Update by ali

[LiCO.git] / LiCO_Journal.tex

diff --git a/LiCO_Journal.tex b/LiCO_Journal.tex
old mode 100755 (executable)
new mode 100644 (file)
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--- a/LiCO_Journal.tex
+++ b/LiCO_Journal.tex
@@ -36,14 +36,16 @@
 \DeclareGraphicsRule{.ps}{pdf}{.pdf}{`ps2pdf -dEPSCrop -dNOSAFER #1 \noexpand\OutputFile}
 \begin{document}
 
 \DeclareGraphicsRule{.ps}{pdf}{.pdf}{`ps2pdf -dEPSCrop -dNOSAFER #1 \noexpand\OutputFile}
 \begin{document}
 

-\title{Lifetime Coverage Optimization Protocol \\
-  in Wireless Sensor Networks}  %LiCO Protocol 
+%\title{Lifetime Coverage Optimization Protocol \\
+%  in Wireless Sensor Networks}
+\title{Perimeter-based Coverage Optimization to Improve \\
+  Lifetime in Wireless Sensor Networks}

 
 \author{Ali Kadhum Idrees,~\IEEEmembership{}
         Karine Deschinkel,~\IEEEmembership{}
         Michel Salomon,~\IEEEmembership{}
         and~Rapha\"el Couturier ~\IEEEmembership{} 
 
 \author{Ali Kadhum Idrees,~\IEEEmembership{}
         Karine Deschinkel,~\IEEEmembership{}
         Michel Salomon,~\IEEEmembership{}
         and~Rapha\"el Couturier ~\IEEEmembership{} 

-        \thanks{The authors are with FEMTO-ST Institute, UMR 6174 CNRS, University of Franche-Comt\'e,
+        \thanks{The authors are with FEMTO-ST Institute, UMR 6174 CNRS, University of Franche-Comte,

           Belfort, France. Email: ali.idness@edu.univ-fcomte.fr, $\lbrace$karine.deschinkel,
           michel.salomon, raphael.couturier$\rbrace$@univ-fcomte.fr}}
 
           Belfort, France. Email: ali.idness@edu.univ-fcomte.fr, $\lbrace$karine.deschinkel,
           michel.salomon, raphael.couturier$\rbrace$@univ-fcomte.fr}}
 


@@ -53,34 +55,35 @@
 \maketitle
 
 \begin{abstract}
 \maketitle
 
 \begin{abstract}

-The most important problem in Wireless Sensor Networks (WSNs) 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
+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
 improve  power  management,  lifetime coverage  optimization  provides  activity

-scheduling which ensures  sensing coverage while minimizing the  energy cost. In
-this paper,  we propose  a such approach  called Lifetime  Coverage Optimization
-protocol (LiCO).   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. A sensor node which runs LiCO
-protocol  repeats   periodically  four  stages:  information   exchange,  leader
-election, optimization decision, and sensing.  More precisely, the scheduling of
-nodes activities (sleep/wakeup  duty cycles) is achieved in each  subregion by a
-leader selected after  cooperation between nodes within the  same subregion. The
-novelty of  approach lies essentially in  the formulation of a  new mathematical
-optimization  model  based  on  perimeter coverage  level  to  schedule  sensors
-activities.  Extensive simulation experiments have been performed using OMNeT++,
-the  discrete event  simulator, to  demonstrate that  LiCO is  capable to  offer
-longer lifetime coverage for WSNs in comparison with some other protols.
+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.
+% A  sensor node  which runs  LiCO  protocol repeats  periodically four  stages:
+%information  exchange,  leader election,  optimization  decision, and  sensing.
+%More precisely, the scheduling of nodes' activities (sleep/wake up duty cycles)
+%is achieved  in each subregion by  a leader selected  after cooperation between
+%nodes within the same 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.

 \end{abstract} 
 
 % Note that keywords are not normally used for peerreview papers.
 \begin{IEEEkeywords}
 \end{abstract} 
 
 % Note that keywords are not normally used for peerreview papers.
 \begin{IEEEkeywords}

-Wireless Sensor Networks, Area Coverage, Network lifetime, Optimization, Scheduling.
+Wireless Sensor Networks, Area Coverage, Network Lifetime, Optimization, Scheduling.

 \end{IEEEkeywords}
 
 \IEEEpeerreviewmaketitle
 
 \end{IEEEkeywords}
 
 \IEEEpeerreviewmaketitle
 

-\section{\uppercase{Introduction}}
+\section{Introduction}

 \label{sec:introduction}
 
 \noindent The continuous progress in Micro Electro-Mechanical Systems (MEMS) and
 \label{sec:introduction}
 
 \noindent The continuous progress in Micro Electro-Mechanical Systems (MEMS) and


@@ -88,26 +91,26 @@ wireless communication hardware  has given rise to the opportunity  to use large
 networks    of     tiny    sensors,    called    Wireless     Sensor    Networks
 (WSN)~\cite{akyildiz2002wireless,puccinelli2005wireless}, to  fulfill monitoring
 tasks.   A  WSN  consists  of  small low-powered  sensors  working  together  by
 networks    of     tiny    sensors,    called    Wireless     Sensor    Networks
 (WSN)~\cite{akyildiz2002wireless,puccinelli2005wireless}, to  fulfill monitoring
 tasks.   A  WSN  consists  of  small low-powered  sensors  working  together  by

-communicating with one another through  multihop radio communications. Each node
+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,
 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  son~\cite{yick2008wireless}.  Typically,  a sensor  node contains
+military, and so on~\cite{yick2008wireless}.   Typically, a sensor node contains

 three main components~\cite{anastasi2009energy}: a  sensing unit able to measure
 physical,  chemical, or  biological  phenomena observed  in  the environment;  a
 three main components~\cite{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  measurements  which  are
-collected; a radio communication unit for data transmission and receiving.
+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
 
 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 the reliability and to exploit node redundancy
+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
 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?   So,  this  last   years  many
+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~\cite{rault2014energy}.
 
 energy-efficient mechanisms have been suggested  to retain energy and extend the
 lifetime of the WSNs~\cite{rault2014energy}.
 


@@ -117,122 +120,130 @@ lifetime of the WSNs~\cite{rault2014energy}.
 
 %\uppercase{\textbf{Our contributions.}}
 
 
 %\uppercase{\textbf{Our contributions.}}
 

-% MICHEL - TO CONTINUED FROM HERE

 This paper makes the following contributions.
 \begin{enumerate}
 This paper makes the following contributions.
 \begin{enumerate}

-\item  We  devise a  framework  to  schedules  nodes to  be  activated
-  alternatively, such that  the network lifetime may  be prolonged ans
-  certain coverage  requirement can still  be met.  This  framework is
-  based on the  division of the area of interest  into several smaller
-  subregions;  on  the division  of  timeline  into periods  of  equal
-  length.  One leader is elected for each subregion in an independent,
-  distributed,  and  simultaneous way  by  the  cooperation among  the
-  sensor nodes within  each subregion, and this is  similar to cluster
-  architecture
-\item We  propose 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.  And a  weighted sum  of these
-  deviations is minimized.
-\item We conducted extensive simulation experiments using the discrete
-  event  simulator  OMNeT++,  to  demonstrate the  efficiency  of  our
-  protocol, compared to  two approaches found in  the literature, DESK
-  \cite{ChinhVu} and  GAF \cite{xu2001geography}, and compared  to our
-  previous work using another optimization model for sensor scheduling
-  \cite{Idrees2}.
+\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~\cite{ChinhVu} and  GAF~\cite{xu2001geography}, and also to  our previous
+  work published in~\cite{Idrees2} which is  based on another optimization model
+  for sensor scheduling.

 \end{enumerate}
 
 \end{enumerate}
 

-
-%Two combined integrated energy-efficient techniques have been used by LiCO protocol in order to maximize the lifetime coverage in WSN: the first, by dividing the area of interest into several smaller subregions based on divide-and-conquer method and then one leader elected for each subregion in an independent, distributed, and simultaneous way by the cooperation among the sensor nodes within each subregion, and this similar to cluster architecture;
+%Two combined integrated energy-efficient techniques have been used by PeCO protocol in order to maximize the lifetime coverage in WSN: the first, by dividing the area of interest into several smaller subregions based on divide-and-conquer method and then one leader elected for each subregion in an independent, distributed, and simultaneous way by the cooperation among the sensor nodes within each subregion, and this similar to cluster architecture;

 % the second, activity scheduling based new optimization model has been used to provide the optimal cover set that will take the mission of sensing during current period. This optimization algorithm is based on a perimeter-coverage model so as to optimize the shared perimeter among the sensors in each subregion, and this represents as a energu-efficient control topology mechanism in WSN.
 
 % the second, activity scheduling based new optimization model has been used to provide the optimal cover set that will take the mission of sensing during current period. This optimization algorithm is based on a perimeter-coverage model so as to optimize the shared perimeter among the sensors in each subregion, and this represents as a energu-efficient control topology mechanism in WSN.
 

-
-The remainder of  the paper is organized as follows.  The next section
-reviews  the related  work  in the  field.  Section~\ref{sec:The  LiCO
-  Protocol   Description}   is   devoted    to   the   LiCO   protocol
-Description.  Section~\ref{cp} gives  the  coverage model  formulation
-which   is    used   to   schedule   the    activation   of   sensors.
-Section~\ref{sec:Simulation Results and Analysis} presents simulations
-results. Finally, we give concluding  remarks and some suggestions for
-future works in Section~\ref{sec:Conclusion and Future Works}.
+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}.

 
 % that show that our protocol outperforms others protocols.
 
 % that show that our protocol outperforms others protocols.

-\section{\uppercase{Related Literature}}
+\section{Related Literature}

 \label{sec:Literature Review}
 
 \label{sec:Literature Review}
 

-

 \noindent  In  this section,  we  summarize  some  related works  regarding  the
 \noindent  In  this section,  we  summarize  some  related works  regarding  the

-coverage problem and distinguish our  LiCO protocol from the works presented in
+coverage problem and  distinguish our PeCO protocol from the  works presented in

 the literature.
 
 the literature.
 

-The most discussed coverage problems  in literature can be classified into three
-types \cite{li2013survey}: area coverage \cite{Misra} where every point inside
-an area is to be  monitored, target coverage \cite{yang2014novel} where the main
-objective is  to cover only a  finite number of discrete  points called targets,
-and barrier coverage \cite{HeShibo}\cite{kim2013maximum} to prevent intruders
-from entering into the region  of interest. In \cite{Deng2012} authors transform
-the area coverage problem to the target coverage problem taking into account the
-intersection points among disks of sensors nodes or between disk of sensor nodes
-and boundaries. In \cite{Huang:2003:CPW:941350.941367} authors prove that if the perimeters of sensors are sufficiently covered, the whole area is sufficiently covered and they provide an algorithm in $O(nd~log~d)$ time to compute the perimeter-coverage of each sensor ($d$ the maximum number of sensors that are neighboring to a sensor, $n$ the total number of sensors in the network). {\it In LiCO 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), 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,
+The most  discussed coverage problems in  literature can be classified  in three
+categories~\cite{li2013survey}   according   to  their   respective   monitoring
+objective.  Hence,  area coverage \cite{Misra}  means that every point  inside a
+fixed area  must be monitored, while  target coverage~\cite{yang2014novel} refers
+to  the objective  of coverage  for a  finite number  of discrete  points called
+targets,  and  barrier coverage~\cite{HeShibo}\cite{kim2013maximum}  focuses  on
+preventing  intruders   from  entering   into  the   region  of   interest.   In
+\cite{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
+\cite{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), 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
 \cite{ling2009energy}.  Active node selection is determined based on the problem
 and the set  of active sensor nodes  is decided at the beginning  of each period
 \cite{ling2009energy}.  Active node selection is determined based on the problem

-requirements  (e.g.  area   monitoring,  connectivity,  power  efficiency).  For
-instance,  Jaggi  et al.  \cite{jaggi2006}  address  the  problem of  maximizing
-network lifetime by dividing sensors into the maximum number of disjoint subsets
-such  that each  subset  can ensure  both  coverage and  connectivity. A  greedy
+requirements (e.g.   area monitoring,  connectivity, or power  efficiency).  For
+instance, Jaggi {\em et al.}~\cite{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.   Vu
 algorithm  is applied  once to  solve  this problem  and the  computed sets  are
 activated  in   succession  to  achieve   the  desired  network   lifetime.   Vu

-\cite{chin2007}, Padmatvathy et al. \cite{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,  LiCO 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 approaches, including centralized,  or distributed algorithms, have been
-proposed     to    extend    the     network    lifetime.      In    distributed
-algorithms~\cite{yangnovel,ChinhVu,qu2013distributed},       information      is
-disseminated  throughout  the  network   and  sensors  decide  cooperatively  by
-communicating with their neighbors which of them will remain in sleep mode for a
-certain         period         of         time.          The         centralized
+\cite{chin2007},  Padmatvathy  {\em   et  al.}~\cite{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.   In distributed
+algorithms~\cite{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~\cite{cardei2005improving,zorbas2010solving,pujari2011high}     always
 algorithms~\cite{cardei2005improving,zorbas2010solving,pujari2011high}     always

-provide nearly or close to optimal  solution since the algorithm has global view
-of the whole  network. But such a method has the  disadvantage of requiring high
-communication costs,  since the  node (located at  the base station)  making the
-decision needs information from all the  sensor nodes in the area and the amount
-of  information can  be huge.   {\it  In order  to be  suitable for  large-scale
-  network,  in the LiCO  protocol, the  area of interest is divided  into several
-  smaller subregions, and in each one, a node called the leader is in charge for
-  selecting the active sensors for the current period.}
-
-A large  variety of coverage scheduling  algorithms has been  developed. Many of
-the existing  algorithms, 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
+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

 \cite{berman04,zorbas2010solving}.  Other  approaches are based  on mathematical
 programming formulations~\cite{cardei2005energy,5714480,pujari2011high,Yang2014}
 \cite{berman04,zorbas2010solving}.  Other  approaches are based  on mathematical
 programming formulations~\cite{cardei2005energy,5714480,pujari2011high,Yang2014}

-and dedicated  techniques (solving with a  branch-and-bound algorithms available
-in optimization solver).   The problem is formulated as  an optimization problem
+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
 (maximization of the lifetime or number of cover sets) under target coverage and

-energy  constraints.   Column   generation  techniques,  well-known  and  widely
+energy  constraints.   Column  generation   techniques,  well-known  and  widely

 practiced techniques for  solving linear programs with too  many variables, have
 also                                                                        been
 practiced techniques for  solving linear programs with too  many variables, have
 also                                                                        been

-used~\cite{castano2013column,rossi2012exact,deschinkel2012column}. {\it In LiCO
-  protocol, each  leader, in  each subregion, solves  an integer program  with 
-the double objective  consisting in minimizing  the overcoverage and the
-  undercoverage of the perimeter of each sensor.  
-
-}
-
+used~\cite{castano2013column,rossi2012exact,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.}

 
 %\noindent Recently, the coverage problem has been received a high attention, which concentrates on how the physical space could be well monitored  after the deployment. Coverage is one of the Quality of Service (QoS) parameters in WSNs, which is highly concerned with power depletion~\cite{zhu2012survey}. Most of the works about the coverage protocols have been suggested in the literature focused on three types of the coverage in WSNs~\cite{mulligan2010coverage}: the first, area coverage means that each point in the area of interest within the sensing range of at least one sensor node; the second, target coverage in which a fixed set of targets need to be monitored; the third, barrier coverage refers to detect the intruders crossing a boundary of WSN. The work in this paper emphasized on the area coverage, so,  some area coverage protocols have been reviewed in this section, and the shortcomings of reviewed approaches are being summarized.
 
 
 %\noindent Recently, the coverage problem has been received a high attention, which concentrates on how the physical space could be well monitored  after the deployment. Coverage is one of the Quality of Service (QoS) parameters in WSNs, which is highly concerned with power depletion~\cite{zhu2012survey}. Most of the works about the coverage protocols have been suggested in the literature focused on three types of the coverage in WSNs~\cite{mulligan2010coverage}: the first, area coverage means that each point in the area of interest within the sensing range of at least one sensor node; the second, target coverage in which a fixed set of targets need to be monitored; the third, barrier coverage refers to detect the intruders crossing a boundary of WSN. The work in this paper emphasized on the area coverage, so,  some area coverage protocols have been reviewed in this section, and the shortcomings of reviewed approaches are being summarized.
 


@@ -270,55 +281,107 @@ the double objective  consisting in minimizing  the overcoverage and the
 
 %\uppercase{\textbf{shortcomings}}. In spite of many energy-efficient protocols for maintaining the coverage and improving the network lifetime in WSNs were proposed, non of them ensure the coverage for the sensing field with optimal minimum number of active sensor nodes, and for a long time as possible. For example, in a full centralized algorithms, an optimal solutions can be given by using optimization approaches, but in the same time, a high energy is consumed for the execution time of the algorithm and the communications among the sensors in the sensing field, so, the  full centralized approaches are not good candidate to use it especially in large WSNs. Whilst, a full distributed algorithms can not give optimal solutions because this algorithms use only local information of the neighboring sensors, but in the same time, the energy consumption during the communications and executing the algorithm is highly lower. Whatever the case, this would result in a shorter lifetime coverage in WSNs.
 
 
 %\uppercase{\textbf{shortcomings}}. In spite of many energy-efficient protocols for maintaining the coverage and improving the network lifetime in WSNs were proposed, non of them ensure the coverage for the sensing field with optimal minimum number of active sensor nodes, and for a long time as possible. For example, in a full centralized algorithms, an optimal solutions can be given by using optimization approaches, but in the same time, a high energy is consumed for the execution time of the algorithm and the communications among the sensors in the sensing field, so, the  full centralized approaches are not good candidate to use it especially in large WSNs. Whilst, a full distributed algorithms can not give optimal solutions because this algorithms use only local information of the neighboring sensors, but in the same time, the energy consumption during the communications and executing the algorithm is highly lower. Whatever the case, this would result in a shorter lifetime coverage in WSNs.
 

-%\uppercase{\textbf{Our Protocol}}. In this paper, a Lifetime Coverage Optimization Protocol, called (LiCO) in WSNs is suggested. The sensing field is divided into smaller subregions by means of divide-and-conquer method, and a LiCO protocol is distributed in each sensor in the subregion. The network lifetime in each subregion is divided into periods, each period includes 4 stages: Information Exchange, Leader election, decision based activity scheduling optimization, and sensing. The leaders are elected in an independent, asynchronous, and distributed way in all the subregions of the WSN. After that, energy-efficient activity scheduling mechanism based new optimization model is performed by each leader in the subregions. This optimization model is based on the perimeter coverage model in order to producing the optimal cover set of active sensors, which are taken the responsibility of sensing during the current period. LiCO protocol merges between two energy efficient mechanisms, which are used the main advantages of the centralized and distributed approaches and avoids the most of their disadvantages.
+%\uppercase{\textbf{Our Protocol}}. In this paper, a Lifetime Coverage Optimization Protocol, called (PeCO) in WSNs is suggested. The sensing field is divided into smaller subregions by means of divide-and-conquer method, and a PeCO protocol is distributed in each sensor in the subregion. The network lifetime in each subregion is divided into periods, each period includes 4 stages: Information Exchange, Leader election, decision based activity scheduling optimization, and sensing. The leaders are elected in an independent, asynchronous, and distributed way in all the subregions of the WSN. After that, energy-efficient activity scheduling mechanism based new optimization model is performed by each leader in the subregions. This optimization model is based on the perimeter coverage model in order to producing the optimal cover set of active sensors, which are taken the responsibility of sensing during the current period. PeCO protocol merges between two energy efficient mechanisms, which are used the main advantages of the centralized and distributed approaches and avoids the most of their disadvantages.
+
+\section{ The PeCO 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.

 
 

-\section{ The LiCO Protocol Description}
-\label{sec:The LiCO Protocol Description}
-\noindent In this section, we describe our Lifetime Coverage Optimization Protocol which is called LiCO in more detail.

 % It is based on two efficient-energy mechanisms: the first, is partitioning the sensing field into smaller subregions, and one leader is elected for each subregion;  the second, a sensor activity scheduling based new optimization model so as to produce the optimal cover set of active sensors for the sensing stage during the period.  Obviously, these two mechanisms can be contribute in extend the network lifetime coverage efficiently. 
 %Before proceeding in the presentation of the main ideas of the protocol, we will briefly describe the perimeter coverage model and give some necessary assumptions and definitions.
 
 % It is based on two efficient-energy mechanisms: the first, is partitioning the sensing field into smaller subregions, and one leader is elected for each subregion;  the second, a sensor activity scheduling based new optimization model so as to produce the optimal cover set of active sensors for the sensing stage during the period.  Obviously, these two mechanisms can be contribute in extend the network lifetime coverage efficiently. 
 %Before proceeding in the presentation of the main ideas of the protocol, we will briefly describe the perimeter coverage model and give some necessary assumptions and definitions.
 

-\subsection{ Assumptions and Models}
-\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 interested area. We assume that all the sensor nodes are homogeneous in terms of  communication, sensing, and processing capabilities and heterogeneous in term of energy supply. The  location  information is available to the  sensor node  either through hardware such as embedded GPS or through 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. Each sensor has a constant sensing range $R_s$. All space points within a disk centered at the sensor with the radius of the sensing range is said to be covered by this sensor. We also assume that the communication range $R_c \geq 2R_s$. In  fact,   Zhang  and Zhou~\cite{Zhang05} proved that if the transmission range fulfills the previous hypothesis, a complete coverage of a convex area implies connectivity among the working nodes in the active mode.
-
-\indent LiCO protocol uses the perimeter-coverage model which states in ~\cite{huang2005coverage} as following: The sensor is said to be perimeter covered if all the points on its perimeter are covered by at least one sensor other than itself. Huang and Tseng in \cite{huang2005coverage} proves that a network area is $k$-covered if and only if each sensor in the network is $k$-perimeter-covered.
+\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,  Zhang and Zhou~\cite{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  Huang and
+Tseng in~\cite{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).

 %According to this model, we named the intersections among the sensor nodes in the sensing field as intersection points. Instead of working with the coverage area, we consider for each sensor a set of intersection points which are determined by using perimeter-coverage model. 
 %According to this model, we named the intersections among the sensor nodes in the sensing field as intersection points. Instead of working with the coverage area, we consider for each sensor a set of intersection points which are determined by using perimeter-coverage model. 

-Figure~\ref{pcmfig} illuminates the perimeter coverage of the sensor node $0$. On this figure, sensor $0$ has $9$ neighbors. We report for each sensor $i$ having an intersection with sensor $0$, the two intersection points,  $iL$ for left point and $iR$ for right point. These intersections points subdivide the perimeter of the sensor $0$ (the perimeter of the disk covered by the sensor)  into portions called segments.
+Figure~\ref{pcm2sensors}(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!]
 
 \begin{figure}[ht!]

-\centering
-\includegraphics[width=75mm]{pcm.jpg}  
-\caption{Perimeter coverage of sensor node 0}
-\label{pcmfig}
+  \centering
+  \begin{tabular}{@{}cr@{}}
+    \includegraphics[width=75mm]{pcm.jpg} & \raisebox{3.25cm}{(a)} \\
+    \includegraphics[width=75mm]{twosensors.jpg} & \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{pcm2sensors}

 \end{figure} 
 
 \end{figure} 
 

-Figure~\ref{twosensors} demonstrates the way of locating the left and right points of a segment for a sensor node $u$ covered by a sensor node $v$. This figure assumes that the neighbor sensor node $v$ is located on the west of a sensor $u$. It is assumed  that the two sensor nodes $v$ and $u$ are located in the positions $(v_x,v_y)$ and $(u_x,u_y)$, respectively. The distance between $v$ and $u$ is computed by $Dist(u,v) = \sqrt{\vert u_x - v_x \vert^2 + \vert u_y - v_y \vert^2}$. The angle $\alpha$ is computed through the formula $\alpha = arccos \left(\dfrac{Dist(u,v)}{2R_s} \right)$. So, the arch of sensor $u$ falling in the angle $[\pi - \alpha,\pi + \alpha]$, is said to be perimeter-covered by sensor node $v$. 
-
-The left and right points of each segment are placed on the line segment $[0,2\pi]$. Figure~\ref{pcmfig} illustrates the segments for the 9 neighbors of sensor $0$. The points reported on the line segment $[0,2\pi]$ separates it in intervals as shown in figure~\ref{expcm}. For example, for each neighboring sensor of sensor 0, place the points  $\alpha^ 1_L$, $\alpha^ 1_R$, $\alpha^ 2_L$, $\alpha^ 2_R$, $\alpha^ 3_L$, $\alpha^ 3_R$, $\alpha^ 4_L$, $\alpha^ 4_R$, $\alpha^ 5_L$, $\alpha^ 5_R$, $\alpha^ 6_L$, $\alpha^ 6_R$, $\alpha^ 7_L$, $\alpha^ 7_R$, $\alpha^ 8_L$, $\alpha^ 8_R$, $\alpha^ 9_L$, and $\alpha^ 9_R$; on the line segment $[0,2\pi]$, and then sort all these points in an ascending order into a list.  Traverse the line segment $[0,2\pi]$ by visiting each point in the sorted list from left to right and determine the coverage level of each interval of the sensor 0 (see figure \ref{expcm}). For each interval, we sum up the number of parts of segments, and we deduce a level of coverage for each interval. For instance, the interval delimited by the points $5L$ and $6L$ contains three parts of segments. That means that this part of the perimeter of the sensor $0$ may be covered by three sensors, sensor $0$ itself and sensors $2$ and $5$. The level of coverage of this interval may reach $3$ if all previously mentioned sensors are active. Let say that sensors $0$, $2$ and $5$ are involved in the coverage of this interval. Table~\ref{my-label} summarizes the level of coverage for each interval and the sensors involved in for sensor node 0 in figure~\ref{pcmfig}. 
+Figure~\ref{pcm2sensors}(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: $$\alpha =  \arccos \left(\dfrac{Dist(u,v)}{2R_s}
+\right).$$ 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{pcm2sensors}(a)  illustrates  the arcs  for  the  nine neighbors  of
+sensor $0$ and  Figure~\ref{expcm} 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{expcm}), 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.
+
+%The points reported on the line segment $[0,2\pi]$ separates it in intervals as shown in figure~\ref{expcm}. For example, for each neighboring sensor of sensor 0, place the points  $\alpha^ 1_L$, $\alpha^ 1_R$, $\alpha^ 2_L$, $\alpha^ 2_R$, $\alpha^ 3_L$, $\alpha^ 3_R$, $\alpha^ 4_L$, $\alpha^ 4_R$, $\alpha^ 5_L$, $\alpha^ 5_R$, $\alpha^ 6_L$, $\alpha^ 6_R$, $\alpha^ 7_L$, $\alpha^ 7_R$, $\alpha^ 8_L$, $\alpha^ 8_R$, $\alpha^ 9_L$, and $\alpha^ 9_R$; on the line segment $[0,2\pi]$, and then sort all these points in an ascending order into a list.  Traverse the line segment $[0,2\pi]$ by visiting each point in the sorted list from left to right and determine the coverage level of each interval of the sensor 0 (see figure \ref{expcm}). For each interval, we sum up the number of parts of segments, and we deduce a level of coverage for each interval. For instance, the interval delimited by the points $5L$ and $6L$ contains three parts of segments. That means that this part of the perimeter of the sensor $0$ may be covered by three sensors, sensor $0$ itself and sensors $2$ and $5$. The level of coverage of this interval may reach $3$ if all previously mentioned sensors are active. Let say that sensors $0$, $2$ and $5$ are involved in the coverage of this interval. Table~\ref{my-label} summarizes the level of coverage for each interval and the sensors involved in for sensor node 0 in figure~\ref{pcm2sensors}(a). 

 % to determine the level of the perimeter coverage for each left and right point of a segment.
 % to determine the level of the perimeter coverage for each left and right point of a segment.

-\begin{figure}[ht!]
-\centering
-\includegraphics[width=75mm]{twosensors.jpg}  
-\caption{Locating the segment of $u$$\rq$s perimeter covered by $v$.}
-\label{twosensors}
-\end{figure} 

 
 

-
-\begin{figure}[ht!]
+\begin{figure*}[t!]

 \centering
 \centering

-\includegraphics[width=75mm]{expcm.pdf}  
-\caption{ Coverage levels for sensor node $0$.}
+\includegraphics[width=127.5mm]{expcm2.jpg}  
+\caption{Maximum coverage levels for perimeter of sensor node $0$.}

 \label{expcm}
 \label{expcm}

-\end{figure} 
-
-
-
-
-
-
-
-
+\end{figure*} 

 
 %For example, consider the sensor node $0$ in figure~\ref{pcmfig}, which has 9 neighbors. Figure~\ref{expcm} shows the perimeter coverage level for all left and right points of a segment that covered by a neighboring sensor nodes. Based on the figure~\ref{expcm}, the set of sensors for each left and right point of the segments illustrated in figure~\ref{ex2pcm} for the sensor node 0.
 
 
 %For example, consider the sensor node $0$ in figure~\ref{pcmfig}, which has 9 neighbors. Figure~\ref{expcm} shows the perimeter coverage level for all left and right points of a segment that covered by a neighboring sensor nodes. Based on the figure~\ref{expcm}, the set of sensors for each left and right point of the segments illustrated in figure~\ref{ex2pcm} for the sensor node 0.
 


@@ -333,44 +396,49 @@ The left and right points of each segment are placed on the line segment $[0,2\p
 
 \fi
 
 
 \fi
 

- \begin{table}[h]
+ \begin{table}[h!]

  \caption{Coverage intervals and contributing sensors for sensor node 0.}
 \begin{tabular}{|c|c|c|c|c|c|c|c|c|}
 \hline
  \caption{Coverage intervals and contributing sensors for sensor node 0.}
 \begin{tabular}{|c|c|c|c|c|c|c|c|c|}
 \hline

-\begin{tabular}[c]{@{}c@{}}The angle \\ $\alpha$ \end{tabular} & \begin{tabular}[c]{@{}c@{}}Segment \\ Left (L) or\\  Right (R)\end{tabular} & \begin{tabular}[c]{@{}c@{}}Sensor \\ Node Id\end{tabular} & \begin{tabular}[c]{@{}c@{}}Interval \\ Coverage\\  Level\end{tabular} & \multicolumn{5}{c|}{\begin{tabular}[c]{@{}c@{}}The Set of Sensors\\ Involved in Interval \\ Coverage\end{tabular}} \\ \hline
-0.0291    & L                                                                         & 1                                                         & 4                                                                     & 0                     & 1                     & 3                    & 4                    &                      \\ \hline
-0.104     & L                                                                         & 2                                                         & 5                                                                     & 0                     & 1                     & 3                    & 4                    & 2                    \\ \hline
-0.3168    & R                                                                         & 3                                                         & 4                                                                     & 0                     & 1                     & 4                    & 2                    &                      \\ \hline
-0.6752    & R                                                                         & 4                                                         & 3                                                                     & 0                     & 1                     & 2                    &                      &                      \\ \hline
-1.8127    & R                                                                         & 1                                                         & 2                                                                     & 0                     & 2                     &                      &                      &                      \\ \hline
-1.9228    & L                                                                         & 5                                                         & 3                                                                     & 0                     & 2                     & 5                    &                      &                      \\ \hline
-2.3959    & L                                                                         & 6                                                         & 4                                                                     & 0                     & 2                     & 5                    & 6                    &                      \\ \hline
-2.4258    & R                                                                         & 2                                                         & 3                                                                     & 0                     & 5                     & 6                    &                      &                      \\ \hline
-2.7868    & L                                                                         & 7                                                         & 4                                                                     & 0                     & 5                     & 6                    & 7                    &                      \\ \hline
-2.8358    & L                                                                         & 8                                                         & 5                                                                     & 0                     & 5                     & 6                    & 7                    & 8                    \\ \hline
-2.9184    & R                                                                         & 5                                                         & 4                                                                     & 0                     & 6                     & 7                    & 8                    &                      \\ \hline
-3.3301    & R                                                                         & 7                                                         & 3                                                                     & 0                     & 6                     & 8                    &                      &                      \\ \hline
-3.9464    & L                                                                         & 9                                                         & 4                                                                     & 0                     & 6                     & 8                    & 9                    &                      \\ \hline
-4.767     & R                                                                         & 6                                                         & 3                                                                     & 0                     & 8                     & 9                    &                      &                      \\ \hline
-4.8425    & L                                                                         & 3                                                         & 4                                                                     & 0                     & 3                     & 8                    & 9                    &                      \\ \hline
-4.9072    & R                                                                         & 8                                                         & 3                                                                     & 0                     & 3                     & 9                    &                      &                      \\ \hline
-5.3804    & L                                                                         & 4                                                         & 4                                                                     & 0                     & 3                     & 4                    & 9                    &                      \\ \hline
-5.9157    & R                                                                         & 9                                                         & 3                                                                     & 0                     & 3                     & 4                    &                      &                      \\ \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}
 
 \label{my-label}
 \end{table}
 
 
 \end{tabular}
 
 \label{my-label}
 \end{table}
 
 

-%The optimization algorithm that used by LiCO protocol based on the perimeter coverage levels of the left and right points of the segments and worked to minimize the number of sensor nodes for each left or right point of the segments within each sensor node. The algorithm minimize the perimeter coverage level of the left and right points of the segments, while, it assures that every perimeter coverage level of the left and right points of the segments greater than or equal to 1.
+%The optimization algorithm that used by PeCO protocol based on the perimeter coverage levels of the left and right points of the segments and worked to minimize the number of sensor nodes for each left or right point of the segments within each sensor node. The algorithm minimize the perimeter coverage level of the left and right points of the segments, while, it assures that every perimeter coverage level of the left and right points of the segments greater than or equal to 1.

 
 

-In LiCO protocol, scheduling of sensor nodes'activities is formulated with an integer program based on coverage intervals and is detailed in section~\ref{cp}.
-
-In the case of sensor node, which has a part of its sensing range outside the border of the WSN sensing field as in figure~\ref{ex4pcm}, the coverage level for this segment is set to $\infty$, and the corresponding interval will not be taken into account by the optimization algorithm.
-\begin{figure}[ht!]
+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{ex4pcm}, 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.
+ 
+\begin{figure}[h!]

 \centering
 \centering

-\includegraphics[width=75mm]{ex4pcm.jpg}  
-\caption{Part of sensing range outside the the border of WSN sensing field.}
+\includegraphics[width=62.5mm]{ex4pcm.jpg}  
+\caption{Sensing range outside the WSN's area of interest.}

 \label{ex4pcm}
 \end{figure} 
 %Figure~\ref{ex5pcm} gives an example to compute the perimeter coverage levels for the left and right points of the segments for a sensor node $0$, which has a part of its sensing range exceeding the border of the sensing field of WSN, and it has a six neighbors. In figure~\ref{ex5pcm}, the sensor node $0$ has two segments outside the border of the network sensing field, so the left and right points of the two segments called $-1L$, $-1R$, $-2L$, and $-2R$.
 \label{ex4pcm}
 \end{figure} 
 %Figure~\ref{ex5pcm} gives an example to compute the perimeter coverage levels for the left and right points of the segments for a sensor node $0$, which has a part of its sensing range exceeding the border of the sensing field of WSN, and it has a six neighbors. In figure~\ref{ex5pcm}, the sensor node $0$ has two segments outside the border of the network sensing field, so the left and right points of the two segments called $-1L$, $-1R$, $-2L$, and $-2R$.


@@ -381,42 +449,67 @@ In the case of sensor node, which has a part of its sensing range outside the bo
 %\label{ex5pcm}
 %\end{figure} 
 
 %\label{ex5pcm}
 %\end{figure} 
 

-

 \subsection{The Main Idea}
 \subsection{The Main Idea}

-\noindent The area  of  interest can  be  divided into smaller areas called subregions and
-then our protocol will be implemented in each subregion simultaneously. LiCO protocol works into periods fashion as shown in figure~\ref{fig2}.
-\begin{figure}[ht!]
+
+\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{fig2}, 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
 \centering

-\includegraphics[width=85mm]{Model.pdf}  
-\caption{LiCO protocol}
+\includegraphics[width=80mm]{Model.pdf}  
+\caption{PeCO protocol.}

 \label{fig2}
 \end{figure} 
 
 \label{fig2}
 \end{figure} 
 

-Each period is divided into 4 stages: Information (INFO) Exchange, Leader  Election, Optimization Decision,  and  Sensing.  For  each  period there  is exactly one set cover responsible for the sensing task. LiCO is more powerful against an unexpected node failure because it works in periods. On the one hand, if the node failure is discovered before taking the decision of the optimization algorithm, the sensor node would not involved to current stage, and, on the other hand, if the sensor failure takes place 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 for  some sensor nodes,  even when they do not join the network to monitor the area. 
-
-We define two types of packets to be used by LiCO protocol.
+We define two types of packets to be used by PeCO protocol:

 %\begin{enumerate}[(a)]
 \begin{itemize} 
 %\begin{enumerate}[(a)]
 \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 inform them to be Active or Sleep during the sensing phase.
+\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}
 %\end{enumerate}
 
 \end{itemize}
 %\end{enumerate}
 

-There are five status for each sensor node in the network :
+Five status are possible for a sensor node in the network:

 %\begin{enumerate}[(a)] 
 \begin{itemize} 
 %\begin{enumerate}[(a)] 
 \begin{itemize} 

-\item LISTENING: Sensor is waiting for a decision (to be active or not)
-\item COMPUTATION: Sensor applies the optimization process as leader
-\item ACTIVE: Sensor is active
-\item SLEEP: Sensor is turned off
-\item COMMUNICATION: Sensor is transmitting or receiving packet
+\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}
 %\end{enumerate}
 %Below, we describe each phase in more details.
 
 \end{itemize}
 %\end{enumerate}
 %Below, we describe each phase in more details.
 

-\subsection{LiCO Protocol Algorithm}
-The pseudo-code for LiCO Protocol is illustrated as follows:
+\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}[h!]                
  % \KwIn{all the parameters related to information exchange}
 
 \begin{algorithm}[h!]                
  % \KwIn{all the parameters related to information exchange}


@@ -426,8 +519,8 @@ The pseudo-code for LiCO Protocol is illustrated as follows:
   
   \If{ $RE_k \geq E_{th}$ }{
       \emph{$s_k.status$ = COMMUNICATION}\;
   
   \If{ $RE_k \geq E_{th}$ }{
       \emph{$s_k.status$ = COMMUNICATION}\;

-      \emph{Send $INFO()$ packet to other nodes in the subregion}\;
-      \emph{Wait $INFO()$ packet from other nodes in the subregion}\; 
+      \emph{Send $INFO()$ packet to other nodes in subregion}\;
+      \emph{Wait $INFO()$ packet from other nodes in subregion}\; 

       \emph{Update K.CurrentSize}\;
       \emph{LeaderID = Leader election}\;
       \If{$ s_k.ID = LeaderID $}{
       \emph{Update K.CurrentSize}\;
       \emph{LeaderID = Leader election}\;
       \If{$ s_k.ID = LeaderID $}{


@@ -438,18 +531,18 @@ The pseudo-code for LiCO Protocol is illustrated as follows:
          % \emph{ Determine the segment points using perimeter coverage model}\;
       }
       
          % \emph{ Determine the segment points using perimeter coverage model}\;
       }
       

-      \If{$ (s_k.ID $ is the same Previous Leader) AND (K.CurrentSize = K.PreviousSize)}{
+      \If{$ (s_k.ID $ is the same Previous Leader) And (K.CurrentSize = K.PreviousSize)}{

       
         \emph{ Use the same previous cover set for current sensing stage}\;
       }
       \Else{
       
         \emph{ Use the same previous cover set for current sensing stage}\;
       }
       \Else{

-            \emph{ Update $a^j_{ik}$ and prepare data to Algorithm}\;
+            \emph{Update $a^j_{ik}$; prepare data for IP~Algorithm}\;

             \emph{$\left\{\left(X_{1},\dots,X_{l},\dots,X_{K}\right)\right\}$ = Execute Integer Program Algorithm($K$)}\;
             \emph{K.PreviousSize = K.CurrentSize}\;
            }
       
         \emph{$s_k.status$ = COMMUNICATION}\;
             \emph{$\left\{\left(X_{1},\dots,X_{l},\dots,X_{K}\right)\right\}$ = Execute Integer Program Algorithm($K$)}\;
             \emph{K.PreviousSize = K.CurrentSize}\;
            }
       
         \emph{$s_k.status$ = COMMUNICATION}\;

-        \emph{Send $ActiveSleep()$ to each node $l$ in subregion} \;
+        \emph{Send $ActiveSleep()$ to each node $l$ in subregion}\;

         \emph{Update $RE_k $}\;
       }          
       \Else{
         \emph{Update $RE_k $}\;
       }          
       \Else{


@@ -459,50 +552,80 @@ The pseudo-code for LiCO Protocol is illustrated as follows:
       }  
   }
   \Else { Exclude $s_k$ from entering in the current sensing stage}
       }  
   }
   \Else { Exclude $s_k$ from entering in the current sensing stage}

-  
- 
-\caption{LiCO($s_k$)}
-\label{alg:LiCO}
-
+\caption{PeCO($s_k$)}
+\label{alg:PeCO}

 \end{algorithm}
 
 \end{algorithm}
 

-\noindent Algorithm 1 gives a brief description of the protocol applied by each sensor node (denoted by $s_k$ for a sensor node indexed by $k$). In this algorithm, the K.CurrentSize and K.PreviousSize refer to the current size and the previous size of sensor nodes still alive in the subregion respectively.
-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 based Embedded GPS  or Location Discovery Algorithm. After that, all the sensors collect position coordinates, remaining energy, sensor node id, and the number of its 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 number of neighbors,  larger remaining  energy, and  then in  case of equality, larger index. Thereafter the leader collects information to formulate and solve the integer program which allows to construct the set of active sensors in the sensing stage.  
-
-
-%After the cooperation among the sensor nodes in the same subregion, the leader will be elected in distributed way, where each sensor node and based on it's information decide who is the leader. The selection criteria for the leader in order  of priority  are: larger number of neighbors,  larger remaining  energy, and  then in  case of equality, larger index. Thereafter,  if the sensor node is leader, it will execute the perimeter-coverage model for each sensor in the subregion in order to determine the segment points which would be used in the next stage by the optimization algorithm of the LiCO protocol. Every sensor node is selected as a leader, it is executed the perimeter coverage model only one time during it's life in the network.
+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.
+
+%After the cooperation among the sensor nodes in the same subregion, the leader will be elected in distributed way, where each sensor node and based on it's information decide who is the leader. The selection criteria for the leader in order  of priority  are: larger number of neighbors,  larger remaining  energy, and  then in  case of equality, larger index. Thereafter,  if the sensor node is leader, it will execute the perimeter-coverage model for each sensor in the subregion in order to determine the segment points which would be used in the next stage by the optimization algorithm of the PeCO protocol. Every sensor node is selected as a leader, it is executed the perimeter coverage model only one time during it's life in the network.

 
 % The leader has the responsibility of applying the integer program algorithm (see section~\ref{cp}), which provides a set of sensors planned to be active in the sensing stage.  As leader, it will send an Active-Sleep packet to each sensor in the same subregion to inform it if it has to be active or not. On the contrary, if the sensor is not the leader, it will wait for the Active-Sleep packet to know its state for the sensing stage.
 
 
 % The leader has the responsibility of applying the integer program algorithm (see section~\ref{cp}), which provides a set of sensors planned to be active in the sensing stage.  As leader, it will send an Active-Sleep packet to each sensor in the same subregion to inform it if it has to be active or not. On the contrary, if the sensor is not the leader, it will wait for the Active-Sleep packet to know its state for the sensing stage.
 

-
-\section{Lifetime Coverage problem formulation}
+\section{Perimeter-based Coverage Problem Formulation}

 \label{cp}
 \label{cp}

-In this section, the coverage model is mathematically formulated.
-For convenience, the notations are described first. 
-%Then the lifetime problem of sensor network is formulated. 
-\noindent $S :$ the set of all sensors in the network.\\
-\noindent $A :$ the set of alive sensors within $S$.\\
-%\noindent $I :$ the set of segment points.\\
-\noindent $I_j :$ the set of coverage intervals (CI)  for sensor $j$.\\
-\noindent $I_j$ refers to the set of intervals which have been defined for each sensor $j$ in section~\ref{sec:The LiCO Protocol Description}.
-\noindent For a coverage interval  $i$,  let  $a^j_{ik}$ denote the indicator function of whether the sensor $k$ is involved in the coverage interval $i$ of sensor $j$, that is:

 
 

+\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}
 \begin{equation}
 a^j_{ik} = \left \{ 
 \begin{array}{lll}

-  1 & \mbox{if the sensor $k$ is involved in the } \\
+  1 & \mbox{if sensor $k$ is involved in the } \\

        &       \mbox{coverage interval $i$ of sensor $j$}, \\
        &       \mbox{coverage interval $i$ of sensor $j$}, \\

-  0 & \mbox{Otherwise.}\\
+  0 & \mbox{otherwise.}\\

 \end{array} \right.
 %\label{eq12} 
 \notag
 \end{equation}
 \end{array} \right.
 %\label{eq12} 
 \notag
 \end{equation}

-Note that $a^k_{ik}=1$ by definition of the interval.\\
+Note that $a^k_{ik}=1$ by definition of the interval.

 %, where the objective is to find the maximum number of non-disjoint sets of sensor nodes such that each set cover can assure the coverage for the whole region so as to extend the network lifetime in WSN. Our model uses the PCL~\cite{huang2005coverage} in order to optimize the lifetime coverage in each subregion.
 %, where the objective is to find the maximum number of non-disjoint sets of sensor nodes such that each set cover can assure the coverage for the whole region so as to extend the network lifetime in WSN. Our model uses the PCL~\cite{huang2005coverage} in order to optimize the lifetime coverage in each subregion.

-%We defined some parameters, which are related to our optimization model. In our model,  we  consider binary variables $X_{k}$, which determine the activation of sensor $k$ in the sensing round $k$. .   
-\noindent We  consider binary variables $X_{k}$ ($X_k=1$ if the sensor $k$ is active or 0 otherwise), which determine the activation of sensor $k$ in the sensing phase. We define the integer variable $M^j_i$ which measures the undercoverage for the coverage interval $i$ for sensor $j$. In the same way, we define the integer variable $V^j_i$, which measures the overcoverage for the coverage interval $i$ for sensor $j$. If we decide to sustain a level of coverage equal to $l$ all along the perimeter of the sensor $j$, we have to ensure that at least $l$ sensors involved in each coverage interval $i$ ($i \in I_j$) 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 $\sum_{k \in K} a^j_{ik} X_k$. To extend the network lifetime, the objective is to active 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 satisfy the level of coverage for all covergae intervals. We uses 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 of active sensors. 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 can not be completely  satisfied, to reach a coverage level as close as possible that the desired one.
-
-
+%We defined some parameters, which are related to our optimization model. In our model,  we  consider binary variables $X_{k}$, which determine the activation of sensor $k$ in the sensing round $k$. .
+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.

 
 %A system of linear constraints is imposed to attempt to keep the coverage level in each coverage interval to within specified PCL. Since it is physically impossible to satisfy all constraints simultaneously, each constraint uses a variable to either record when the coverage level is achieved, or to record the deviation from the desired coverage level. These additional variables are embedded into an objective function to be minimized. 
 
 
 %A system of linear constraints is imposed to attempt to keep the coverage level in each coverage interval to within specified PCL. Since it is physically impossible to satisfy all constraints simultaneously, each constraint uses a variable to either record when the coverage level is achieved, or to record the deviation from the desired coverage level. These additional variables are embedded into an objective function to be minimized. 
 


@@ -524,14 +647,9 @@ Note that $a^k_{ik}=1$ by definition of the interval.\\
 
 %\noindent $V^j_i (overcoverage): $ integer value $\in  \mathbb{N}$ for segment point $i$ of sensor $j$.
 
 
 %\noindent $V^j_i (overcoverage): $ integer value $\in  \mathbb{N}$ for segment point $i$ of sensor $j$.
 

-
-
-
-
-\noindent Our coverage optimization problem can be mathematically formulated as follows: \\
+Our coverage optimization problem can then be mathematically expressed as follows: 

 %Objective:
 %Objective:

-
-\begin{equation} \label{eq:ip2r}
+\begin{equation} %\label{eq:ip2r}

 \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 )&\\
 \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 )&\\


@@ -545,27 +663,35 @@ Note that $a^k_{ik}=1$ by definition of the interval.\\
 X_{k} \in \{0,1\}, \forall k \in A
 \end{array}
 \right.
 X_{k} \in \{0,1\}, \forall k \in A
 \end{array}
 \right.

+\notag

 \end{equation}
 \end{equation}

-
-
-\noindent $\alpha^j_i$ 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 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 \cite{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{\uppercase{PERFORMANCE EVALUATION AND ANALYSIS}}  
+$\alpha^j_i$ 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
+\cite{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}
 %\noindent \subsection{Simulation Framework}
 
 \subsection{Simulation Settings}
 %\label{sub1}
 \label{sec:Simulation Results and Analysis}
 %\noindent \subsection{Simulation Framework}
 
 \subsection{Simulation Settings}
 %\label{sub1}

-In this section, we focus on the performance of LiCO protocol, which is distributed in each sensor node in the sixteen subregions of WSN. We use the same energy consumption model which is used in~\cite{Idrees2}. Table~\ref{table3} gives the chosen parameters setting.
+
+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~\cite{Idrees2}.
+Table~\ref{table3} gives the chosen parameters settings.

 
 \begin{table}[ht]
 
 \begin{table}[ht]

-\caption{Relevant parameters for network initializing.}
+\caption{Relevant parameters for network initialization.}

 % title of Table
 \centering
 % used for centering table
 % title of Table
 \centering
 % used for centering table


@@ -576,14 +702,14 @@ Parameter & Value  \\ [0.5ex]
    
 \hline
 % inserts single horizontal line
    
 \hline
 % inserts single horizontal line

-Sensing  Field  & $(50 \times 25)~m^2 $   \\
+Sensing field & $(50 \times 25)~m^2 $   \\

 
 

-Nodes Number &  100, 150, 200, 250 and 300~nodes   \\
+WSN size &  100, 150, 200, 250, and 300~nodes   \\

 %\hline
 %\hline

-Initial Energy  & 500-700~joules  \\  
+Initial energy  & in range 500-700~Joules  \\  

 %\hline
 %\hline

-Sensing Period & 60 Minutes \\
-$E_{th}$ & 36 Joules\\
+Sensing period & duration of 60 minutes \\
+$E_{th}$ & 36~Joules\\

 $R_s$ & 5~m   \\     
 %\hline
 $\alpha^j_i$ & 0.6   \\
 $R_s$ & 5~m   \\     
 %\hline
 $\alpha^j_i$ & 0.6   \\


@@ -595,213 +721,286 @@ $\beta^j_i$ & 0.4
 \label{table3}
 % is used to refer this table in the text
 \end{table}
 \label{table3}
 % is used to refer this table in the text
 \end{table}

-Simulations with five  different node densities going from  100 to 250~nodes were
-performed  considering  each  time  25~randomly generated  networks,  to  obtain
-experimental results  which are relevant. All simulations are repeated 25 times and the results are averaged. 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  it's  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) by 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 rounds.
-
-The values of $\alpha^j_i$ and $\beta^j_i$ have been chosen in a way that ensuring a good network coverage and for a longer time during the lifetime of the WSN.  We have given a higher priority for 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 given a little bit lower value for $\beta^j_i$ so as to minimize the number of active sensor nodes that contribute in covering the interval i in sensor j.
-
-In the simulations,  we introduce the following performance  metrics to evaluate
-the efficiency of our approach:
+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{enumerate}[i)]
 \begin{itemize}
 
 %\begin{enumerate}[i)]
 \begin{itemize}

-\item {{\bf Network Lifetime}:} we define the network lifetime as the time until
-  the  coverage  ratio  drops  below  a  predefined  threshold.   We  denote  by
-  $Lifetime_{95}$ (respectively $Lifetime_{50}$) the amount of time during which
-  the  network can  satisfy an  area coverage  greater than  $95\%$ (respectively
-  $50\%$). We assume that the sensor  network can fulfill its task until all its
-  nodes have  been drained of their  energy or it  becomes disconnected. Network
-  connectivity  is crucial because  an active  sensor node  without connectivity
-  towards a base  station cannot transmit any information  regarding an observed
-  event in the area that it monitors.
-  
-    
-\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 to compute the
-  coverage ratio: 
-\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  our simulations, we have  a layout of  $N = 51
-\times 26 = 1326$ grid points.
-
-
-\item{{\bf Number of Active Sensors Ratio(ASR)}:} It is important to have as few active nodes as possible in each round,
-in  order to  minimize  the communication  overhead  and maximize  the
-network lifetime. The Active Sensors Ratio is defined as follows:
-\begin{equation*}
-\scriptsize
-\mbox{ASR}(\%) =  \frac{\sum\limits_{r=1}^R \mbox{$A_r$}}{\mbox{$S$}} \times 100 .
-\end{equation*}
-Where: $A_r^t$ is the number of active sensors in the subregion $r$ in the current sensing stage, $S$ is the total number of sensors in the network, and $R$ is the total number of the subregions in the network.
-
- 
-
-\item {{\bf  Energy Consumption}:}  energy consumption (EC)  can be seen  as the
-  total   energy   consumed   by   the   sensors   during   $Lifetime_{95}$   or
-  $Lifetime_{50}$, divided  by the number of periods.  Formally, the computation
-  of EC can be expressed as follows:
+\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:

   \begin{equation*}
     \scriptsize
   \begin{equation*}
     \scriptsize

-    \mbox{EC} = \frac{\sum\limits_{m=1}^{M} \left( E^{\mbox{com}}_m+E^{\mbox{list}}_m+E^{\mbox{comp}}_m  
-      + E^{a}_m+E^{s}_m \right)}{M},
+    \mbox{CR}(\%) = \frac{\mbox{$n$}}{\mbox{$N$}} \times 100

   \end{equation*}
   \end{equation*}

-
-where $M$  corresponds to the number  of periods. The total energy consumed by
-the sensors (EC) comes through taking into consideration four main energy factors. The  first one, denoted $E^{\scriptsize  \mbox{com}}_m$, represent the
-energy consumption  spent by  all the nodes  for wireless  communications during
-period $m$.   $E^{\scriptsize \mbox{list}}_m$,  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 $m$.  $E^{\scriptsize \mbox{comp}}_m$
-refers to the energy needed by all the leader nodes to solve the integer program
-during a period.  Finally, $E^a_{m}$ and $E^s_{m}$ indicate  the energy consumed
-by the whole network in the sensing phase (active and sleeping nodes).
-
-
+  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:
+  \begin{equation*}
+    \scriptsize
+    \mbox{ASR}(\%) =  \frac{\sum\limits_{r=1}^R \mbox{$|A_r^p|$}}{\mbox{$|S|$}} \times 100
+  \end{equation*}
+  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:
+  \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
+  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}
 %\end{enumerate}
 
 \subsection{Simulation Results}
 \end{itemize}
 %\end{enumerate}
 
 \subsection{Simulation Results}

-In this section, we present the simulation results of LiCO protocol and the other protocols using a discrete event simulator OMNeT++ \cite{varga} to run different series of simulations. We implemented all protocols precisely on a laptop DELL with Intel Core~i3~2370~M (2.4 GHz)  processor (2 cores) and the MIPS (Million Instructions  Per Second) rate equal to 35330. To be consistent  with the use of a sensor node with Atmels AVR ATmega103L microcontroller (6 MHz) and  a MIPS rate  equal to 6,  the original execution time on the laptop is multiplied by  2944.2 $\left(\frac{35330}{2} \times  \frac{1}{6} \right)$  so as to use it by the energy consumption model especially, after the computation and listening. Employing the modeling language for Mathematical Programming (AMPL)~\cite{AMPL}, the associated integer program instance is generated in a standard format, which is then read and solved by the optimization solver GLPK (GNU linear Programming Kit available in the public domain) \cite{glpk} through a Branch-and-Bound method. 
- 
-We compared LiCO protocol to three other approaches: the first, called DESK and proposed  by ~\cite{ChinhVu}  is a fully distributed  coverage  algorithm;  the second, called GAF  ~\cite{xu2001geography}, consists in dividing the region
-into fixed  squares.  During the decision  phase, in each square,  one sensor is
-chosen to remain active during the sensing phase; the third, DiLCO protocol~\cite{Idrees2} is an improved version on the work presented in ~\cite{idrees2014coverage}. Note that the LiCO protocol is based on the same framework as that of DiLCO. For these two protocols, the division of the region of interest in 16 subregions was chosen since it produces the best results. The difference between the two protocols relies on the use of the integer programming to provide the set of sensors that have to be activated in each sensing phase. Whereas DiLCO protocol tries to satisfy the coverage of a set of primary points, LiCO protocol tries to reach a desired level of coverage $l$ for each sensor's perimeter. In the experimentations, we chose a level of coverage equal to 1 ($l=1$).

 
 

-\subsubsection{\textbf{Coverage Ratio}}
-Figure~\ref{fig333} shows the average coverage ratio for 200 deployed nodes obtained with the four methods.
- 
+In  order  to  assess and  analyze  the  performance  of  our protocol  we  have
+implemented PeCO protocol in  OMNeT++~\cite{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 (2.4~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)~\cite{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) \cite{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
+\cite{ChinhVu}. The second one,  called GAF~\cite{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~\cite{Idrees2}, is  an improved version
+of a research work we presented in~\cite{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{fig333}  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] {R/CR.eps} 
 \parskip 0pt    
 \begin{figure}[h!]
 \centering
  \includegraphics[scale=0.5] {R/CR.eps} 

-\caption{The coverage ratio for 200 deployed nodes}
+\caption{Coverage ratio for 200 deployed nodes.}

 \label{fig333}
 \end{figure} 
 
 \label{fig333}
 \end{figure} 
 

-DESK,  GAF, and DiLCO provide a little better coverage ratio with 99.99\%, 99.91\%, and 99.02\% against 98.76\% produced by LiCO for the first periods. This is due to the fact that DiLCO protocol put in sleep mode redundant sensors using optimization (which lightly decreases the coverage ratio) while there are more active nodes in the case of others methods. But when the number of periods exceeds 70 periods, it clearly appears that LiCO 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).
+%When the number of periods increases, coverage ratio produced by DESK and GAF protocols decreases. This is due to dead nodes. However, DiLCO protocol maintains almost a good coverage from the round 31 to the round 63 and it is close to PeCO protocol. The coverage ratio of PeCO protocol is better than other approaches from the period 64.

 
 

-%When the number of periods increases, coverage ratio produced by DESK and GAF protocols decreases. This is due to dead nodes. However, DiLCO protocol maintains almost a good coverage from the round 31 to the round 63 and it is close to LiCO protocol. The coverage ratio of LiCO protocol is better than other approaches from the period 64.
+%because the optimization algorithm used by PeCO has been optimized the lifetime coverage based on the perimeter coverage model, so it provided acceptable coverage for a larger number of periods and prolonging the network lifetime based on the perimeter of the sensor nodes in each subregion of WSN. Although some nodes are dead, sensor activity scheduling based optimization of PeCO selected another nodes to ensure the coverage of the area of interest. i.e. DiLCO-16 showed a good coverage in the beginning then PeCO, when the number of periods increases, the coverage ratio decreases due to died sensor nodes. Meanwhile, thanks to sensor activity scheduling based new optimization model, which is used by PeCO protocol to ensure a longer lifetime coverage in comparison with other approaches. 

 
 

-%because the optimization algorithm used by LiCO has been optimized the lifetime coverage based on the perimeter coverage model, so it provided acceptable coverage for a larger number of periods and prolonging the network lifetime based on the perimeter of the sensor nodes in each subregion of WSN. Although some nodes are dead, sensor activity scheduling based optimization of LiCO selected another nodes to ensure the coverage of the area of interest. i.e. DiLCO-16 showed a good coverage in the beginning then LiCO, when the number of periods increases, the coverage ratio decreases due to died sensor nodes. Meanwhile, thanks to sensor activity scheduling based new optimization model, which is used by LiCO protocol to ensure a longer lifetime coverage in comparison with other approaches. 

 
 

+\subsubsection{\bf Active Sensors Ratio}

 
 

-\subsubsection{\textbf{Active Sensors Ratio}} 
-Having active nodes as few as possible in each period is essential in order to minimize the energy consumption and so maximize the network lifetime. Figure~\ref{fig444} shows the average active nodes ratio for 200 deployed nodes. 
+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{fig444}
+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{fig333}.

 
 \begin{figure}[h!]
 \centering
 \includegraphics[scale=0.5]{R/ASR.eps}  
 
 \begin{figure}[h!]
 \centering
 \includegraphics[scale=0.5]{R/ASR.eps}  

-\caption{The active sensors ratio for 200 deployed nodes }
+\caption{Active sensors ratio for 200 deployed nodes.}

 \label{fig444}
 \end{figure} 
 
 \label{fig444}
 \end{figure} 
 

-We observe that DESK and GAF have 30.36 \% and 34.96 \% active nodes for the first fourteen rounds and DiLCO and LiCO protocols compete perfectly with only 17.92 \% and 20.16 \% active nodes during the same time interval. As the number of periods increases, LiCO protocol has a lower number of active nodes in comparison with the three other approaches, while keeping of greater coverage ratio as shown in figure \ref{fig333}.
-
-\subsubsection{\textbf{The Energy Consumption}}
-We study the effect of the energy consumed by the WSN during the communication, computation, listening, active, and sleep modes for different network densities and compare it for the four approaches. Figures~\ref{fig3EC95} and \ref{fig3EC50} illustrate the energy consumption for different network sizes and for $Lifetime95$ and $Lifetime50$. 
+\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{fig3EC}(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!]
 
 \begin{figure}[h!]

-\centering
-\includegraphics[scale=0.5]{R/EC95.eps} 
-\caption{The Energy Consumption per period with $Lifetime_{95}$}
-\label{fig3EC95}
-\end{figure} 
-                                           
-\begin{figure}[h!]
-\centering
-\includegraphics[scale=0.5]{R/EC50.eps} 
-\caption{The Energy Consumption per period with $Lifetime_{50}$}
-\label{fig3EC50}
+  \centering
+  \begin{tabular}{@{}cr@{}}
+    \includegraphics[scale=0.475]{R/EC95.eps} & \raisebox{2.75cm}{(a)} \\
+    \includegraphics[scale=0.475]{R/EC50.eps} & \raisebox{2.75cm}{(b)}
+  \end{tabular}
+  \caption{Energy consumption per period for (a)~$Lifetime_{95}$ and (b)~$Lifetime_{50}$.}
+  \label{fig3EC}

 \end{figure} 
 
 \end{figure} 
 

-The results show that our LiCO protocol is the most competitive from the energy consumption point of view. As shown in figures~\ref{fig3EC95} and \ref{fig3EC50}, LiCO 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 this optimization program allows to reduce significantly the number of active sensors and so the energy consumption while keeping a good coverage level.
-%The optimization algorithm, which used by LiCO protocol,  was improved the lifetime coverage efficiently based on the perimeter coverage model.
+%The optimization algorithm, which used by PeCO protocol,  was improved the lifetime coverage efficiently based on the perimeter coverage model.

 
  %The other approaches have a high energy consumption due to activating a larger number of sensors. In fact,  a distributed  method on the subregions greatly reduces the number of communications and the time of listening so thanks to the partitioning of the initial network into several independent subnetworks. 
 
 
 %\subsubsection{Execution Time}
 
 
  %The other approaches have a high energy consumption due to activating a larger number of sensors. In fact,  a distributed  method on the subregions greatly reduces the number of communications and the time of listening so thanks to the partitioning of the initial network into several independent subnetworks. 
 
 
 %\subsubsection{Execution Time}
 

-\subsubsection{\textbf{The Network Lifetime}}
-We observe the superiority of LiCO and DiLCO protocols against other two approaches in prolonging the network lifetime. In figures~\ref{fig3LT95} and \ref{fig3LT50}, network lifetime, $Lifetime95$ and $Lifetime50$ respectively, are illustrated for different network sizes.  
-
-\begin{figure}[h!]
-\centering
-\includegraphics[scale=0.5]{R/LT95.eps}  
-\caption{The Network Lifetime for $Lifetime_{95}$}
-\label{fig3LT95}
-\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{fig3LT}(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{fig3LT}(b) that the lifetime
+is about twice longer with  PeCO compared to DESK protocol.  The performance
+difference    is    more    obvious   in    Figure~\ref{fig3LT}(b)    than    in
+Figure~\ref{fig3LT}(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!]
 
 \begin{figure}[h!]

-\centering
-\includegraphics[scale=0.5]{R/LT50.eps}  
-\caption{The Network Lifetime for $Lifetime_{50}$}
-\label{fig3LT50}
+  \centering
+  \begin{tabular}{@{}cr@{}}
+    \includegraphics[scale=0.475]{R/LT95.eps} & \raisebox{2.75cm}{(a)} \\  
+    \includegraphics[scale=0.475]{R/LT50.eps} & \raisebox{2.75cm}{(b)}
+  \end{tabular}
+  \caption{Network Lifetime for (a)~$Lifetime_{95}$ \\
+    and (b)~$Lifetime_{50}$.}
+  \label{fig3LT}

 \end{figure} 
 
 \end{figure} 
 

-As highlighted by figures~\ref{fig3LT95} and \ref{fig3LT50}, the network lifetime obviously increases when the size of the network increases, and it is clearly larger with DiLCO and LiCO protocols compared with the two other methods. For instance, for a network of 300 sensors, the coverage ratio is greater than 50\% about two times longer with LiCO compared to DESK method.
+%By choosing the best suited nodes, for each period, by optimizing the coverage and lifetime of the network to cover the area of interest and by letting the other ones sleep in order to be used later in next rounds, PeCO protocol efficiently prolonged the network lifetime especially for a coverage ratio greater than $50 \%$, whilst it stayed very near to  DiLCO-16 protocol for $95 \%$.

 
 

-%By choosing the best suited nodes, for each period, by optimizing the coverage and lifetime of the network to cover the area of interest and by letting the other ones sleep in order to be used later in next rounds, LiCO protocol efficiently prolonged the network lifetime especially for a coverage ratio greater than $50 \%$, whilst it stayed very near to  DiLCO-16 protocol for $95 \%$.  
-Figure~\ref{figLTALL} introduces the comparisons of the lifetime coverage for different coverage ratios for LiCO and DiLCO protocols. 
-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. Indeed there are applications that do not require a 100\% coverage of the surveillance region. LiCO might be an interesting  method  since it achieves a good balance between a high level coverage ratio and network lifetime.
+Figure~\ref{figLTALL}  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!]
 
 \begin{figure}[h!]

-\centering
-\includegraphics[scale=0.5]{R/LTa.eps}  
-\caption{The Network Lifetime for different coverage ratios}
+\centering \includegraphics[scale=0.5]{R/LTa.eps}
+\caption{Network lifetime for different coverage ratios.}

 \label{figLTALL}
 \end{figure} 
 
 \label{figLTALL}
 \end{figure} 
 

-
-%Comparison shows that LiCO protocol, which are used distributed optimization over the subregions, is the more relevance one for most coverage ratios and WSN sizes because it is robust to network disconnection during the network lifetime as well as it consume less energy in comparison with other approaches. LiCO protocol gave acceptable coverage ratio for a larger number of periods using new optimization algorithm that based on a perimeter coverage model. It also means that distributing the algorithm in each node and subdividing the sensing field into many subregions, which are managed independently and simultaneously, is the most relevant way to maximize the lifetime of a network.
+%Comparison shows that PeCO protocol, which are used distributed optimization over the subregions, is the more relevance one for most coverage ratios and WSN sizes because it is robust to network disconnection during the network lifetime as well as it consume less energy in comparison with other approaches. PeCO protocol gave acceptable coverage ratio for a larger number of periods using new optimization algorithm that based on a perimeter coverage model. It also means that distributing the algorithm in each node and subdividing the sensing field into many subregions, which are managed independently and simultaneously, is the most relevant way to maximize the lifetime of a network.

 
 
 
 

-\section{\uppercase{Conclusion and Future Works}}
+\section{Conclusion and Future Works}

 \label{sec:Conclusion and Future Works}
 \label{sec:Conclusion and Future Works}

-In this paper we have studied the problem of lifetime coverage optimization in
-WSNs. We designed a protocol LiCO that schedules node activities (wakeup and sleep) with the objective of maintaining a good coverage ratio while maximizing the network lifetime. This protocol is applied on each subregion of the area of interest. It works in periods and is based on the resolution of an integer program to select the subset of sensors operating in active mode 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.

 
 

- 
-
-
-%To cope with this problem, the area of interest is divided into a smaller subregions using  divide-and-conquer method, and then a LiCO protocol for optimizing the lifetime coverage in each subregion. LiCO protocol combines two efficient techniques:  network
+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.
+
+%To cope with this problem, the area of interest is divided into a smaller subregions using  divide-and-conquer method, and then a PeCO protocol for optimizing the lifetime coverage in each subregion. PeCO protocol combines two efficient techniques:  network

 %leader election, which executes the perimeter coverage model (only one time), the optimization algorithm, and sending the schedule produced by the optimization algorithm to other nodes in the subregion ; the second, sensor activity scheduling based optimization in which a new lifetime coverage optimization model is proposed. The main challenges include how to select the  most efficient leader in each subregion and the best schedule of sensor nodes that will optimize the network lifetime coverage
 %in the subregion. 
 %The network lifetime coverage in each subregion is divided into
 %periods, each period consists  of four stages: (i) Information Exchange,
 %(ii) Leader Election, (iii) a Decision based new optimization model in order to
 %select the  nodes remaining  active for the last stage,  and  (iv) Sensing.
 %leader election, which executes the perimeter coverage model (only one time), the optimization algorithm, and sending the schedule produced by the optimization algorithm to other nodes in the subregion ; the second, sensor activity scheduling based optimization in which a new lifetime coverage optimization model is proposed. The main challenges include how to select the  most efficient leader in each subregion and the best schedule of sensor nodes that will optimize the network lifetime coverage
 %in the subregion. 
 %The network lifetime coverage in each subregion is divided into
 %periods, each period consists  of four stages: (i) Information Exchange,
 %(ii) Leader Election, (iii) a Decision based new optimization model in order to
 %select the  nodes remaining  active for the last stage,  and  (iv) Sensing.

-We carried out severals simulations to evaluate the proposed protocol.  The  simulation results show that LiCO is  is more energy-efficient than other approaches, with respect to lifetime, coverage ratio, active sensors ratio, and energy consumption. 
-%Indeed, when dealing with large and dense WSNs, a distributed optimization approach on the subregions of WSN like the one we are proposed allows to reduce the difficulty of a single global optimization problem by partitioning it in many smaller problems, one per subregion, that can be solved more easily.
-
-We have identified different research directions that arise out of the work presented here. 
-We plan to extend our framework such that the schedules are planned for multiple periods in advance.
+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.
+%Indeed, when dealing with large and dense WSNs, a distributed optimization approach on the subregions of WSN like the one we are proposed allows to reduce the difficulty of a single global optimization problem by partitioning it in many smaller problems, one per subregion, that can be solved more easily. We have  identified different  research directions  that arise  out of  the work presented here.
+We plan to extend our framework so that the schedules are planned for multiple
+sensing periods.

 %in order to compute all active sensor schedules in only one step for many periods;
 %in order to compute all active sensor schedules in only one step for many periods;

-We also want to improve our integer program to take into account the heterogeneous sensors, which do not have the same energy, processing,  sensing and communication capabilities;
+We also want  to improve our integer program to  take into account heterogeneous
+sensors  from both  energy  and node  characteristics point of views.

 %the third, we are investigating new optimization model based on the sensing range so as to maximize the lifetime coverage in WSN;
 %the third, we are investigating new optimization model based on the sensing range so as to maximize the lifetime coverage in WSN;

-Finally, our final goal is to implement our protocol using a sensor-testbed to evaluate their performance in real world applications.
+Finally,  it   would  be   interesting  to  implement   our  protocol   using  a
+sensor-testbed to evaluate it in real world applications.

 
 

-\section*{\uppercase{Acknowledgements}}
-\noindent As a Ph.D. student, Ali Kadhum IDREES would like to gratefully acknowledge the University of Babylon - IRAQ for the financial support and Campus France for the received support.
+\section*{Acknowledgments}

 
 

- 
+\noindent  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). 

 
 
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