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 % v4.0 released April 2013
 
 \documentclass{gENO2e}
-%\usepackage[linesnumbered,ruled,vlined,commentsnumbered]{algorithm2e}
-%\renewcommand{\algorithmcfname}{ALGORITHM}
+
 \usepackage{indentfirst}
+\usepackage{color}
+\usepackage[algo2e,ruled,vlined]{algorithm2e}
 \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}};}
-
+\title{{\itshape Perimeter-based Coverage Optimization \\
+  to Improve Lifetime in Wireless Sensor Networks}}
 
+\author{Ali Kadhum Idrees$^{a,b}$, 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 Bourgogne Franche-Comt\'e, Belfort, France}} \\ 
+  $^{b}${\em{Department of Computer Science, University of Babylon, Babylon, Iraq}}
+}         
+         
 \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
+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.
+scheduling which ensures  sensing coverage while minimizing the  energy cost. An approach called Perimeter-based  Coverage Optimization protocol
+(PeCO) is proposed. 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 the 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 compared to 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
+The continuous progress in Micro  Electro-Mechanical Systems (MEMS) and wireless
+communication hardware has given rise to the opportunity of using 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
+user by means of sink nodes. The features  of a WSN makes it suitable for a wide
+range of applications 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.
+communication unit for data transmission and reception.
 
 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
+communication is provided 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
+recharge 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 is it possible 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.
+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
+\item A  framework is devised  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 the proposed  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 A new  mathematical optimization model is proposed.  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.
+  the literature, a  mixed-integer program based on  the perimeter
+  coverage of each sensor is formulated.  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 Extensive  simulation experiments are  conducted using the  discrete event
+  simulator OMNeT++,  to demonstrate  the efficiency of  the PeCO protocol.   The  PeCO  protocol has been compared to  two approaches  found  in  the  literature:
+  DESK~\citep{ChinhVu} and GAF~\citep{xu2001geography}, and also to the
+  protocol DiLCO published in~\citep{Idrees2}. DiLCO  uses the same framework as
+  PeCO but 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}
+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
+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.
+This section  summarizes some related  works regarding the coverage  problem and
+presents  specific aspects  of the  PeCO protocol  common with  other literature
+works.
 
 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
+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
+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.}
+\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   disks    of   sensor    nodes   and    boundaries.    In
+\citep{huang2005coverage} authors  prove that if  the perimeters of  the 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, the 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
+non-disjoint)  \citep{wang2011coverage},  where  each set  completely  covers  a
+region of interest,  and to successively activate these set covers. 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 decided  at the
+beginning of each  period \citep{ling2009energy}. In fact,  many authors propose
+algorithms       working       in       such      a       periodic       fashion
+\citep{chin2007,yan2008design,pc10}.  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.
+activated in succession to achieve  the desired network lifetime. {\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{ChinhVu,qu2013distributed,yangnovel}  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  information on its immediate neighbors only  (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  optimal solutions 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 WSN,  the higher  the
+communication  energy  cost.  {\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  the PeCO protocol
+  is scalable  and 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
+\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.}
-
-
-
-The authors in \citep{Idrees2} propose a Distributed Lifetime Coverage Optimization (DiLCO) protocol, maintains the coverage and improves the lifetime in WSNs. It is  an improved version
-of a research work they presented in~\citep{idrees2014coverage}.  First, they partition the area of interest into subregions using a divide-and-conquer method. DiLCO protocol is then distributed on the sensor nodes in each subregion in a second step. DiLCO protocol combines two techniques: a leader election in each subregion, followed by an optimization-based node activity scheduling performed by each elected leader. The proposed DiLCO protocol is a periodic protocol where each period is decomposed into 4 phases: information exchange, leader election, decision, and sensing. The simulations show that DiLCO is able to increase the WSN lifetime and provides improved coverage performance. {\it  In the PeCO
-  protocol, We have proposed a new mathematical optimization model. Instead of trying to
-cover a set of specified points/targets as in DiLCO protocol, 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. The idea is that an optimal scheduling will be obtained by minimizing a weighted sum of these deviations.}
-  
-  
+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: minimizing  the overcoverage and
+  the undercoverage of the perimeter of each sensor.}
+
+The  authors   in  \citep{Idrees2}  propose  a   Distributed  Lifetime  Coverage
+Optimization (DiLCO)  protocol, which  maintains the  coverage and  improves the
+lifetime  in WSNs.   It is  an  improved version  of a  research work  presented
+in~\citep{idrees2014coverage}.  First, the area  of interest is partitioned into
+subregions  using  a  divide-and-conquer  method. The  DiLCO  protocol  is  then
+distributed on the sensor  nodes in each subregion in a  second step. Hence this
+protocol combines two techniques: a  leader election in each subregion, followed
+by  an optimization-based  node activity  scheduling performed  by each  elected
+leader. The proposed DiLCO protocol is  a periodic protocol where each period is
+decomposed into 4  phases: information exchange, leader  election, decision, and
+sensing. The  simulations show that DiLCO  is able to increase  the WSN lifetime
+and provides  improved coverage performance.  {\it  In the PeCO protocol,  a new
+  mathematical optimization model is proposed. Instead  of trying to cover a set
+  of specified points/targets as in the  DiLCO protocol, an integer
+  program based  on the perimeter  coverage of  each sensor is formulated. The  model involves
+  integer  variables to  capture  the  deviations between  the  actual level  of
+  coverage and the  required level. The idea is that  an optimal scheduling will
+  be obtained by minimizing a weighted sum of these deviations.}
   
-
 \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
+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
+of interest.  All  the sensor nodes are  supposed to be 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 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). 
+algorithms. A Boolean disk coverage model,  which is the most widely used sensor
+coverage model  in the  literature, is  considered 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.  The communication range  $R_c$ is assumed to satisfy : $R_c
+\geq 2  \cdot R_s$.  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 is  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.
+Figure~\ref{figure1}(a) shows the coverage of  sensor node~$0$.  On this figure,
+sensor~$0$  has nine  neighbors. For each neighbor  the two points
+resulting from  the intersection  of the  two sensing  areas have been reported  on  its perimeter  (the
+perimeter of the  disk covered by the  sensor~$0$).  These  points are
+denoted for neighbor~$i$ by $iL$ and  $iR$, respectively for left and right from
+a  neighboring point  of view.   The  resulting couples  of intersection  points
+subdivide the perimeter of sensor~$0$ into portions called arcs.
 
 \begin{figure}[ht!]
   \centering
@@ -260,52 +261,48 @@ arcs.
   \label{figure1}
 \end{figure} 
 
-Figure~\ref{figure1}(b) describes the geometric information used to find the
+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:
+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 as follows:
+$$
+  Dist(u,v)=\sqrt{(u_x - v_x)^2 + (u_y-v_y)^2},
+$$
+while the angle~$\alpha$ is obtained through the formula:
  \[
-\alpha =  \arccos \left(\frac{Dist(u,v)}{2R_s}
-\right).
+\alpha = \arccos \left(\frac{Dist(u,v)}{2R_s} \right).
 \] 
-The arc on the perimeter of~$u$ defined by the angular interval $[\pi
-  - \alpha,\pi + \alpha]$ is said to be perimeter-covered by sensor~$v$.
+The  arc  on the  perimeter  of~$u$  defined by  the  angular  interval $[\pi  -
+  \alpha,\pi + \alpha]$ is then 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
+sensor $0$ and  Table~\ref{my-label} 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 $3$
+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}  
+\includegraphics[width=0.95\linewidth]{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{table}
+\tbl{Coverage intervals and contributing sensors for 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
@@ -332,41 +329,43 @@ above is thus given by the sixth line of the table.
 
 \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
+In  the  PeCO protocol,  the  scheduling  of  the  sensor nodes'  activities  is
+formulated    with    a    mixed-integer     program    based    on    coverage
+intervals~\citep{doi:10.1155/2010/926075}.  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 $\infty$
+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
+%\newpage
 \begin{figure}[h!]
 \centering
-\includegraphics[width=62.5mm]{figure3.eps}  
+\includegraphics[width=57.5mm]{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
+\end{figure}
+
+\vspace{-0.25cm}
+
+\subsection{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 the protocol
+will  be executed  in  a distributed  way in  each  subregion simultaneously  to
+schedule nodes' activities  for one sensing period. Sensor nodes  are assumed to
+be deployed  almost uniformly over the  region. The regular subdivision  is made
+such that the number of hops between  any pairs of sensors inside a subregion is
+less than or equal to 3.
+
+As shown  in Figure~\ref{figure4}, node  activity scheduling is produced  by the
+proposed 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
@@ -375,7 +374,8 @@ 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.
+the area. Sensing  period duration is adapted according to  the QoS requirements
+of the application.
 
 \begin{figure}[t!]
 \centering
@@ -384,19 +384,16 @@ the area.
 \label{figure4}
 \end{figure} 
 
-We define two types of packets to be used by PeCO protocol:
-
+Two types of packets used by the PeCO protocol are defined:
 \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.
+  the 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
@@ -406,89 +403,91 @@ Five statuses are possible for a sensor node in the network:
 \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.
-
+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{algorithm2e}      
+  \label{alg:PeCO}
+  \caption{PeCO pseudocode}
+  \eIf{$RE_k \geq E_{th}$}{
+    $s_k.status$ = COMMUNICATION\;
+    Send $INFO()$ packet to other nodes in subregion\;
+    Wait $INFO()$ packet from other nodes in subregion\;
+    Update K.CurrentSize\;
+    LeaderID = Leader election\;
+    \eIf{$s_k.ID = LeaderID$}{
+      $s_k.status$ = COMPUTATION\;
+      \If{$ s_k.ID $ is Not previously selected as a Leader}{
+        Execute the perimeter coverage model\;
+      }
+      \eIf{($s_k.ID $ is the same Previous Leader) {\bf and} \\
+        \indent (K.CurrentSize = K.PreviousSize)}{
+        Use the same previous cover set for current sensing stage\;
+      }{
+        Update $a^j_{ik}$; prepare data for IP~Algorithm\;
+        $\left\{\left(X_{1},\dots,X_{l},\dots,X_{K}\right)\right\}$ = Execute Integer Program Algorithm($K$)\;
+        K.PreviousSize = K.CurrentSize\;
+      }
+      $s_k.status$ = COMMUNICATION\;
+      Send $ActiveSleep()$ to each node $l$ in subregion\;
+      Update $RE_k $\;
+    }{
+      $s_k.status$ = LISTENING\;
+      Wait $ActiveSleep()$ packet from the Leader\;
+      Update $RE_k $\;
+    }
+  }{
+    Exclude $s_k$ from entering in the current sensing stage\;
+  }
+\end{algorithm2e}
+
+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.   At the  beginning  of  the  first period  $K.PreviousSize$  is
+initialized to  zero.  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.
+Both INFO packet and ActiveSleep packet contain two parts: header and data payload. The sensor ID is included in the header, where the header size is 8 bits. The data part includes position coordinates (64 bits), remaining energy (32 bits), and the number of one-hop live neighbors (8 bits). Therefore the size of the INFO packet is 112 bits. The ActiveSleep packet is 16 bits size, 8 bits for the header and 8 bits for data part that includes only sensor status (0 or 1).
+The sensors  inside a same  region cooperate to  elect a leader.   The selection
+criteria for the leader are (in order  of priority):
+\begin{enumerate}
+\item larger number of neighbors;
+\item larger  remaining energy;
+\item and then,  in case  of equality,  larger indexes.
+\end{enumerate}
+Once chosen, the leader collects information  to formulate and solve the integer
+program  which allows  to build  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.\\
+In  this  section,  the   perimeter-based  coverage  problem  is  mathematically
+formulated.    It    has    been    proved   to    be    a    NP-hard    problem
+by \citep{doi:10.1155/2010/926075}. Authors  study the coverage of  the perimeter
+of a  large object requiring  to be monitored.  For the proposed  formulation in
+this paper,  the large  object to  be monitored  is the  sensor itself  (or more
+precisely its sensing area).
+
+The following notations are used  throughout the section.
+
 First, the following sets:
 \begin{itemize}
-\item $S$ represents the set of WSN sensor nodes;
+\item $S$ represents the set of 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
+$I_j$ refers to the set of  coverage intervals which has been defined according
+to the  method introduced in  Subsection~\ref{CI}. For a coverage  interval $i$,
+let $a^j_{ik}$ denote  the indicator function of whether  sensor~$k$ is involved
 in coverage interval~$i$ of sensor~$j$, that is:
 \begin{equation}
 a^j_{ik} = \left \{ 
@@ -500,126 +499,129 @@ a^j_{ik} = \left \{
 \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.
+Second,  several 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 a 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 $V^j_i$.
+
+To sustain a  level of coverage equal  to $l$ all along the  perimeter of sensor
+$j$, at  least $l$  sensors involved in  each coverage interval  $i \in  I_j$ of
+sensor $j$ have  to be 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 these deviations are minimized, 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.
+
+The coverage optimization problem can then be mathematically expressed as follows:
+\begin{equation}
+  \begin{aligned}
+    \text{Minimize } & \sum_{j \in S} \sum_{i \in I_j} (\alpha^j_i ~ M^j_i + \beta^j_i ~ V^j_i ) \\
+    \text{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 \\
+    & M^j_i, V^j_i \in \mathbb{R}^{+} 
+  \end{aligned}
 \end{equation}
 
+
+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 $l$.   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 : $M_{i}^{j}=l-l^{i}$, $V_{i}^{j}=0$. Conversely,
+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:  $M_{i}^{j}=0$,
+$V_{i}^{j}=l^{i}-l$.
+
 $\alpha^j_i$ 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.
+weights associated with  coverage intervals of the specified part  of a region may
+be given by  a relatively larger magnitude than weights  associated with another
+region. This kind of mixed-integer program  is inspired from the model developed
+for   brachytherapy  treatment   planning  to optimize  dose   distribution
+\citep{0031-9155-44-1-012}.  The choice of the values for variables $\alpha$ and
+$\beta$  should be  made according  to the  needs of  the application.  $\alpha$
+should be  large enough  to prevent  undercoverage and so  to reach  the highest
+possible coverage ratio. $\beta$ should  be large enough to prevent overcoverage
+and so to activate a minimum  number of sensors.  The mixed-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.
+and the  energy  consumption   model  used is described in 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 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   \\
-
+$E_{th}$ & 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
+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
+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
+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.
+be active during at most 20 periods. the information exchange to update the coverage
+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 the network to
+be more  reliable but would  have resulted in  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.
 
 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.
+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. Subsection~\ref{sec:Impact} investigates more deeply how the values of
+both parameters affect the performance of the PeCO protocol.
 
 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
@@ -630,44 +632,43 @@ 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, the sensor field is discretized as
+  observe the area of interest. Here the sensor field is discretized as
   a regular grid, which yields the following equation:
-  
-
-\[
+  \begin{equation*}
     \scriptsize
     \mbox{CR}(\%) = \frac{\mbox{$n$}}{\mbox{$N$}} \times 100
-\]
-
-
+  \end{equation*}
   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
+  points in the sensing field. A layout of $N~=~51~\times~26~=~1326$~grid points
+  is considered in the simulations.
+\item {\bf Active Sensors Ratio (ASR)}: a  major objective of the proposed 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:
- 
-\[
-    \scriptsize
-    \mbox{ASR}(\%) =  \frac{\sum\limits_{r=1}^R \mbox{$|A_r^p|$}}{\mbox{$|J|$}} \times 100
-\]
-
+  \begin{equation*}
+   \scriptsize
+   \mbox{ASR}(\%) =  \frac{\sum\limits_{r=1}^R \mbox{$|A_r^p|$}}{\mbox{$|J|$}} \times 100
+  \end{equation*}
   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.
+  sensing period~$p$, $R$  is the number of subregions, and  $|J|$ is the number
+  of sensors in the network.
+  
+\item {\bf Energy Saving Ratio (ESR)}:this metric, which shows the ability of a protocol to save energy, is defined by:
+\begin{equation*}
+\scriptsize
+\mbox{ESR}(\%) = \frac{\mbox{Number of alive sensors during this round}}
+{\mbox{Total number of sensors in the network}} \times 100.
+\end{equation*}  
 \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:
-
-\[  
-  \scriptsize
+  \begin{equation*} 
+    \scriptsize
     \mbox{EC} = \frac{\sum\limits_{p=1}^{P} \left( E^{\mbox{com}}_p+E^{\mbox{list}}_p+E^{\mbox{comp}}_p  
       + E^{a}_p+E^{s}_p \right)}{P},
-\]
- 
+  \end{equation*}
   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
@@ -676,57 +677,88 @@ approach.
   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).
+  program  during  a  period   (COMPUTATION  status).   Finally,  $E^a_{p}$  and
+  $E^s_{p}$ indicate  the energy consumed  by the  WSN during the  sensing phase
+  ({\it active} and {\it 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.
+
+The PeCO  protocol has been implemented  in  OMNeT++~\citep{varga}   simulator in  order  to  assess and  analyze  its  performance. 
+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  $\left(\frac{35330}{2}
+\times \frac{1}{6} \right)$.  Energy consumption  is calculated according to the
+power consumption values, in milliWatt  per second, given in Table~\ref{tab:EC},
+based on the energy model proposed in \citep{ChinhVu}.
+
+\begin{table}[h]
+\centering
+\caption{Power consumption values}
+\label{tab:EC}
+\begin{tabular}{|l||cccc|}
+  \hline
+  {\bf Sensor status} & MCU & Radio & Sensing & {\it Power (mW)} \\
+  \hline
+  LISTENING & On & On & On & 20.05 \\
+  ACTIVE & On & Off & On & 9.72 \\
+  SLEEP & Off & Off & Off & 0.02 \\
+  COMPUTATION & On & On & On & 26.83 \\
+  \hline
+  \multicolumn{4}{|l}{Energy needed to send or receive a 2-bit content message} & 0.515 \\
+  \hline
+\end{tabular}
+\end{table}
+
+The modeling  language for Mathematical Programming  (AMPL)~\citep{AMPL} is used
+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.
+In practice, executing GLPK on a sensor node is obviously intractable due to the
+huge memory  use. Fortunately, to  solve the  optimization problem, the use of
+commercial  solvers  like  CPLEX  \citep{iamigo:cplex}  which  are  less  memory
+consuming and more efficient is possible, or a lightweight heuristic may be implemented. For example,
+for  a WSN  of 200  sensor nodes,  a leader  node has  to deal  with constraints
+induced  by about  12 sensor  nodes.  In  that case,  to solve  the optimization
+problem  a memory  consumption of  more  than 1~MB  can be  observed with  GLPK,
+whereas less than 300~KB would be needed with CPLEX.
+
+Besides  PeCO,   three  other  protocols   will  be  evaluated   for  comparison
+purposes. 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 presented
+in~\citep{idrees2014coverage}. 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. Of course, this  number of
+subregions should be adapted  according to the size of the  area of interest and
+the number of sensors.  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.  The DiLCO  protocol  tries  to satisfy  the
+coverage of a set of primary points,  whereas the objective of the PeCO protocol
+is  to reach  a desired  level of  coverage for  each sensor  perimeter. In the
+experimentations, a level of coverage equal to one ($l=1$) is chosen
+.
+
+\subsubsection{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 and PeCO protocols put more  redundant sensors to sleep
+status  (which slightly  decreases  the  coverage ratio),  while  the two  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!]
@@ -736,20 +768,17 @@ substantial increase of the coverage performance.
 \label{figure5}
 \end{figure} 
 
+\subsubsection{Active Sensors Ratio}
 
-
-
-\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}.
+Minimizing the number of 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. DESK and GAF have 30.36~\% and 34.96~\% active nodes for
+the first fourteen  rounds, and the 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, the PeCO protocol has a lower number of active nodes in
+comparison with the  three other approaches and exhibits a  slow decrease, while
+keeping a greater coverage ratio as shown in Figure \ref{figure5}.
 
 \begin{figure}[h!]
 \centering
@@ -758,82 +787,115 @@ Figure \ref{figure5}.
 \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.
+\subsubsection{Energy Saving Ratio} 
+
+
+The  simulation  results  show  that the  protocol  PeCO  saves
+  efficiently energy by  turning off some sensors during the  sensing phase.  As
+  shown in  Figure~\ref{figure7}, GAF provides  better energy saving than  PeCO for
+  the  first fifty  rounds. Indeed  GAF  balances the  energy consumption  among
+  sensor nodes inside each small fixed grid  and thus permits to extend the life
+  of sensors in each grid fairly. However, at  the same time it turns on a large
+  number of sensors and that leads  later to quickly deplete sensor's batteries.
+  DESK algorithm  shows less energy  saving compared with other  approaches.  In
+  comparison  with PeCO,  DiLCO protocol  usually provides  lower energy  saving
+  ratios. Moreover,  it can  be noticed  that after  round fifty,  PeCO protocol
+  exhibits the slowest decrease among all the considered protocols.
+
+\begin{figure}[h!]
+%\centering
+% \begin{multicols}{6}
+\centering
+\includegraphics[scale=0.5]{figure7.eps} %\\~ ~ ~(a)
+\caption{Energy Saving Ratio for 200 deployed nodes.}
+\label{figure7}
+\end{figure}
+
+\subsubsection{Energy Consumption}
+
+The  effect  of  the  energy  consumed by  the  WSN  during  the  communication,
+computation,  listening,  active, and  sleep  status  is studied  for  different
+network densities  and the  four approaches  compared.  Figures~\ref{figure8}(a)
+and (b)  illustrate the energy consumption  for different network sizes  and for
+$Lifetime_{95}$ and $Lifetime_{50}$.  The results show  that the PeCO protocol is the most
+competitive from the energy consumption point of view. As shown by both figures,
+PeCO consumes much less energy than the  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 also  the energy consumption  while keeping  a good
+coverage level. The energy overhead  when increasing network
+size is the lowest with PeCO.
 
 \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)}
+    \includegraphics[scale=0.5]{figure8a.eps} & \raisebox{2.75cm}{(a)} \\
+    \includegraphics[scale=0.5]{figure8b.eps} & \raisebox{2.75cm}{(b)}
   \end{tabular}
   \caption{Energy consumption per period for (a)~$Lifetime_{95}$ and (b)~$Lifetime_{50}$.}
-  \label{figure7}
+  \label{figure8}
 \end{figure} 
 
+\subsubsection{Network Lifetime}
 
-
-\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\%.
+In comparison with the   two   other  approaches, PeCO and DiLCO  protocols  are better for prolonging   the  network   lifetime.    In
+Figures~\ref{figure9}(a) and  (b), $Lifetime_{95}$  and $Lifetime_{50}$ are  shown for
+different  network  sizes.  As  can  be  seen  in  these figures,  the  lifetime
+increases with the size of the network,  and it is clearly larger for the DiLCO and
+PeCO protocols.  For  instance, for a network of 300~sensors  and coverage ratio
+greater than  50\%, it can be observed on Figure~\ref{figure9}(b) that the  lifetime is
+about  twice  longer with  PeCO  compared  to  the DESK protocol.   The  performance
+difference    is   more    obvious    in    Figure~\ref{figure9}(b)   than    in
+Figure~\ref{figure9}(a) because the gain induced by protocols (PeCO and DiLCO) increases with
+time, and the lifetime with a coverage over 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)}
+    \includegraphics[scale=0.5]{figure9a.eps} & \raisebox{2.75cm}{(a)} \\  
+    \includegraphics[scale=0.5]{figure9b.eps} & \raisebox{2.75cm}{(b)}
   \end{tabular}
-  \caption{Network Lifetime for (a)~$Lifetime_{95}$ \\
-    and (b)~$Lifetime_{50}$.}
-  \label{figure8}
+  \caption{Network Lifetime for (a)~$Lifetime_{95}$ and (b)~$Lifetime_{50}$.}
+  \label{figure9}
 \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.
+Figure~\ref{figure10} compares the lifetime coverage  of the DiLCO and PeCO protocols
+for  different   coverage  ratios.   Protocol/70,  Protocol/80,
+Protocol/85, Protocol/90,  and Protocol/95 correspond to the  amount of time during  which the
+network  can satisfy  an  area  coverage greater  than  $70\%$, $80\%$,  $85\%$,
+$90\%$, 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. For example, forest
+fire application might require complete coverage
+in summer seasons while only require 80$\%$ of the area to be covered in rainy seasons~\citep{li2011transforming}. As another example, birds habit study requires only 70$\%$-coverage at nighttime when the birds are sleeping while requires 100$\%$-coverage at daytime when the birds are active~\citep{1279193}. 
+ PeCO always  outperforms DiLCO  for the  three  lower coverage  ratios, moreover  the
+improvements grow  with the network  size. DiLCO outperforms PeCO when the coverage ratio is required to be $>90\%$, but PeCO extends the network lifetime significantly when coverage ratio can be relaxed.
 
 \begin{figure}[h!]
-\centering \includegraphics[scale=0.5]{figure9.eps}
+\centering \includegraphics[scale=0.55]{figure10.eps}
 \caption{Network lifetime for different coverage ratios.}
-\label{figure9}
+\label{figure10}
 \end{figure} 
 
+\subsubsection{Impact of $\alpha$ and $\beta$ on PeCO's performance}
+\label{sec:Impact}
+
+Table~\ref{my-labelx}  shows network  lifetime results  for different  values of
+$\alpha$ and $\beta$, and  a network size equal to 200 sensor  nodes. On the one
+hand,  the choice  of $\beta  \gg \alpha$  prevents the  overcoverage, and  also
+limits 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
+$Lifetime_{50}$ with  $\beta \gg  \alpha$: a  large number  of periods  with low
+coverage ratio.  On the other hand, when  $\alpha \gg \beta$ is chosen, 
+the coverage is  favored even if some areas may  be overcovered, so a high coverage ratio is
+reached,  but a  large number  of sensors  are activated  to achieve  this goal.
+Therefore  the  network  lifetime  is  reduced.   The  choice  $\alpha=0.6$  and
+$\beta=0.4$ seems to  achieve the best compromise between  lifetime and coverage
+ratio.   That explains  why  this  setting  has been chosen for the  experiments
+presented in the previous subsections.
+
 
-\subsubsection{\bf Impact of $\alpha$ and $\beta$ on PeCO's performance}
-Table~\ref{my-labelx} explains all possible network lifetime result of the relation between the different values of $\alpha$ and $\beta$, and for a network size equal to 200 sensor nodes. As can be seen in Table~\ref{my-labelx},  it is obvious and clear that when $\alpha$ decreased and $\beta$ increased by any step, the network lifetime for $Lifetime_{50}$ increased and the $Lifetime_{95}$ decreased. Therefore, selecting the values of $\alpha$ and $\beta$ depend on the application type used in the sensor nework. In PeCO protocol, $\alpha$ and $\beta$ are chosen based on the largest value of network lifetime for $Lifetime_{95}$.
 
 \begin{table}[h]
 \centering
@@ -848,7 +910,7 @@ $\alpha$ & $\beta$ & $Lifetime_{50}$ & $Lifetime_{95}$ \\ \hline
 0.3 & 0.7 & 134 & 0 \\ \hline
 0.4 & 0.6 & 125 & 0 \\ \hline
 0.5 & 0.5 & 118 & 30 \\ \hline
-0.6 & 0.4 & 94 & 57 \\ \hline
+{\bf 0.6} & {\bf 0.4} & {\bf 94} & {\bf 57} \\ \hline
 0.7 & 0.3 & 97 & 49 \\ \hline
 0.8 & 0.2 & 90 & 52 \\ \hline
 0.9 & 0.1 & 77 & 50 \\ \hline
@@ -860,35 +922,36 @@ $\alpha$ & $\beta$ & $Lifetime_{50}$ & $Lifetime_{95}$ \\ \hline
 \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
+In this paper the problem of perimeter coverage optimization in
+WSNs has been studied.  A new  protocol called  Perimeter-based  Coverage
+Optimization is designed. This protocol 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.  This  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. Several simulations have
+been carried out 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.
+
+This framework will be extented so that the schedules  are planned for multiple
+sensing  periods. The  integer program  would be improved to take  into
+account heterogeneous sensors from both energy and node characteristics point of
+views.  Finally, it would be interesting  to implement the PeCO protocol using a
 sensor-testbed to evaluate it in real world applications.
 
+\subsection*{Acknowledgments}
+The  authors  are   deeply  grateful  to  the  anonymous   reviewers  for  their
+constructive advice,  which improved the  technical quality  of the paper.  As a
+Ph.D.   student, Ali  Kadhum Idrees  would  like to  gratefully acknowledge  the
+University of  Babylon - Iraq  for financial support  and Campus France  for the
+received support. This work is also partially funded by the Labex ACTION program
+(contract ANR-11-LABX-01-01).  
+ 
 \bibliographystyle{gENO}
-\bibliography{articleeo}
-
+\bibliography{biblio} 
 
 \end{document}
