version R4 pour soumission

[LiCO.git] / LiCO_Journal.tex

diff --git a/LiCO_Journal.tex b/LiCO_Journal.tex
index a71497461d5dfa53350c56917929e6b77a28af37..051f1116dd59e60d1a62b4649110a63b683c369b 100644 (file)
--- a/LiCO_Journal.tex
+++ b/LiCO_Journal.tex
@@ -38,14 +38,14 @@
 
 %\title{Lifetime Coverage Optimization Protocol \\
 %  in Wireless Sensor Networks}
 
 %\title{Lifetime Coverage Optimization Protocol \\
 %  in Wireless Sensor Networks}

-\title{Perimeter-based Coverage Optimization Protocol \\
-  to Improve Lifetime 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}}
 


@@ -56,28 +56,29 @@
 
 \begin{abstract}
 The most important problem in a Wireless Sensor Network (WSN) is to optimize the
 
 \begin{abstract}
 The most important problem in a Wireless Sensor Network (WSN) is to optimize the

-use of its limited energy provision, so  that it can fulfill its monitoring task
-as  long as  possible. Among  known  available approaches  that can  be used  to
+use of its limited energy provision, so that it can fulfill its monitoring task
+as long as  possible. Among  known  available approaches  that can  be used  to

 improve  power  management,  lifetime coverage  optimization  provides  activity
 improve  power  management,  lifetime coverage  optimization  provides  activity

-scheduling which ensures  sensing coverage while minimizing the  energy cost. In
-this paper,  we propose such an approach  called 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/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  perimeter coverage level  to schedule
+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
 sensors' activities.  Extensive simulation experiments have been performed using

-OMNeT++, the  discrete event simulator, to  demonstrate that LiCO is  capable to
+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}
 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}

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

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


@@ -104,12 +105,12 @@ 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
 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}.
 


@@ -121,39 +122,39 @@ lifetime of the WSNs~\cite{rault2014energy}.
 
 This paper makes the following contributions.
 \begin{enumerate}
 
 This paper makes the following contributions.
 \begin{enumerate}

-\item We devise a framework to schedule nodes to be activated alternatively such
+\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
   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  if divided into
-  several smaller subregions and on the other hand the time line is divided into
+  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.
   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  propose a new mathematical  optimization model.  Instead of  trying to
+\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
   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.  So  that an
+  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.
   optimal scheduling  will be  obtained by  minimizing a  weighted sum  of these
   deviations.

-\item We  conducted extensive simulation  experiments, using the  discrete event
-  simulator OMNeT++, to demonstrate the  efficiency of our protocol. We compared
-  our   LiCO   protocol   to   two   approaches   found   in   the   literature:
+\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}
 
   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}
 

-%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 rest  of the paper is  organized as follows.  In the next section  we review
 % 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 rest  of the paper is  organized as follows.  In the next section  we review

-some related work in the  field. Section~\ref{sec:The LiCO Protocol Description}
-is devoted to the LiCO protocol  description and Section~\ref{cp} focuses on the
+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
 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   given  for   future  works   in
+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.
 Section~\ref{sec:Conclusion and Future Works}.
 
 % that show that our protocol outperforms others protocols.


@@ -161,25 +162,25 @@ Section~\ref{sec:Conclusion and Future Works}.
 \label{sec:Literature Review}
 
 \noindent  In  this section,  we  summarize  some  related works  regarding  the
 \label{sec:Literature Review}
 
 \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 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
 the literature.
 
 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} refer
+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
 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 to  the  target
+\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
 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

-neighboring  to  a  sensor and  $n$  is  the  total  number of  sensors  in  the
-network. {\it In LiCO protocol, instead  of determining the level of coverage of
+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.}
 
   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.}
 


@@ -198,35 +199,35 @@ 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  {\em   et  al.}~\cite{pc10},  propose  algorithms
 working in a periodic fashion where a  cover set is computed at the beginning of
 activated  in   succession  to  achieve   the  desired  network   lifetime.   Vu
 \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,  LiCO protocol works  in periods,
+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.}
 
   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
+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
 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 a such approach is  to avoid long range communications and thus
+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
 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 take a bad decision leading to a global suboptimal solution.  Conversely,
+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
 centralized

-algorithms~\cite{cardei2005improving,zorbas2010solving,pujari2011high}    always
+algorithms~\cite{cardei2005improving,zorbas2010solving,pujari2011high}     always

 provide nearly  or close to  optimal solution since  the algorithm has  a global
 view of the whole network. The disadvantage of a centralized method is obviously
 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  very huge since
-long range communications will be needed. In fact the larger the WNS, the higher
-the  communication and  thus energy  cost.   {\it In  order to  be suitable  for
-  large-scale networks,  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. Thus our
-  protocol  is  scalable  and  a  globally distributed  method,  whereas  it  is
-  centralized in each subregion.}
-
-Various  coverage scheduling  algorithms have  been developed  this last  years.
+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
 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


@@ -239,7 +240,7 @@ optimization  solver).  The  problem is  formulated as  an optimization  problem
 energy  constraints.   Column  generation   techniques,  well-known  and  widely
 practiced techniques for  solving linear programs with too  many variables, have
 also                                                                        been
 energy  constraints.   Column  generation   techniques,  well-known  and  widely
 practiced techniques for  solving linear programs with too  many variables, have
 also                                                                        been

-used~\cite{castano2013column,rossi2012exact,deschinkel2012column}. {\it  In LiCO
+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.}
   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.}


@@ -280,12 +281,12 @@ used~\cite{castano2013column,rossi2012exact,deschinkel2012column}. {\it  In LiCO
 
 %\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 LiCO Protocol Description}
-\label{sec:The LiCO Protocol Description}
+\section{ The PeCO Protocol Description}
+\label{sec:The PeCO Protocol Description}

 
 

-\noindent  In  this  section,  we  describe in  details  our  Lifetime  Coverage
+\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
 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


@@ -302,7 +303,7 @@ 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
 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

-energy provision  point of  view.  The  location information  is available  to a
+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
 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


@@ -314,10 +315,10 @@ 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}
 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,  a
+proved  that if  the  transmission  range fulfills  the  previous hypothesis,  the

 complete coverage of a convex area implies connectivity among active nodes.
 
 complete coverage of a convex area implies connectivity among active nodes.
 

-\indent  LiCO protocol  uses the  same perimeter-coverage  model than  Huang and
+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
 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


@@ -326,17 +327,17 @@ $k$-covered if and only if each sensor in the network is $k$-perimeter-covered (
 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
 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  intersection  of  the  two  sensing
+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
 areas. These points are denoted for  neighbor~$i$ by $iL$ and $iR$, respectively

-for  left and  right from  neighbor  point of  view.  The  resulting couples  of
+for  left and  right from  a neighboing  point of  view.  The  resulting couples  of

 intersection points subdivide  the perimeter of sensor~$0$  into portions called
 arcs.
 
 \begin{figure}[ht!]
   \centering
   \begin{tabular}{@{}cr@{}}
 intersection points subdivide  the perimeter of sensor~$0$  into portions called
 arcs.
 
 \begin{figure}[ht!]
   \centering
   \begin{tabular}{@{}cr@{}}

-    \includegraphics[width=75mm]{pcm.jpg} & \raisebox{3.25cm}{(a)}
-    \\ \includegraphics[width=75mm]{twosensors.jpg} & \raisebox{2.75cm}{(b)}
+    \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 $v$.}
   \end{tabular}
   \caption{(a) Perimeter  coverage of sensor node  0 and (b) finding  the arc of
     $u$'s perimeter covered by $v$.}


@@ -350,25 +351,24 @@ 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
 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  $\alpha  = arccos  \left(\dfrac{Dist(u,v)}{2R_s}
-\right)$.   So, the  arc on  the perimeter  of node~$u$  defined by  the angular
-interval $[\pi - \alpha,\pi + \alpha]$ is said to be perimeter-covered by sensor
-node $v$.
+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
 
 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
+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
 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  first  intersection point  after  point~zero,  and  the maximum  level  of
+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 $3$
 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 $0$.
+(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.
 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.


@@ -376,9 +376,9 @@ 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.
 
 %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.
 

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

 \centering
 \centering

-\includegraphics[width=137.5mm]{expcm2.jpg}  
+\includegraphics[width=127.5mm]{expcm2.jpg}  

 \caption{Maximum coverage levels for perimeter of sensor node $0$.}
 \label{expcm}
 \end{figure*} 
 \caption{Maximum coverage levels for perimeter of sensor node $0$.}
 \label{expcm}
 \end{figure*} 


@@ -396,7 +396,7 @@ above is thus given by the sixth line of the table.
 
 \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


@@ -425,17 +425,17 @@ above is thus given by the sixth line of the table.
 \end{table}
 
 
 \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
+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
 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 $\infty$
+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.
  
 and  the  corresponding  interval  will  not   be  taken  into  account  by  the
 optimization algorithm.
  

-\begin{figure}[t!]
+\begin{figure}[h!]

 \centering
 \includegraphics[width=62.5mm]{ex4pcm.jpg}  
 \caption{Sensing range outside the WSN's area of interest.}
 \centering
 \includegraphics[width=62.5mm]{ex4pcm.jpg}  
 \caption{Sensing range outside the WSN's area of interest.}


@@ -456,14 +456,14 @@ 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.
 
 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
+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
 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

-LiCO, are more  robust against an unexpected  node failure. On the  one hand, if
-node failure is discovered before  taking the decision, the corresponding sensor
-node will  not be considered  by the optimization  algorithm, and, on  the other
+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
 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


@@ -477,11 +477,11 @@ the area.
 \begin{figure}[t!]
 \centering
 \includegraphics[width=80mm]{Model.pdf}  
 \begin{figure}[t!]
 \centering
 \includegraphics[width=80mm]{Model.pdf}  

-\caption{LiCO protocol.}
+\caption{PeCO protocol.}

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

-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} 
 \item INFO  packet: sent  by each  sensor node to  all the  nodes inside  a same
 %\begin{enumerate}[(a)]
 \begin{itemize} 
 \item INFO  packet: sent  by each  sensor node to  all the  nodes inside  a same


@@ -505,10 +505,10 @@ Five status are possible for a sensor node in the network:
 %\end{enumerate}
 %Below, we describe each phase in more details.
 
 %\end{enumerate}
 %Below, we describe each phase in more details.
 

-\subsection{LiCO Protocol Algorithm}
+\subsection{PeCO Protocol Algorithm}

 
 \noindent The  pseudocode implementing the  protocol on  a node is  given below.
 
 \noindent The  pseudocode implementing the  protocol on  a node is  given below.

-More  precisely,  Algorithm~\ref{alg:LiCO}  gives  a brief  description  of  the
+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!]                
 protocol applied by a sensor node $s_k$ where $k$ is the node index in the WSN.
 
 \begin{algorithm}[h!]                


@@ -542,7 +542,7 @@ protocol applied by a sensor node $s_k$ where $k$ is the node index in the WSN.
            }
       
         \emph{$s_k.status$ = COMMUNICATION}\;
            }
       
         \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{


@@ -552,34 +552,33 @@ protocol applied by a sensor node $s_k$ where $k$ is the node index in the WSN.
       }  
   }
   \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}
 

-In this  algorithm, K.CurrentSize and  K.PreviousSize refer to the  current size
-and the  previous size of  the subnetwork  in the subregion  respectively.  That
-means the number  of sensor nodes which are still  alive.  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  number 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 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}
 
 \noindent In this  section, the coverage model is  mathematically formulated. We
 \label{cp}
 
 \noindent In this  section, the coverage model is  mathematically formulated. We

-start  with a  description of  the notations  that will  be used  throughout the
+start  with a  description of the notations that will  be used  throughout the

 section.
 
 First, we have the following sets:
 section.
 
 First, we have the following sets:


@@ -591,7 +590,7 @@ First, we have the following sets:
 \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 $i$,
 \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 $a^j_{ik}$ denote  the indicator function of whether  sensor~$k$ is involved
+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 \{ 
 in coverage interval~$i$ of sensor~$j$, that is:
 \begin{equation}
 a^j_{ik} = \left \{ 


@@ -669,9 +668,9 @@ X_{k} \in \{0,1\}, \forall k \in A
 $\alpha^j_i$ 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
 $\alpha^j_i$ 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
+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
 region. This  kind of integer program  is inspired from the  model developed for

-brachytherapy    treatment   planning    for   optimizing    dose   distribution
+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
 \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


@@ -727,7 +726,7 @@ 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
 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 it's energy provision reaches a
+randomly drawn in the interval $[500-700]$.   If its energy provision reaches a

 value below  the threshold $E_{th}=36$~Joules,  the minimum energy needed  for a
 node  to stay  active during  one period,  it will  no more  participate in  the
 coverage task. This value corresponds to the energy needed by the sensing phase,
 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,


@@ -737,11 +736,11 @@ 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
 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 for
+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
 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 which contribute
+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
 in covering the interval.
 
 We introduce the following performance metrics to evaluate the efficiency of our


@@ -769,7 +768,7 @@ approach.
   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
   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 nodes  as few  as possible,  in order  to minimize  the communication
+  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*}
   overhead and maximize the WSN lifetime. The active sensors ratio is defined as
   follows:
   \begin{equation*}


@@ -804,9 +803,9 @@ approach.
 \subsection{Simulation Results}
 
 In  order  to  assess and  analyze  the  performance  of  our protocol  we  have
 \subsection{Simulation Results}
 
 In  order  to  assess and  analyze  the  performance  of  our protocol  we  have

-implemented LiCO protocol in  OMNeT++~\cite{varga} simulator.  Besides LiCO, two
+implemented PeCO protocol in  OMNeT++~\cite{varga} simulator.  Besides PeCO, two

 other  protocols,  described  in  the  next paragraph,  will  be  evaluated  for
 other  protocols,  described  in  the  next paragraph,  will  be  evaluated  for

-comparison purposes.   The simulations were run  on a laptop DELL  with an Intel
+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
 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


@@ -817,35 +816,35 @@ 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.
 
 optimization solver  GLPK (GNU  linear Programming Kit  available in  the public
 domain) \cite{glpk} through a Branch-and-Bound method.
 

-As said previously, the LiCO is  compared with three other approaches. The first
+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
 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

-LiCO and  DiLCO protocols are  based on the  same framework. In  particular, the
-choice for the simulations of a partitioning in 16~subregions was chosen because
-it corresponds to the configuration producing  the better results for DiLCO. The
+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,
 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 LiCO protocol objective is to reach a desired level of coverage for each
+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
 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 little better
-coverage ratio with respectively 99.99\%,  99.91\%, and 99.02\%, against 98.76\%
-produced by  LiCO for the  first periods. This  is due to  the fact that  at the
-beginning  DiLCO protocol  puts in  sleep status  more redundant  sensors (which
+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
 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  LiCO provides a better  coverage ratio and keeps  a coverage ratio
+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
 greater  than 50\%  for  longer periods  (15  more compared  to  DiLCO, 40  more

-compared to DESK). The energy saved by  LiCO in the early periods allows later a
+compared to DESK). The energy saved by  PeCO in the early periods allows later a

 substantial increase of the coverage performance.
 
 \parskip 0pt    
 substantial increase of the coverage performance.
 
 \parskip 0pt    


@@ -856,22 +855,22 @@ substantial increase of the coverage performance.
 \label{fig333}
 \end{figure} 
 
 \label{fig333}
 \end{figure} 
 

-%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.
+%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.

 
 

-%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. 
+%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. 

 
 
 \subsubsection{\bf Active Sensors Ratio}
 
 Having the less active sensor nodes in  each period is essential to minimize the
 
 
 \subsubsection{\bf Active Sensors Ratio}
 
 Having the less active sensor nodes in  each period is essential to minimize the

-energy consumption  and so  maximize the network  lifetime.  Figure~\ref{fig444}
+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
 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 LiCO  protocols compete perfectly  with only 17.92  \% and
+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
 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
+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
 the three other approaches, while keeping a greater coverage ratio as shown in

-figure \ref{fig333}.
+Figure \ref{fig333}.

 
 \begin{figure}[h!]
 \centering
 
 \begin{figure}[h!]
 \centering


@@ -882,13 +881,13 @@ figure \ref{fig333}.
 
 \subsubsection{\bf Energy Consumption}
 
 
 \subsubsection{\bf Energy Consumption}
 

-We study the effect of the energy  consumed by the WSN during the communication,
+We studied the effect of the energy  consumed by the WSN during the communication,

 computation, listening, active, and sleep status for different network densities
 computation, listening, active, and sleep status for different network densities

-and  compare  it for  the  four  approaches.  Figures~\ref{fig3EC}(a)  and  (b)
+and  compared  it for  the  four  approaches.  Figures~\ref{fig3EC}(a)  and  (b)

 illustrate  the  energy   consumption  for  different  network   sizes  and  for
 illustrate  the  energy   consumption  for  different  network   sizes  and  for

-$Lifetime95$ and  $Lifetime50$. The results show  that our LiCO protocol  is the
+$Lifetime95$ and  $Lifetime50$. The results show  that our PeCO protocol  is the

 most competitive  from the energy  consumption point of  view. As shown  in both
 most competitive  from the energy  consumption point of  view. As shown  in both

-figures, LiCO consumes much less energy than the three other methods.  One might
+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
 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


@@ -905,7 +904,7 @@ while keeping a good coverage level.
   \label{fig3EC}
 \end{figure} 
 
   \label{fig3EC}
 \end{figure} 
 

-%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. 
 
 
  %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. 
 


@@ -914,17 +913,17 @@ while keeping a good coverage level.
 
 \subsubsection{\bf Network Lifetime}
 
 
 \subsubsection{\bf Network Lifetime}
 

-We observe the superiority of LiCO and DiLCO protocols in comparison against the
+We observe the superiority of PeCO and DiLCO protocols in comparison with the

 two    other   approaches    in    prolonging   the    network   lifetime.    In
 two    other   approaches    in    prolonging   the    network   lifetime.    In

-figures~\ref{fig3LT}(a)  and (b),  $Lifetime95$ and  $Lifetime50$ are  shown for
+Figures~\ref{fig3LT}(a)  and (b),  $Lifetime95$ and  $Lifetime50$ are  shown for

 different  network  sizes.   As  highlighted  by  these  figures,  the  lifetime
 different  network  sizes.   As  highlighted  by  these  figures,  the  lifetime

-increases with the size  of the network, and it is clearly  the larger for DiLCO
-and LiCO  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 two times longer with  LiCO 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
-the time, and the lifetime with a coverage  of 50\% is far more longer than with
+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!]
 95\%.
 
 \begin{figure}[h!]


@@ -938,19 +937,19 @@ the time, and the lifetime with a coverage  of 50\% is far more longer than with
   \label{fig3LT}
 \end{figure} 
 
   \label{fig3LT}
 \end{figure} 
 

-%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 $95 \%$.
+%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 $95 \%$.

 
 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 $95\%$
 
 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  Protocol is DiLCO  or LiCO.  Indeed there  are applications
-that do not require a 100\% coverage of  the area to be monitored. LiCO might be
+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
 an interesting  method since  it achieves  a good balance  between a  high level

-coverage ratio and network lifetime. LiCO always outperforms DiLCO for the three
+coverage ratio and network lifetime. PeCO always outperforms DiLCO for the three

 lower  coverage  ratios,  moreover  the   improvements  grow  with  the  network
 lower  coverage  ratios,  moreover  the   improvements  grow  with  the  network

-size. DiLCO is better  for coverage ratios near 100\%, but in  that case LiCO is
-not so bad for the smallest network sizes.
+size. DiLCO is better  for coverage ratios near 100\%, but in  that case PeCO is
+not ineffective for the smallest network sizes.

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


@@ -958,14 +957,14 @@ not so bad for the smallest network sizes.
 \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{Conclusion and Future Works}
 \label{sec:Conclusion and Future Works}
 
 
 
 \section{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 new protocol, called Lifetime  Coverage Optimization, which
+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
 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


@@ -976,19 +975,19 @@ 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.
 
 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
+%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  several simulations  to  evaluate the  proposed protocol.   The
-simulation  results  show   that  LiCO  is  more   energy-efficient  than  other
+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.
 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
+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;
 We also want  to improve our integer program to  take into account heterogeneous
 sensing 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 heterogeneous


@@ -999,10 +998,10 @@ sensor-testbed to evaluate it in real world applications.
 
 \section*{Acknowledgments}
 
 
 \section*{Acknowledgments}
 

-\noindent  As a  Ph.D.   student, Ali  Kadhum IDREES  would  like to  gratefully
+\noindent  As a  Ph.D.   student, Ali Kadhum IDREES  would  like to  gratefully

 acknowledge the  University of Babylon -  IRAQ for financial support  and Campus
 acknowledge the  University of Babylon -  IRAQ for financial support  and Campus

-France for the  received support. This work has also been supported by the Labex
-ACTION.
+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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