure the  desired coverage  level. As the  number of  alive sensors
+decreases, it becomes impossible to reach  the desired level of coverage for all
+coverage intervals. Therefore  variables  $M^j_i$ and $V^j_i$ are introduced as a measure
+of the  deviation between  the desired  number of active  sensors in  a coverage
+interval and  the effective  number. And  we try  to minimize  these deviations,
+first to  force the  activation of  a minimal  number of  sensors to  ensure the
+desired coverage level, and if the desired level cannot be completely satisfied,
+to reach a coverage level as close as possible to the desired one.
+
+
+
+
+Our coverage optimization problem can then be mathematically expressed as follows: 
+
+\begin{equation} 
+\left \{
+\begin{array}{ll}
+\min \sum_{j \in S} \sum_{i \in I_j} (\alpha^j_i ~ M^j_i + \beta^j_i ~ V^j_i )&\\
+\textrm{subject to :}&\\
+\sum_{k \in A} ( a^j_{ik} ~ X_{k}) + M^j_i  = l \quad \forall i \in I_j, \forall j \in S\\
+\sum_{k \in A} ( a^j_{ik} ~ X_{k}) - V^j_i  = l \quad \forall i \in I_j, \forall j \in S\\
+X_{k} \in \{0,1\}, \forall k \in A
+\end{array}
+\right.
+\end{equation}
+
+$\alpha^j_i$ and $\beta^j_i$  are nonnegative weights selected  according to the
+relative importance of satisfying the associated level of coverage. For example,
+weights associated with  coverage intervals of a specified part  of a region may
+be  given by a  relatively larger  magnitude than  weights associated  with another
+region. This  kind of integer program  is inspired from the  model developed for
+brachytherapy treatment planning  for optimizing dose  distribution
+\citep{0031-9155-44-1-012}. The integer  program must be solved by  the leader in
+each subregion at the beginning of  each sensing phase, whenever the environment
+has  changed (new  leader,  death of  some  sensors). Note  that  the number  of
+constraints in the model is constant  (constraints of coverage expressed for all
+sensors), whereas the number of variables $X_k$ decreases over periods, since 
+only alive  sensors (sensors with enough energy to  be alive during one
+sensing phase) are considered in the model.
+
+\section{Performance Evaluation and Analysis}  
+\label{sec:Simulation Results and Analysis}
+
+
+\subsection{Simulation Settings}
+
+
+The WSN  area of interest is  supposed to be divided  into 16~regular subregions
+and we use the same energy consumption model as in our previous work~\citep{Idrees2}.
+Table~\ref{table3} gives the chosen parameters settings.
+
+\begin{table}[ht]
+\tbl{Relevant parameters for network initialization \label{table3}}{
+
+\centering
+
+\begin{tabular}{c|c}
+
+\hline
+Parameter & Value  \\ [0.5ex]
+   
+\hline
+% inserts single horizontal line
+Sensing field & $(50 \times 25)~m^2 $   \\
+
+WSN size &  100, 150, 200, 250, and 300~nodes   \\
+
+Initial energy  & in range 500-700~Joules  \\  
+
+Sensing period & duration of 60 minutes \\
+$E_{th}$ & 36~Joules\\
+$R_s$ & 5~m   \\     
+$R_c$ & 10~m   \\   
+$\alpha^j_i$ & 0.6   \\
+
+$\beta^j_i$ & 0.4
+
+\end{tabular}}
+
+
+\end{table}
+To  obtain  experimental  results  which are  relevant,  simulations  with  five
+different node densities going from  100 to 300~nodes were performed considering
+each time 25~randomly  generated networks. The nodes are deployed  on a field of
+interest of $(50 \times 25)~m^2 $ in such a way that they cover the field with a
+high coverage ratio. Each node has an  initial energy level, in Joules, which is
+randomly drawn in the interval $[500-700]$.   If its energy provision reaches a
+value below  the threshold $E_{th}=36$~Joules,  the minimum energy needed  for a
+node  to stay  active during  one period,  it will  no longer  participate in  the
+coverage task. This value corresponds to the energy needed by the sensing phase,
+obtained by multiplying  the energy consumed in the active state  (9.72 mW) with the
+time in  seconds for one  period (3600 seconds), and  adding the energy  for the
+pre-sensing phases.  According  to the interval of initial energy,  a sensor may
+be active during at most 20 periods.
+
+The values  of $\alpha^j_i$ and  $\beta^j_i$ have been  chosen to ensure  a good
+network coverage and a longer WSN lifetime.  Higher priority is given to
+the  undercoverage  (by  setting  the  $\alpha^j_i$ with  a  larger  value  than
+$\beta^j_i$)  so as  to prevent  the non-coverage  for the  interval~$i$ of  the
+sensor~$j$.  On the  other hand,  
+$\beta^j_i$ is assigned to a value which is slightly lower so as to minimize the number of active sensor nodes which contribute
+in covering the interval.
+
+The following performance metrics are used to evaluate the efficiency of the
+approach.
+
+
+\begin{itemize}
+\item {\bf Network Lifetime}: the lifetime  is defined as the time elapsed until
+  the  coverage  ratio  falls  below a  fixed  threshold.   $Lifetime_{95}$  and
+  $Lifetime_{50}$  denote, respectively,  the  amount of  time  during which  is
+  guaranteed a  level of coverage  greater than $95\%$  and $50\%$. The  WSN can
+  fulfill the expected  monitoring task until all its nodes  have depleted their
+  energy or if the network is no  more connected. This last condition is crucial
+  because without  network connectivity a  sensor may not be  able to send  to a
+  base station an event it has sensed.
+\item {\bf  Coverage Ratio (CR)} : it  measures how  well the  WSN is  able to
+  observe the area of interest. In our  case, the sensor field is discretized as
+  a regular grid, which yields the following equation:
+  
+
+\[
+    \scriptsize
+    \mbox{CR}(\%) = \frac{\mbox{$n$}}{\mbox{$N$}} \times 100
+\]
+
+
+  where $n$  is the  number of covered  grid points by  active sensors  of every
+  subregions during  the current sensing phase  and $N$ is total  number of grid
+  points in  the sensing  field.  In  simulations  a  layout of
+  $N~=~51~\times~26~=~1326$~grid points is considered.
+\item {\bf Active Sensors Ratio (ASR)}: a  major objective of our protocol is to
+  activate  as few nodes as possible,  in order  to minimize  the communication
+  overhead and maximize the WSN lifetime. The active sensors ratio is defined as
+  follows:
+ 
+\[
+    \scriptsize
+    \mbox{ASR}(\%) =  \frac{\sum\limits_{r=1}^R \mbox{$|A_r^p|$}}{\mbox{$|J|$}} \times 100
+\]
+
+  where $|A_r^p|$ is  the number of active  sensors in the subregion  $r$ in the
+  current sensing period~$p$, $|J|$ is the number of sensors in the network, and
+  $R$ is the number of subregions.
+\item {\bf Energy Consumption (EC)}: energy consumption can be seen as the total
+  energy  consumed by  the  sensors during  $Lifetime_{95}$ or  $Lifetime_{50}$,
+  divided by  the number of  periods. The value of  EC is computed  according to
+  this formula:
+
+\[  
+  \scriptsize
+    \mbox{EC} = \frac{\sum\limits_{p=1}^{P} \left( E^{\mbox{com}}_p+E^{\mbox{list}}_p+E^{\mbox{comp}}_p  
+      + E^{a}_p+E^{s}_p \right)}{P},
+\]
+ 
+  where $P$ corresponds  to the number of periods. The  total energy consumed by
+  the  sensors  comes  through  taking   into  consideration  four  main  energy
+  factors. The first one, denoted $E^{\scriptsize \mbox{com}}_p$, represents the
+  energy consumption spent  by all the nodes for  wireless communications during
+  period $p$.  $E^{\scriptsize \mbox{list}}_p$,  the next factor, corresponds to
+  the energy  consumed by the sensors  in LISTENING status before  receiving the
+  decision to go active or sleep in period $p$.  $E^{\scriptsize \mbox{comp}}_p$
+  refers to  the energy  needed by  all the  leader nodes  to solve  the integer
+  program during a period.  Finally, $E^a_{p}$ and $E^s_{p}$ indicate the energy
+  consumed by the WSN during the sensing phase (active and sleeping nodes).
+\end{itemize}
+
+
+\subsection{Simulation Results}
+
+In  order  to  assess and  analyze  the  performance  of  our protocol  we  have
+implemented PeCO protocol in  OMNeT++~\citep{varga} simulator.  Besides PeCO, two
+other  protocols,  described  in  the  next paragraph,  will  be  evaluated  for
+comparison purposes.   The simulations were run  on a DELL laptop  with an Intel
+Core~i3~2370~M (1.8~GHz)  processor (2  cores) whose MIPS  (Million Instructions
+Per Second) rate  is equal to 35330. To  be consistent with the use  of a sensor
+node based on  Atmels AVR ATmega103L microcontroller (6~MHz) having  a MIPS rate
+equal to 6,  the original execution time  on the laptop is  multiplied by 2944.2
+$\left(\frac{35330}{2} \times  \frac{1}{6} \right)$.  The modeling  language for
+Mathematical Programming (AMPL)~\citep{AMPL} is  employed to generate the integer
+program instance  in a  standard format, which  is then read  and solved  by the
+optimization solver  GLPK (GNU  linear Programming Kit  available in  the public
+domain) \citep{glpk} through a Branch-and-Bound method.
+
+As said previously, the PeCO is  compared to three other approaches. The first
+one,  called  DESK,  is  a  fully distributed  coverage  algorithm  proposed  by
+\citep{ChinhVu}. The second one,  called GAF~\citep{xu2001geography}, consists in
+dividing  the monitoring  area into  fixed  squares. Then,  during the  decision
+phase, in each square, one sensor is  chosen to remain active during the sensing
+phase. The last  one, the DiLCO protocol~\citep{Idrees2}, is  an improved version
+of a research work we presented in~\citep{idrees2014coverage}. Let us notice that
+PeCO and  DiLCO protocols are  based on the  same framework. In  particular, the
+choice for the simulations of a partitioning in 16~subregions was made because
+it corresponds to the configuration producing  the best results for DiLCO. The
+protocols are distinguished  from one another by the formulation  of the integer
+program providing the set of sensors which  have to be activated in each sensing
+phase. DiLCO protocol tries to satisfy the coverage of a set of primary points,
+whereas the PeCO protocol objective is to reach a desired level of coverage for each
+sensor perimeter. In our experimentations, we chose a level of coverage equal to
+one ($l=1$).
+
+\subsubsection{\bf Coverage Ratio}
+
+Figure~\ref{figure5}  shows the  average coverage  ratio for  200 deployed  nodes
+obtained with the  four protocols. DESK, GAF, and DiLCO  provide a slightly better
+coverage ratio with respectively 99.99\%,  99.91\%, and 99.02\%, compared to the 98.76\%
+produced by  PeCO for the  first periods. This  is due to  the fact that  at the
+beginning the DiLCO protocol  puts to  sleep status  more redundant  sensors (which
+slightly decreases the coverage ratio), while the three other protocols activate
+more sensor  nodes. Later, when the  number of periods is  beyond~70, it clearly
+appears that  PeCO provides a better  coverage ratio and keeps  a coverage ratio
+greater  than 50\%  for  longer periods  (15  more compared  to  DiLCO, 40  more
+compared to DESK). The energy saved by  PeCO in the early periods allows later a
+substantial increase of the coverage performance.
+
+\parskip 0pt    
+\begin{figure}[h!]
+\centering
+ \includegraphics[scale=0.5] {figure5.eps} 
+\caption{Coverage ratio for 200 deployed nodes.}
+\label{figure5}
+\end{figure} 
+
+
+
+
+\subsubsection{\bf Active Sensors Ratio}
+
+Having the less active sensor nodes in  each period is essential to minimize the
+energy consumption  and thus to  maximize the network  lifetime.  Figure~\ref{figure6}
+shows the  average active nodes ratio  for 200 deployed nodes.   We observe that
+DESK and  GAF have 30.36  \% and  34.96 \% active  nodes for the  first fourteen
+rounds and  DiLCO and PeCO  protocols compete perfectly  with only 17.92~\% and
+20.16~\% active  nodes during the same  time interval. As the  number of periods
+increases, PeCO protocol  has a lower number of active  nodes in comparison with
+the three other approaches, while keeping a greater coverage ratio as shown in
+Figure \ref{figure5}.
+
+\begin{figure}[h!]
+\centering
+\includegraphics[scale=0.5]{figure6.eps}  
+\caption{Active sensors ratio for 200 deployed nodes.}
+\label{figure6}
+\end{figure} 
+
+\subsubsection{\bf Energy Consumption}
+
+We studied the effect of the energy  consumed by the WSN during the communication,
+computation, listening, active, and sleep status for different network densities
+and  compared  it for  the  four  approaches.  Figures~\ref{figure7}(a)  and  (b)
+illustrate  the  energy   consumption  for  different  network   sizes  and  for
+$Lifetime95$ and  $Lifetime50$. The results show  that our PeCO protocol  is the
+most competitive  from the energy  consumption point of  view. As shown  in both
+figures, PeCO consumes much less energy than the three other methods.  One might
+think that the  resolution of the integer  program is too costly  in energy, but
+the  results show  that it  is very  beneficial to  lose a  bit of  time in  the
+selection of  sensors to  activate.  Indeed the  optimization program  allows to
+reduce significantly the number of active  sensors and so the energy consumption
+while keeping a good coverage level.
+
+\begin{figure}[h!]
+  \centering
+  \begin{tabular}{@{}cr@{}}
+    \includegraphics[scale=0.475]{figure7a.eps} & \raisebox{2.75cm}{(a)} \\
+    \includegraphics[scale=0.475]{figure7b.eps} & \raisebox{2.75cm}{(b)}
+  \end{tabular}
+  \caption{Energy consumption per period for (a)~$Lifetime_{95}$ and (b)~$Lifetime_{50}$.}
+  \label{figure7}
+\end{figure} 
+
+
+
+\subsubsection{\bf Network Lifetime}
+
+We observe the superiority of PeCO and DiLCO protocols in comparison with the
+two    other   approaches    in    prolonging   the    network   lifetime.    In
+Figures~\ref{figure8}(a)  and (b),  $Lifetime95$ and  $Lifetime50$ are  shown for
+different  network  sizes.   As  highlighted  by  these  figures,  the  lifetime
+increases with the size  of the network, and it is clearly   largest for DiLCO
+and PeCO  protocols.  For instance,  for a  network of 300~sensors  and coverage
+ratio greater than 50\%, we can  see on Figure~\ref{figure8}(b) that the lifetime
+is about twice longer with  PeCO compared to DESK protocol.  The performance
+difference    is    more    obvious   in    Figure~\ref{figure8}(b)    than    in
+Figure~\ref{figure8}(a) because the gain induced  by our protocols increases with
+ time, and the lifetime with a coverage  of 50\% is far  longer than with
+95\%.
+
+\begin{figure}[h!]
+  \centering
+  \begin{tabular}{@{}cr@{}}
+    \includegraphics[scale=0.475]{figure8a.eps} & \raisebox{2.75cm}{(a)} \\  
+    \includegraphics[scale=0.475]{figure8b.eps} & \raisebox{2.75cm}{(b)}
+  \end{tabular}
+  \caption{Network Lifetime for (a)~$Lifetime_{95}$ \\
+    and (b)~$Lifetime_{50}$.}
+  \label{figure8}
+\end{figure} 
+
+
+
+Figure~\ref{figure9}  compares  the  lifetime  coverage of  our  protocols  for
+different coverage  ratios. We denote by  Protocol/50, Protocol/80, Protocol/85,
+Protocol/90, and  Protocol/95 the amount  of time  during which the  network can
+satisfy an area coverage greater than $50\%$, $80\%$, $85\%$, $90\%$, and $95\%$
+respectively, where the term Protocol refers to  DiLCO  or PeCO.  Indeed there  are applications
+that do not require a 100\% coverage of  the area to be monitored. PeCO might be
+an interesting  method since  it achieves  a good balance  between a  high level
+coverage ratio and network lifetime. PeCO always outperforms DiLCO for the three
+lower  coverage  ratios,  moreover  the   improvements  grow  with  the  network
+size. DiLCO is better  for coverage ratios near 100\%, but in  that case PeCO is
+not ineffective for the smallest network sizes.
+
+\begin{figure}[h!]
+\centering \includegraphics[scale=0.5]{figure9.eps}
+\caption{Network lifetime for different coverage ratios.}
+\label{figure9}
+\end{figure} 
+
+
+
+
+\section{Conclusion and Future Works}
+\label{sec:Conclusion and Future Works}
+
+In this paper  we have studied the problem of  Perimeter-based Coverage Optimization in
+WSNs. We have designed  a new protocol, called Perimeter-based  Coverage Optimization, which
+schedules nodes'  activities (wake up  and sleep  stages) with the  objective of
+maintaining a  good coverage ratio  while maximizing the network  lifetime. This
+protocol is  applied in a distributed  way in regular subregions  obtained after
+partitioning the area of interest in a preliminary step. It works in periods and
+is based on the resolution of an integer program to select the subset of sensors
+operating in active status for each period. Our work is original in so far as it
+proposes for  the first  time an  integer program  scheduling the  activation of
+sensors  based on  their perimeter  coverage level,  instead of  using a  set of
+targets/points to be covered.
+
+
+We  have carried out  several simulations  to  evaluate the  proposed protocol.   The
+simulation  results  show   that  PeCO  is  more   energy-efficient  than  other
+approaches, with respect to lifetime,  coverage ratio, active sensors ratio, and
+energy consumption.
+
+We plan to extend our framework so that the schedules are planned for multiple
+sensing periods.
+
+We also want  to improve our integer program to  take into account heterogeneous
+sensors  from both  energy  and node  characteristics point of views.
+
+Finally,  it   would  be   interesting  to  implement   our  protocol   using  a
+sensor-testbed to evaluate it in real world applications.
+
+\bibliographystyle{gENO}
+\bibliography{biblio}
+
+
+\end{document}
diff --git a/PeCO-EO/reponse.tex b/PeCO-EO/reponse.tex
index b10b1d9..1b8643c 100644
--- a/PeCO-EO/reponse.tex
+++ b/PeCO-EO/reponse.tex
@@ -56,32 +56,33 @@ This paper proposes a scheduling technique for WSN to maximize coverage and netw
 
 \noindent {\bf 1.} The paper makes use of the existing integer optimization model to govern the state of each sensor node within the WSN to maximize coverage and network lifetime. This formulation of the  coverage problem is different from the literature in the sense that they use the perimeter coverage measures to optimize coverage as opposed to the targets/points coverage. The methodology uses existing methods and the original contribution lies only in the application of these methods for the coverage scheduling problem.\\
 
-\textcolor{blue}{\textbf{\textsc{Answer:}                             }}.\\
+\textcolor{blue}{\textbf{\textsc{Answer:} To the best of our knowledge, no integer linear programming based on perimeter coverage has been already proposed in the literature. As specified in the paper, in section 4, it is inspired from one model developed for brachytherapy treatment planning for optimizing dose distribution. In this model the deviation between an actual dose distribution and a required dose distribution in each organ is minimized. In WSN the deviations between the actual level of coverage and the required level are minimized. Outside this parallel between these two applications the mathematical formulation is completly different.                            }}\\
 
 
 \noindent {\bf 2.} The theory seems mathematically sound. However, the assumption made on the selection criteria for the leader seems too vague.  \\
 
-\textcolor{blue}{\textbf{\textsc{Answer:}  The selection criteria for the leader inside each subregion is explained in page 8, lines 50-51. After information exchange among the sensor nodes in the subregion, each node will have all required information to decide if it is a leader or not. The decision is based on selecting the sensor node that have a larger number of one-hop neighbors. If there is more than one sensor node has the same number of one-hop neighbors, the node that has larger remaining energy will be selected as a leader. If there is more than one sensor node with the same number of neighbors and remaining energy, the sensor node that has larger index will be selected as a leader. In fact, we gave a high priority to the number of neighbors to reduce the communication energy consumption  }}.\\
+\textcolor{blue}{\textbf{\textsc{Answer:}  The selection criteria for the leader inside each subregion is explained in page 8, lines 50-51. After information exchange among the sensor nodes in the subregion, each node will have all required information to decide if it is a leader or not. The decision is based on selecting the sensor node that has a larger number of one-hop neighbors. If this value is the same for many sensors, the node that has the largest remaining energy will be selected as a leader. If there exists sensors with  the same number of neighbors and the same value for the remaining energy, the sensor node that has the largest  index will be selected as a leader. }}\\
+%{\bf In fact, we gave a high priority to the number of neighbors to reduce the communication energy consumption - PAS CLAIR  }}.\\
 
 
 \noindent {\bf 3.} The communication and information sharing required to cooperate and make these
 decisions was not discussed.  \\
 
-\textcolor{blue}{\textbf{\textsc{Answer:}  The communication and information sharing required to cooperate and make these decisions was discussed in page 8, lines 48-49}}.\\
+\textcolor{blue}{\textbf{\textsc{Answer:}  The communication and information sharing required to cooperate and make these decisions was discussed in page 8, lines 48-49. Position coordinates, remaining energy, sensor node ID and number of one-hop neighbors are exchanged.}}\\
 
 
 
 \noindent {\bf 4.} The definitions of the undercoverage and overcoverage variables are not clear. I suggest
 adding some information about these values, since without it, you cannot understand how M and V are computed for the optimization problem.  \\
 
-\textcolor{blue}{\textbf{\textsc{Answer:}                    }}.\\
+\textcolor{blue}{\textbf{\textsc{Answer:} The perimeter of each sensor may be cut in parts called coverage intervals (CI). The level of coverage of one CI is defined as  the number of active sensors neighbours covering this part of the perimeter. If a given level of coverage $l$ is required  for one sensor, the sensor is said to be undercovered (respectively overcovered) if the level of coverage of one of its CI is less (respectively greater) than $l$. In other terms, we define undercoverage and overcoverage through the use of variables $M_{i}^{j}$ and $V_{i}^{j}$ for one sensor $j$ and its coverage interval $i$. If the sensor $j$ is undercovered, there exists at least one of its CI (say $i$) for which the number of active sensors (denoted by $l^{i}$) covering this part of the perimeter is less than $l$ and in this case : $M_{i}^{j}=l-l^{i}$, $V_{i}^{j}=0$. In the contrary, if the sensor $j$ is overcovered, there exists at least one of its CI (say $i$) for which the number of active sensors (denoted by $l^{i}$) covering this part of the perimeter is greater than $l$ and in this case : $M_{i}^{j}=0$, $V_{i}^{j}=l^{i}-l$.                       }}\\
 
 
 
 \noindent {\bf 5.} Can you mathematically justify how you chose the values of alpha and beta? This is not
 very clear. I would suggest possibly adding more results showing how the algorithm performs with different alphas and betas.  \\
 
-\textcolor{blue}{\textbf{\textsc{Answer:}                }}.\\
+\textcolor{blue}{\textbf{\textsc{Answer:} The choice of alpha and beta should be made according to the needs of the application. alpha should be enough large to prevent undercoverage and so to reach the highest possible coverage ratio. beta should be enough large to prevent overcoverage and so to activate a minimum number of sensors. The values of $\alpha_{i}^{j}$ can be identical for all coverage intervals $i$ of one sensor $j$ in order to express that the perimeter of each sensor should be uniformly covered, but  $\alpha_{i}^{j}$ values can be differenciated between sensors to force some regions to be better covered than others. The choice of $\beta \gg \alpha$  prevents the overcoverage, and so limit the activation of a large number of sensors, but as $\alpha$ is  low, some areas may be poorly covered. This explains the results obtained for {\it Lifetime50} with $\beta \gg \alpha$: a large number of periods with low coverage ratio. With $\alpha \gg \beta$, we priviligie the coverage even if some areas may be overcovered, so high coverage ratio is reached, but a large number of sensors are activated to achieve this goal. Therefore network lifetime is reduced. The choice $\alpha=0.6$ and $\beta=0.4$ seems to achieve the best compromise between lifetime and coverage ratio.                }}\\
 
 
 
@@ -89,18 +90,18 @@ very clear. I would suggest possibly adding more results showing how the algorit
 However, the clarity in the literature review is a little off. Some of the descriptions of the method
 s used are very vague and do not bring out their key contributions. Some references are not consistent and I suggest using the journals template to adjust them for overall consistency.   \\
 
-\textcolor{blue}{\textbf{\textsc{Answer:}                               }}.\\
+\textcolor{blue}{\textbf{\textsc{Answer:}                               }}\\
 
 
 
 \noindent {\bf 7.} The methodology is implemented in OMNeT++ (network simulator) and tested against 2 existing algorithms and a previously developed method by the authors. The simulation results are thorough and show that the proposed method improves the coverage and network lifetime compared with the 3 existing methods. The results are similar to previous work done by their team.   \\
 
-\textcolor{blue}{\textbf{\textsc{Answer:}                             }}.\\
+\textcolor{blue}{\textbf{\textsc{Answer:} Although the study conducted in this paper reuses the same protocol presented in our previous work, we focus in this paper on the mathematical optimization model developed to schedule nodes activities.  We deliberately chose to keep the same performance indicators to compare the results obtained with this new formulation with other existing algorithms.                            }}\\
 
 
 \noindent {\bf 8.}  Since this paper is attacking the coverage problem, I would like to see more information on the amount of coverage the algorithm is achieving. It seems that there is a tradeoff in this algorithm that allows the network to increase its lifetime but does not improve the coverage ratio. This may be an issue if this approach is used in an application that requires high coverage ratio.   \\
 
-\textcolor{blue}{\textbf{\textsc{Answer:}                                 }}.\\
+\textcolor{blue}{\textbf{\textsc{Answer:}  Your remark is interesting. Indeed, figures 8(a) and (b) highlight this result. PeCO methods allows to achieve a coverage ratio greater than $50\%$ for many more periods than the others three methods, but for applications requiring an high level of coverage (greater than $95\%$), DilCO method is more efficient.                                 }}\\
 
 %%%%%%%%%%%%%%%%%%%%%%  ENGLISH and GRAMMER %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
@@ -108,77 +109,78 @@ s used are very vague and do not bring out their key contributions. Some referen
 
 \noindent {\ding{90} The first paragraph of every section is not indented.  }  \\
 
-\textcolor{blue}{\textbf{\textsc{Answer:} Corrected. The first paragraph of every section is indented in the new version. }}.\\
+\textcolor{blue}{\textbf{\textsc{Answer:} Right, fixed. The first paragraph of every section is indented in the new version. }}\\
 
 
 \noindent {\ding{90} You seem to be writing in the first person. I suggest rewriting sentences that include “we” “our” or “I” in the third person. (There are too many instances to list them all. They are easily found using the find tool.)  }  \\
 
-\textcolor{blue}{\textbf{\textsc{Answer:}      }}.\\
+\textcolor{blue}{\textbf{\textsc{Answer:}  It is very common to find sentences with "we" and "our" in scientific papers to explain the work made by the authors. Nevertheless we agree with the reviewer and we reformulated some sentences in the paper to avoid too many uses of the first person. }}\\
 
 
 \noindent {\ding{90}  Run-on sentence: Page 2 lines 43-48}  \\
 
-\textcolor{blue}{\textbf{\textsc{Answer:}       }}.\\
+\textcolor{blue}{\textbf{\textsc{Answer:} We rewrote this sentence in two separated sentences.     }}\\
 
 
 
 \noindent {\ding{90} Add an “and” after the comma on page 3 line 34.}  \\
 
-\textcolor{blue}{\textbf{\textsc{Answer:}   Corrected.  }}.\\
+\textcolor{blue}{\textbf{\textsc{Answer:}   Right, fixed  }}\\
 
 
 \noindent {\ding{90}  “model as” instead of “Than” on page 10 line 12.}  \\
 
-\textcolor{blue}{\textbf{\textsc{Answer:} Corrected. }}.\\
+\textcolor{blue}{\textbf{\textsc{Answer:} Right, fixed }}\\
 
 
 \noindent {\ding{90} “no longer” instead of “no more” on page 10 line 31.}  \\
 
-\textcolor{blue}{\textbf{\textsc{Answer:} Corrected }}.\\
+\textcolor{blue}{\textbf{\textsc{Answer:} Right, fixed }}\\
 
 
 \noindent {\ding{90} “in the active state” add the on page 10 line 34. }  \\
 
-\textcolor{blue}{\textbf{\textsc{Answer:} Corrected }}.\\
+\textcolor{blue}{\textbf{\textsc{Answer:} Right, fixed }}\\
 
 
 
 \noindent { \ding{90} Lots of English and grammar mistakes. I recommend rereading the paper line by line and adjusting the sentences that do not make sense.} \\
 
-\textcolor{blue}{\textbf{\textsc{Answer:}      }}.\\
+\textcolor{blue}{\textbf{\textsc{Answer:} ?????? relecture par Ingrid     }}.\\
 
 
 
 
 \section*{Response to Reviewer No. 2 Comments}
-The paper entitled "Perimeter-based Coverage Optimization to Improve Lifetime in Wireless Sensor Networks", by Ali Kadhum Idrees, Karine Deschinkela, Michel Salomon and Raphael Couturier proposes a new protocol for Wireless Sensor Networks called PeCO (Perimeter-based Coverage Optimization protocol) that aims at optimizing the use of energy by conjointly exploiting a spatial and temporal subdivision. The protocol is based on solving a Mixed Integer Linear Program at each leader node, and at each iteration of the protocol. The results obtained by PeCO are compared with three other competitors.
+The paper entitled "Perimeter-based Coverage Optimization to Improve Lifetime in Wireless Sensor Networks", by Ali Kadhum Idrees, Karine Deschinkela, Michel Salomon and Raphael Couturier proposes a new protocol for Wireless Sensor Networks called PeCO (Perimeter-based Coverage Optimization protocol) that aims at optimizing the use of energy by conjointly exploiting a spatial and temporal subdivision. The protocol is based on solving a Mixed Integer Linear Program at each leader node, and at each iteration of the protocol. The results obtained by PeCO are compared with three other competitors.\\
 
 
-\noindent\textcolor{black}{\textbf{\Large MAJOR COMMENTS:}} \\
+\noindent\textcolor{black}{\textbf{MAJOR COMMENTS:}} \\
 
-\noindent {\ding{90} The protocol framework is not described in details. In particular, the spatial and temporal subdivision (page 2, line 11) that is at the core of PeCO, is not described nor justified in much detail. How to implement an efficient spatial subdivision? On page 10, line 11, the number of subdivisions is said to be equal to 16, but the clustering algorithm used is not mentioned. Is this number dependent of the size of the sensing area? Of the number of sensors? Of the sensing range? The proposed protocol cannot be adopted by practitioners if such an important step is not documented. Temporal subdivision suffers from the same lack of description and justification: why should time intervals have the same duration? If they have the same duration, how should this common duration should be chosen?   }  \\
+\noindent {\bf 1.} The protocol framework is not described in details. In particular, the spatial and temporal subdivision (page 2, line 11) that is at the core of PeCO, is not described nor justified in much detail. How to implement an efficient spatial subdivision? On page 10, line 11, the number of subdivisions is said to be equal to 16, but the clustering algorithm used is not mentioned. Is this number dependent of the size of the sensing area? Of the number of sensors? Of the sensing range? The proposed protocol cannot be adopted by practitioners if such an important step is not documented. Temporal subdivision suffers from the same lack of description and justification: why should time intervals have the same duration? If they have the same duration, how should this common duration should be chosen?    \\
 
-\textcolor{blue}{\textbf{\textsc{Answer:}                                 }}.\\
+\textcolor{blue}{\textbf{\textsc{Answer:} Spatial and temporal choices of subdivision are not the topics of the paper. In the study, we assume that the deployment of sensors is almost uniformly over the region. So we only need to fix a regular division of the region into subregions to make the problem tractable. The subdivision is made such that the number of hops between any pairs of sensors inside a subregion is less than or equal to 3. Concerning the choice of the sensing period duration, it is correlated with the types of applications, with the amount of initial energy in sensors batteries and also with the duration of the exchange phase. All applications do not have the same requirements of Quality of Service. Here information exchange is executed every hour but the length of the sensing period could be reduced and adapted dynamically. On the one hand a small sensing period would allow to be more reliable but would have higher communication costs. On the other hand the choice of a long duration may cause problems in case of nodes failure during the sensing period.}}\\
 
 
-\noindent {\ding{90}  Page 9, Section 4, is the Perimeter-based coverage problem NP-hard? This question is important for justifying the use of a Mixed Integer Linear Programming model. }  \\
+\noindent {\bf 2.}Page 9, Section 4, is the Perimeter-based coverage problem NP-hard? This question is important for justifying the use of a Mixed Integer Linear Programming model.   \\
 
-\textcolor{blue}{\textbf{\textsc{Answer:}                                       }}.\\
+\textcolor{blue}{\textbf{\textsc{Answer:} The perimeter scheduling coverage problem is NP-hard in general, it  has been proved 
+ in the paper entitled "Perimeter Coverage Scheduling in Wireless Sensor Networks Using Sensors with a Single Continuous Cover Range" from  Ka-Shun Hung and King-Shan Lui (EURASIP Journal on Wireless Communications and Networking 2010, 2010:926075  doi:10.1155/2010/926075). In this paper, authors study the coverage of the perimeter of a large object requiring to be monitored. In our study, the large object to be monitored is the sensor itself (or more precisely its sensing area).  	                                    }}\\
 
 
-\noindent {\ding{90}  Page 9, the major problem with the present paper is, in my opinion, the objective function of the Mixed Integer Linear Program (2). It is not described in the paper, and looks like an attempt to address a multiobjective problem (like minimizing overcoverage and undercoverage). However, using a weighted sum is well known not to be an efficient way to address biobjective problems. The introduction of various performance metrics in Section 5.1 also suggests that the authors have not decided exactly which objective function to use, and compare their protocols against competitors without mentioning the exact purpose of each of them. If the performance metrics list given in Section 5.1 is exhaustive, then the authors should mention at the beginning of the paper what are the aims of the protocol, and explain how the protocol is built to optimize these objectives. }  \\
+\noindent {\bf 3.} Page 9, the major problem with the present paper is, in my opinion, the objective function of the Mixed Integer Linear Program (2). It is not described in the paper, and looks like an attempt to address a multiobjective problem (like minimizing overcoverage and undercoverage). However, using a weighted sum is well known not to be an efficient way to address biobjective problems. The introduction of various performance metrics in Section 5.1 also suggests that the authors have not decided exactly which objective function to use, and compare their protocols against competitors without mentioning the exact purpose of each of them. If the performance metrics list given in Section 5.1 is exhaustive, then the authors should mention at the beginning of the paper what are the aims of the protocol, and explain how the protocol is built to optimize these objectives.  \\
 
-\textcolor{blue}{\textbf{\textsc{Answer:}                                           }}.\\
+\textcolor{blue}{\textbf{\textsc{Answer:}  As far as we know, representing the objective function as a weighted sum of criteria to be minimized in case of multicriteria optimization is a classical method.                                        }}\\
 
 
-\noindent {\ding{90} Page 11 Section 5.2, the sensor nodes are said to be based on Atmels AVR ATmega103L microcontroller. If I am not mistaken, these devices have 128 KBytes of memory, and I didn't find any clue that they can run an operating system like Linux. This point is of primary importance for the proposed protocol, since GLPK (a C API) is supposed to be executed by the cluster leader. In addition to that, GLPK requires a non negligible amount of memory to run properly, and the Atmels AVR ATmega103L microcontroller might be insufficient for that purpose. The authors are urged to provide references of previous works showing that these technical constraints are not preventing their protocol to be implemented on the aforementioned microcontroller. Then, on page 13, in Section "5.2.3 Energy Consumption", the estimation of $E_p^com$ for the considered microcontroller seems quite challenging and should be carefully documented. Indeed, this is a key point in providing a fair comparison of PeCO with its competitors.  }  \\
+\noindent {\bf 4.}Page 11 Section 5.2, the sensor nodes are said to be based on Atmels AVR ATmega103L microcontroller. If I am not mistaken, these devices have 128 KBytes of memory, and I didn't find any clue that they can run an operating system like Linux. This point is of primary importance for the proposed protocol, since GLPK (a C API) is supposed to be executed by the cluster leader. In addition to that, GLPK requires a non negligible amount of memory to run properly, and the Atmels AVR ATmega103L microcontroller might be insufficient for that purpose. The authors are urged to provide references of previous works showing that these technical constraints are not preventing their protocol to be implemented on the aforementioned microcontroller. Then, on page 13, in Section "5.2.3 Energy Consumption", the estimation of $E_p^{com}$ for the considered microcontroller seems quite challenging and should be carefully documented. Indeed, this is a key point in providing a fair comparison of PeCO with its competitors.    \\
 
-\textcolor{blue}{\textbf{\textsc{Answer:}                                              }}.\\
+\textcolor{blue}{\textbf{\textsc{Answer:}                                              }}\\
 
 
 
 
-\noindent\textcolor{black}{\textbf{\Large MINOR COMMENTS:}} \\
+\noindent\textcolor{black}{\textbf{MINOR COMMENTS:}} \\
 
 
 \noindent {\ding{90} Page 12, lines 7-15, the authors mention that DiLCO protocol is close to PeCO. This should be mentioned earlier in the paper, ideally in Section 2 (Related Literature), along with the detailed description of DESK and GAF, the competitors of the proposed protocol, PeCO.  }  \\
@@ -189,86 +191,85 @@ The paper entitled "Perimeter-based Coverage Optimization to Improve Lifetime in
 
 \noindent {\ding{90} Page 2, line 20, "An optimal scheduling" should be replaced with "An optimal schedule" }  \\
 
-\textcolor{blue}{\textbf{\textsc{Answer:} Corrected }}.\\
+\textcolor{blue}{\textbf{\textsc{Answer:} Right, fixed }}.\\
 
 
 
 \noindent {\ding{90}  Page 4, we first read (line 23) "we assume that each sensor node can directly transmit its measurements to a mobile sink", then on line 30, "We also assume that the communication range Rc satisfies $Rc >=2Rs$. In fact, Zhang and Hou (2005) proved that if the transmission range fulfills the previous hypothesis, the complete coverage of a convex area implies connectivity among active nodes.". These two assumptions seems redundant. }  \\
 
-\textcolor{blue}{\textbf{\textsc{Answer:}          }}.\\
+\textcolor{blue}{\textbf{\textsc{Answer:} Yes, you are right and we removed sentences about the sink. Indeed we consider multi-hops communication.}}.\\
 
 
 
 \noindent {\ding{90}   Page 4, line 37, a definition for k-covered is missing (the sentence is an equivalence property).}  \\
 
-\textcolor{blue}{\textbf{\textsc{Answer:}        }}.\\
+\textcolor{blue}{\textbf{\textsc{Answer:} Right. A network area is said to be $k$-covered if every point in the area covered by at least k sensors. We added this definition in the paper}}.\\
 
 
 
 
 \noindent {\ding{90}  Page 5, lines 34 and 37, replace [0, $2\pi$] with [0, $2\pi$) }  \\
 
-\textcolor{blue}{\textbf{\textsc{Answer:} Corrected }}.\\
+\textcolor{blue}{\textbf{\textsc{Answer:} Right, fixed }}.\\
 
 
 
 
 \noindent {\ding{90}  Page 5, line 36 and 43, replace "figure 2" with "Figure 2" }  \\
 
-\textcolor{blue}{\textbf{\textsc{Answer:} Corrected }}.\\
+\textcolor{blue}{\textbf{\textsc{Answer:} Right, fixed }}.\\
 
 
 
 
 \noindent {\ding{90}  Page 5, line 50, replace "section 4" with "Section 4" }  \\
 
-\textcolor{blue}{\textbf{\textsc{Answer:} Corrected }}.\\
+\textcolor{blue}{\textbf{\textsc{Answer:} Right, fixed }}.\\
 
 
 \noindent {\ding{90}   Page 5, line 51, replace "figure 3" with "Figure 3"}  \\
 
-\textcolor{blue}{\textbf{\textsc{Answer:} Corrected }}.\\
+\textcolor{blue}{\textbf{\textsc{Answer:} Right, fixed }}.\\
 
 
 \noindent {\ding{90}  Page 7, line 20 "regular homogeneous subregions" is too vague. }  \\
 
-\textcolor{blue}{\textbf{\textsc{Answer:}           }}.\\
+\textcolor{blue}{\textbf{\textsc{Answer:} As mentioned in the previous remark, the spatial subdivision was not clearly explained in the paper. We added a discussion about this question in the article. Thank you for highlighting it. A FAIRE          }}.\\
 
 
 \noindent {\ding{90}   Page 7, line 24, replace "figure 4" with "Figure 4"}  \\
 
-\textcolor{blue}{\textbf{\textsc{Answer:} Corrected }}.\\
+\textcolor{blue}{\textbf{\textsc{Answer:} Right, fixed }}.\\
 
 
 \noindent {\ding{90}  Page 7, line 47, replace "Five status" with "Five statuses" }  \\
 
-\textcolor{blue}{\textbf{\textsc{Answer:} Corrected }}.\\
+\textcolor{blue}{\textbf{\textsc{Answer:} Right, fixed }}.\\
 
 
 
 \noindent {\ding{90}  Page 9, the constraints of the Mixed Integer Linear Program (2) are not numbered. There are two inequalities for overcoverage and undercoverage that are used to define Mij and Vij. Why not using replacing these inequalities by equalities? }  \\
 
-\textcolor{blue}{\textbf{\textsc{Answer:}           }}.\\
-
+\textcolor{blue}{\textbf{\textsc{Answer:}  In fact, replacing these inequalities by equalities does not impact the final result because of the structure of the integer programming. For minimizing the objective function, $M_{i}^{j}$ and $V_{i}^{j}$ should be set to the smallest possible value such that the inequalities are satisfied. It is explained in the answer 4 for the reviewer 1. So, at optimality, constraints are satisfied with equality. So, we thank for your remark and we changed it in the formulation, even if there is no incidence about the final result.}}\\
 
 \noindent {\ding{90}  Page 10, line 50, "or if the network is no more connected". In order to assess this, the communication range should be known, but it is not given in Table 2. }  \\
 
-\textcolor{blue}{\textbf{\textsc{Answer:}                    }}.\\
+\textcolor{blue}{\textbf{\textsc{Answer:} Right, fixed}}.\\
 
 
 \noindent {\ding{90}  Page 10, line 53, the "Coverage ratio" definition is provided for a given period p? Then in the formula on top of page 11, N is set to 51 times 26, why? Is it somehow related to the sensing area having size 50 times 25? }  \\
 
-\textcolor{blue}{\textbf{\textsc{Answer:} Yes, the "Coverage ratio" definition is provided for a given period p. N is set to 51 times 26 = 1326 grid points because  we discretized the sensing field as a regular grid. Yes, it is related to the sensing area having size 50 times 25. }}.\\
+\textcolor{blue}{\textbf{\textsc{Answer:} Yes, the "Coverage ratio" definition is provided for a given period p. N is set to 51 times 26 = 1326 grid points because  we discretized the sensing field as a regular grid, a point on the contour and a point every meter. Yes, it is related to the sensing area having size 50 meters times 25 meters. }}\\
 
 
 \noindent {\ding{90}  Page 11, line 17 in the formula of ASR, |S| should be replaced with J (where J is defined page 4 line 16). }  \\
 
-\textcolor{blue}{\textbf{\textsc{Answer:} Corrected }}.\\
+\textcolor{blue}{\textbf{\textsc{Answer:} Right, fixed }}.\\
 
 
 \noindent {\ding{90}  Page 13, line 41 and 43, replace "figure 8" with "Figure 8" }  \\
 
-\textcolor{blue}{\textbf{\textsc{Answer:} Corrected }}.\\
+\textcolor{blue}{\textbf{\textsc{Answer:} Right, fixed }}.\\
 
 
 
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2.39.5