X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/LiCO.git/blobdiff_plain/69295a437968b7724acd8bc875a6b8943817854a..d713a949431c9d95cd50776edaf8225fbfd7cee1:/PeCO-EO/articleeo.tex?ds=inline

diff --git a/PeCO-EO/articleeo.tex b/PeCO-EO/articleeo.tex
index 0acbf9b..c0c6f7b 100644
--- a/PeCO-EO/articleeo.tex
+++ b/PeCO-EO/articleeo.tex
@@ -24,18 +24,16 @@ The most important problem in a Wireless Sensor Network (WSN) is to optimize the
 use of its limited energy provision, so that it can fulfill its monitoring task
 as long as  possible. Among  known  available approaches  that can  be used  to
 improve  power  management,  lifetime coverage  optimization  provides  activity
-scheduling which ensures sensing coverage while minimizing the energy cost. In
-this paper,  we propose such an approach called Perimeter-based Coverage Optimization
+scheduling which ensures sensing coverage while minimizing the energy cost. We propose such an approach called Perimeter-based Coverage Optimization
 protocol (PeCO). It is a  hybrid of centralized and distributed methods: the
 region of interest is first subdivided into subregions and our protocol is then
 distributed among sensor nodes in each  subregion.
 The novelty of our approach lies essentially in the formulation of a new
 mathematical optimization  model based on the  perimeter coverage level  to schedule
-sensors' activities.  Extensive simulation experiments have been performed using
-OMNeT++, the  discrete event simulator, to  demonstrate that PeCO  can
+sensors' activities.  Extensive simulation experiments demonstrate that PeCO  can
 offer longer lifetime coverage for WSNs in comparison with some other protocols.
 
-\begin{keywords}Wireless Sensor Networks, Area Coverage, Network Lifetime, Optimization, Scheduling.
+\begin{keywords}Wireless Sensor Networks, Area Coverage, Energy efficiency, Optimization, Scheduling.
 \end{keywords}
 
 \end{abstract}
@@ -47,14 +45,14 @@ offer longer lifetime coverage for WSNs in comparison with some other protocols.
 \noindent The continuous progress in Micro Electro-Mechanical Systems (MEMS) and
 wireless communication hardware  has given rise to the opportunity  to use large
 networks    of     tiny    sensors,    called    Wireless     Sensor    Networks
-(WSN)~\cite{akyildiz2002wireless,puccinelli2005wireless}, to  fulfill monitoring
+(WSN)~\citep{akyildiz2002wireless,puccinelli2005wireless}, to  fulfill monitoring
 tasks.   A  WSN  consists  of  small low-powered  sensors  working  together  by
 communicating with one another through multi-hop radio communications. Each node
 can send the data  it collects in its environment, thanks to  its sensor, to the
 user by means of  sink nodes. The features of a WSN made  it suitable for a wide
 range of application  in areas such as business,  environment, health, industry,
-military, and so on~\cite{yick2008wireless}.   Typically, a sensor node contains
-three main components~\cite{anastasi2009energy}: a  sensing unit able to measure
+military, and so on~\citep{yick2008wireless}.   Typically, a sensor node contains
+three main components~\citep{anastasi2009energy}: a  sensing unit able to measure
 physical,  chemical, or  biological  phenomena observed  in  the environment;  a
 processing unit which will process and store the collected measurements; a radio
 communication unit for data transmission and receiving.
@@ -70,8 +68,7 @@ low power sleep mode and thus save  energy. Overall, the main question that must
 be answered is: how to extend the lifetime coverage of a WSN as long as possible
 while  ensuring   a  high  level  of   coverage?   These past few years  many
 energy-efficient mechanisms have been suggested  to retain energy and extend the
-lifetime of the WSNs~\cite{rault2014energy}.
-
+lifetime of the WSNs~\citep{rault2014energy}.\\\\
 This paper makes the following contributions.
 \begin{enumerate}
 \item We have devised a framework to schedule nodes to be activated alternatively such
@@ -92,8 +89,8 @@ This paper makes the following contributions.
 \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
+  DESK~\citep{ChinhVu} and  GAF~\citep{xu2001geography}, and also to  our previous
+  work published in~\citep{Idrees2} which is  based on another optimization model
   for sensor scheduling.
 \end{enumerate}
 
@@ -111,7 +108,6 @@ 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.
 \section{Related Literature}
 \label{sec:Literature Review}
 
@@ -120,16 +116,16 @@ 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
-fixed area  must be monitored, while  target coverage~\cite{yang2014novel} refers
+categories~\citep{li2013survey}   according   to  their   respective   monitoring
+objective.  Hence,  area coverage \citep{Misra}  means that every point  inside a
+fixed area  must be monitored, while  target coverage~\citep{yang2014novel} refers
 to  the objective  of coverage  for a  finite number  of discrete  points called
-targets,  and  barrier coverage~\cite{HeShibo}\cite{kim2013maximum}  focuses  on
+targets,  and  barrier coverage~\citep{HeShibo,kim2013maximum}  focuses  on
 preventing  intruders   from  entering   into  the   region  of   interest.   In
-\cite{Deng2012}  authors  transform the  area  coverage  problem into  the  target
+\citep{Deng2012}  authors  transform the  area  coverage  problem into  the  target
 coverage one taking into account the  intersection points among disks of sensors
 nodes    or   between    disk   of    sensor   nodes    and   boundaries.     In
-\cite{Huang:2003:CPW:941350.941367}  authors prove  that  if  the perimeters  of
+\citep{Huang:2003:CPW:941350.941367}  authors prove  that  if  the perimeters  of
 sensors are sufficiently  covered it will be  the case for the  whole area. They
 provide an algorithm in $O(nd~log~d)$  time to compute the perimeter-coverage of
 each  sensor,  where  $d$  denotes  the  maximum  number  of  sensors  that  are
@@ -140,18 +136,18 @@ network. {\it In PeCO protocol, instead  of determining the level of coverage of
 
 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)\cite{wang2011coverage}, where  each set completely  covers a  region of interest,  and to
+non-disjoint)\citep{wang2011coverage}, where  each set completely  covers a  region of interest,  and to
 activate these set  covers successively. The network activity can  be planned in
 advance and scheduled  for the entire network lifetime or  organized in periods,
 and the set  of active sensor nodes  is decided at the beginning  of each period
-\cite{ling2009energy}.  Active node selection is determined based on the problem
+\citep{ling2009energy}.  Active node selection is determined based on the problem
 requirements (e.g.   area monitoring,  connectivity, or power  efficiency).  For
-instance, Jaggi {\em et al.}~\cite{jaggi2006}  address the problem of maximizing
+instance, \citet{jaggi2006}  address the problem of maximizing
 the lifetime  by dividing sensors  into the  maximum number of  disjoint subsets
 such  that each  subset  can ensure  both coverage  and  connectivity. A  greedy
 algorithm  is applied  once to  solve  this problem  and the  computed sets  are
-activated  in   succession  to  achieve   the  desired  network   lifetime.   Vu
-\cite{chin2007},  \cite{yan2008design}, Padmatvathy  {\em   et  al.}~\cite{pc10},  propose  algorithms
+activated  in   succession  to  achieve   the  desired  network   lifetime.   
+\citet{chin2007},  \citet{yan2008design}, \citet{pc10},  propose  algorithms
 working in a periodic fashion where a  cover set is computed at the beginning of
 each period.   {\it Motivated by  these works,  PeCO protocol works  in periods,
   where each  period contains a  preliminary phase for information  exchange and
@@ -159,14 +155,14 @@ each period.   {\it Motivated by  these works,  PeCO protocol works  in periods,
   sensing task.}
 
 Various centralized  and distributed approaches, or  even a mixing  of these two
-concepts, have  been proposed  to extend the  network lifetime \cite{zhou2009variable}.   In distributed algorithms~\cite{Tian02,yangnovel,ChinhVu,qu2013distributed} each sensor decides of its
+concepts, have  been proposed  to extend the  network lifetime \citep{zhou2009variable}.   In distributed algorithms~\citep{Tian02,yangnovel,ChinhVu,qu2013distributed} each sensor decides of its
 own activity scheduling  after an information exchange with  its neighbors.  The
 main interest of such an approach is to avoid long range communications and thus
 to reduce the energy dedicated to the communications.  Unfortunately, since each
 node has only information on  its immediate neighbors (usually the one-hop ones)
 it may make a bad decision leading to a global suboptimal solution.  Conversely,
 centralized
-algorithms~\cite{cardei2005improving,zorbas2010solving,pujari2011high}     always
+algorithms~\citep{cardei2005improving,zorbas2010solving,pujari2011high}     always
 provide nearly  or close to  optimal solution since  the algorithm has  a global
 view of the whole network. The disadvantage of a centralized method is obviously
 its high  cost in communications needed to  transmit to a single  node, the base
@@ -185,56 +181,20 @@ 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}
+\citep{berman04,zorbas2010solving}.  Other  approaches are based  on mathematical
+programming formulations~\citep{cardei2005energy,5714480,pujari2011high,Yang2014}
 and dedicated techniques (solving with a branch-and-bound algorithm available in
 optimization  solver).  The  problem is  formulated as  an optimization  problem
 (maximization of the lifetime or number of cover sets) under target coverage and
 energy  constraints.   Column  generation   techniques,  well-known  and  widely
 practiced techniques for  solving linear programs with too  many variables, have
 also                                                                        been
-used~\cite{castano2013column,rossi2012exact,deschinkel2012column}. {\it  In the PeCO
+used~\citep{castano2013column,doi:10.1080/0305215X.2012.687732,deschinkel2012column}. {\it  In the PeCO
   protocol, each  leader, in charge  of a  subregion, solves an  integer program
   which has a twofold objective: minimize the overcoverage and the undercoverage
   of the perimeter of each sensor.}
 
-%\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.
-
-%The problem of k-coverage in WSNs was addressed~\cite{ammari2012centralized}. It mathematically formulated and the spacial sensor density for full k-coverage determined, where the relation between the communication range and the sensing range constructed by this work to retain the k-coverage and connectivity in WSN. After that, a four configuration protocols have proposed for treating the k-coverage in WSNs.  
-
-%In~\cite{rebai2014branch}, the problem of full grid coverage is formulated using two integer linear programming models: the first, a model that takes into account only the overall coverage constraint; the second, both the connectivity and the full grid coverage constraints have taken into consideration. This work did not take into account the energy constraint.
-
-%Li et al.~\cite{li2011transforming} presented a framework to convert any complete coverage problem to a partial coverage one with any coverage ratio by means of executing a complete coverage algorithm to find a full coverage sets with virtual radii and transforming the coverage sets to a partial coverage sets by adjusting sensing radii.  The properties of the original algorithms can be maintained by this framework and the transformation process has a low execution time.
-
-%The authors in~\cite{liu2014generalized} explained that in some applications of WSNs such as structural health monitoring (SHM) and volcano monitoring, the traditional coverage model which is a geographic area defined for individual sensors is not always valid. For this reason, they define a generalized coverage model, which is not need to have the coverage area of individual nodes, but only based on a function to determine whether a set of
-%sensor nodes is capable of satisfy the requested monitoring task for a certain area. They have proposed two approaches to divide the deployed nodes into suitable cover sets, which can be used to prolong the network lifetime. 
- 
-%The work in~\cite{wang2010preserving} addressed the target area coverage problem by proposing a geometric-based activity scheduling scheme, named GAS, to fully cover the target area in WSNs. The authors deals with small area (target area coverage), which can be monitored by a single sensor instead of area coverage, which focuses on a large area that should be monitored by many sensors cooperatively. They explained that GAS is capable to monitor the target area by using a few sensors as possible and it can produce as many cover sets as possible.
-
-%Cho et al.~\cite{cho2007distributed} proposed a distributed node scheduling protocol, which can retain sensing coverage needed by applications
-%and increase network lifetime via putting in sleep mode some redundant nodes. In this work, the effective sensing area (ESA) concept of a sensor node is used, which refers to the sensing area that is not overlapping with another sensor's sensing area. A sensor node and by compute it's ESA can be determine whether it will be active or sleep. The suggested  work permits to sensor nodes to be in sleep mode opportunistically whilst fulfill the needed sensing coverage.
- 
-%In~\cite{quang2008algorithm}, the authors defined a maximum sensing coverage region problem (MSCR) in WSNs and then proposed an algorithm to solve it. The
-%maximum observed area fully covered by a minimum active sensors. In this work, the major property is to getting rid from the redundant sensors  in high-density WSNs and putting them in sleep mode, and choosing a smaller number of active sensors so as to be sure  that the full area is k-covered, and all events appeared in that area can be precisely and timely detected. This algorithm minimized the total energy consumption and increased the lifetime.
-
-%A novel method to divide the sensors in the WSN, called node coverage grouping (NCG) suggested~\cite{lin2010partitioning}. The sensors in the connectivity group are within sensing range of each other, and the data collected by them in the same group are supposed to be similar. They are proved that dividing n sensors via NCG into connectivity groups is a NP-hard problem. So, a heuristic algorithm of NCG with time complexity of $O(n^3)$ is proposed.
-%For some applications, such as monitoring an ecosystem with extremely diversified environment, It might be premature assumption that sensors near to each other sense similar data.
-
-%In~\cite{zaidi2009minimum}, the problem of minimum cost coverage in which full coverage is performed by using the minimum number of sensors for an arbitrary geometric shape region is addressed.  a geometric solution to the minimum cost coverage problem under a deterministic deployment is proposed. The probabilistic coverage solution which provides a relationship between the probability of coverage and the number of randomly deployed sensors in an arbitrarily-shaped region is suggested. The authors are clarified that with a random deployment about seven times more nodes are required to supply full coverage.
-
-%A graph theoretical framework for connectivity-based coverage with configurable coverage granularity was proposed~\cite{dong2012distributed}. A new coverage criterion and scheduling approach is proposed based on cycle partition. This method is capable of build a sparse coverage set in distributed way by means of only connectivity information. This work considers only the communication range of the sensor is smaller two times the sensing range of sensor.
-
-%Liu et al.~\cite{liu2010energy} formulated maximum disjoint sets problem for retaining coverage and connectivity in WSN. Two algorithms are proposed for solving this problem, heuristic algorithm and network flow algorithm. This work did not take into account the sensor node failure, which is an unpredictable event because the two solutions are full centralized algorithms.
 
-%The work that presented in~\cite{aslanyan2013optimal} solved the coverage and connectivity problem in sensor networks in
-%an integrated way. The network lifetime is divided in a fixed number of rounds. A coverage bitmap of sensors of the domain has been generated in each round and based on this bitmap,  it has been decided which sensors
-%stay active or turn it to sleep. They checked the connection of the graph via laplacian of adjancy graph of active sensors in each round.  the generation of coverage bitmap by using  Minkowski technique, the network is able to providing the desired ratio of coverage. They have been defined the  connected coverage problem as an optimization problem and a centralized genetic algorithm is used to find the solution.
-
-%Several algorithms to retain the coverage and maximize the network lifetime were proposed in~\cite{cardei2006energy,wang2011coverage}. 
-
-%\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 (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 P{\scshape e}CO Protocol Description}
 \label{sec:The PeCO Protocol Description}
@@ -245,8 +205,6 @@ 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.
 
-% 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}
 \label{CI}
@@ -267,17 +225,16 @@ 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}
+$R_c$ satisfies $R_c  \geq 2 \cdot R_s$. In fact,  \citet{Zhang05}
 proved  that if  the  transmission  range fulfills  the  previous hypothesis,  the
 complete coverage of a convex area implies connectivity among active nodes.
 
-The PeCO protocol  uses the  same perimeter-coverage  model as  Huang and
-Tseng in~\cite{huang2005coverage}. It  can be expressed as follows:  a sensor is
+The PeCO protocol  uses the  same perimeter-coverage  model as \citet{huang2005coverage}. It  can be expressed as follows:  a sensor is
 said to be perimeter  covered if all the points on its  perimeter are covered by
 at least  one sensor  other than  itself.  They  proved that  a network  area is
 $k$-covered if and only if each sensor in the network is $k$-perimeter-covered (perimeter covered by at least $k$ sensors).
-%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{pcm2sensors}(a)  shows  the coverage  of  sensor  node~$0$. On  this
+ 
+Figure~\ref{figure1}(a)  shows  the coverage  of  sensor  node~$0$. On  this
 figure, we can  see that sensor~$0$ has  nine neighbors and we  have reported on
 its  perimeter (the  perimeter  of the  disk  covered by  the  sensor) for  each
 neighbor  the  two  points  resulting  from the intersection  of  the  two  sensing
@@ -289,15 +246,15 @@ arcs.
 \begin{figure}[ht!]
   \centering
   \begin{tabular}{@{}cr@{}}
-    \includegraphics[width=75mm]{figure1a.tiff} & \raisebox{3.25cm}{(a)} \\
-    \includegraphics[width=75mm]{figure1b.tiff} & \raisebox{2.75cm}{(b)}
+    \includegraphics[width=75mm]{figure1a.eps} & \raisebox{3.25cm}{(a)} \\
+    \includegraphics[width=75mm]{figure1b.eps} & \raisebox{2.75cm}{(b)}
   \end{tabular}
   \caption{(a) Perimeter  coverage of sensor node  0 and (b) finding  the arc of
     $u$'s perimeter covered by $v$.}
-  \label{pcm2sensors}
+  \label{figure1}
 \end{figure} 
 
-Figure~\ref{pcm2sensors}(b) describes the geometric information used to find the
+Figure~\ref{figure1}(b) describes the geometric information used to find the
 locations of the  left and right points of  an arc on the perimeter  of a sensor
 node~$u$ covered by a sensor node~$v$. Node~$v$ is supposed to be located on the
 west  side of  sensor~$u$,  with  the following  respective  coordinates in  the
@@ -314,8 +271,8 @@ The arc on the perimeter of~$u$ defined by the angular interval $[\pi
 
 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
+Figure~\ref{figure1}(a)  illustrates  the arcs  for  the  nine neighbors  of
+sensor $0$ and  figure~\ref{figure2} gives the position of  the corresponding arcs
 in  the interval  $[0,2\pi]$. More  precisely, we  can see  that the  points are
 ordered according  to the  measures of  the angles  defined by  their respective
 positions. The intersection points are  then visited one after another, starting
@@ -324,23 +281,20 @@ 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
+(the value is highlighted in yellow  at the bottom of figure~\ref{figure2}), which
 means that at most 2~neighbors can cover  the perimeter in addition to node $0$. 
 Table~\ref{my-label} summarizes for each coverage  interval the maximum level of
 coverage and  the sensor  nodes covering the  perimeter.  The  example discussed
 above is thus given by the sixth line of the table.
 
-%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*}[t!]
 \centering
-\includegraphics[width=127.5mm]{figure2.tiff}  
+\includegraphics[width=127.5mm]{figure2.eps}  
 \caption{Maximum coverage levels for perimeter of sensor node $0$.}
-\label{expcm}
+\label{figure2}
 \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.
 
 
 
@@ -373,29 +327,24 @@ above is thus given by the sixth line of the table.
 \end{table}
 
 
-%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 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 $\infty$
+figure~\ref{figure3}, the maximum coverage level for  this arc is set to $\infty$
 and  the  corresponding  interval  will  not   be  taken  into  account  by  the
 optimization algorithm.
- 
+
+ \newpage
 \begin{figure}[h!]
 \centering
-\includegraphics[width=62.5mm]{figure3.tiff}  
+\includegraphics[width=62.5mm]{figure3.eps}  
 \caption{Sensing range outside the WSN's area of interest.}
-\label{ex4pcm}
+\label{figure3}
 \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 $-2R$.
-%\begin{figure}[ht!]
-%\centering
-%\includegraphics[width=75mm]{ex5pcm.jpg}  
-%\caption{Coverage intervals and contributing sensors for sensor node 0 having a  part of its sensing range outside the border.}
-%\label{ex5pcm}
-%\end{figure} 
+
 
 \subsection{The Main Idea}
 
@@ -404,7 +353,7 @@ 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
+As  shown in  figure~\ref{figure4}, node  activity  scheduling is  produced by  our
 protocol in a periodic manner. Each period is divided into 4 stages: Information
 (INFO)  Exchange,  Leader Election,  Decision  (the  result of  an  optimization
 problem),  and  Sensing.   For  each  period there  is  exactly  one  set  cover
@@ -424,13 +373,13 @@ the area.
 
 \begin{figure}[t!]
 \centering
-\includegraphics[width=80mm]{figure4.tiff}  
+\includegraphics[width=80mm]{figure4.eps}  
 \caption{PeCO protocol.}
-\label{fig2}
+\label{figure4}
 \end{figure} 
 
 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
   subregion for information exchange.
@@ -438,10 +387,10 @@ We define two types of packets to be used by PeCO protocol:
   to transmit to  them their respective status (stay Active  or go Sleep) during
   sensing phase.
 \end{itemize}
-%\end{enumerate}
+
 
 Five status are possible for a sensor node in the network:
-%\begin{enumerate}[(a)] 
+
 \begin{itemize} 
 \item LISTENING: waits for a decision (to be active or not);
 \item COMPUTATION: executes the optimization algorithm as leader to
@@ -450,8 +399,7 @@ Five status are possible for a sensor node in the network:
 \item SLEEP: node is turned off;
 \item COMMUNICATION: transmits or receives packets.
 \end{itemize}
-%\end{enumerate}
-%Below, we describe each phase in more details.
+
 
 \subsection{PeCO Protocol Algorithm}
 
@@ -460,53 +408,49 @@ 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.
 
 
-\iffalse
+
 \begin{algorithm}      
  % \KwIn{all the parameters related to information exchange}
 %  \KwOut{$winer-node$ (: the id of the winner sensor node, which is the leader of current round)}
-  \BlankLine
+%  \BlankLine
   %\emph{Initialize the sensor node and determine it's position and subregion} \; 
   
-  \If{ $RE_k \geq E_{th}$ }{
-      \emph{$s_k.status$ = COMMUNICATION}\;
-      \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 $}{
-         \emph{$s_k.status$ = COMPUTATION}\;
-         
-      \If{$ s_k.ID $ is Not previously selected as a Leader }{
-          \emph{ Execute the 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)}{
-      
-      	 \emph{ Use the same previous cover set for current sensing stage}\;
-      }
-      \Else{
-            \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{Send $ActiveSleep()$ to each node $l$ in subregion}\;
-        \emph{Update $RE_k $}\;
-      }	  
-      \Else{
-        \emph{$s_k.status$ = LISTENING}\;
-        \emph{Wait $ActiveSleep()$ packet from the Leader}\;
-        \emph{Update $RE_k $}\;
-      }  
-  }
-  \Else { Exclude $s_k$ from entering in the current sensing stage}
-  }
-%\caption{PeCO($s_k$)}
+\noindent{\bf If} $RE_k \geq E_{th}$ {\bf then}\\
+\hspace*{0.6cm} \emph{$s_k.status$ = COMMUNICATION;}\\
+\hspace*{0.6cm}  \emph{Send $INFO()$ packet to other nodes in subregion;}\\
+\hspace*{0.6cm}  \emph{Wait $INFO()$ packet from other nodes in subregion;}\\
+\hspace*{0.6cm} \emph{Update K.CurrentSize;}\\
+\hspace*{0.6cm}  \emph{LeaderID = Leader election;}\\
+\hspace*{0.6cm} {\bf If} $ s_k.ID = LeaderID $ {\bf then}\\
+\hspace*{1.2cm}   \emph{$s_k.status$ = COMPUTATION;}\\
+\hspace*{1.2cm}{\bf If} \emph{$ s_k.ID $ is Not previously selected as a Leader} {\bf then}\\
+\hspace*{1.8cm} \emph{ Execute the perimeter coverage model;}\\
+\hspace*{1.2cm} {\bf end}\\
+\hspace*{1.2cm}{\bf If} \emph{($s_k.ID $ is the same Previous Leader)~And~(K.CurrentSize = K.PreviousSize)}\\
+\hspace*{1.8cm} \emph{ Use the same previous cover set for current sensing stage;}\\
+\hspace*{1.2cm}  {\bf end}\\
+\hspace*{1.2cm}  {\bf else}\\
+\hspace*{1.8cm}\emph{Update $a^j_{ik}$; prepare data for IP~Algorithm;}\\
+\hspace*{1.8cm} \emph{$\left\{\left(X_{1},\dots,X_{l},\dots,X_{K}\right)\right\}$ = Execute Integer Program Algorithm($K$);}\\
+\hspace*{1.8cm} \emph{K.PreviousSize = K.CurrentSize;}\\
+\hspace*{1.2cm}  {\bf end}\\
+\hspace*{1.2cm}\emph{$s_k.status$ = COMMUNICATION;}\\
+\hspace*{1.2cm}\emph{Send $ActiveSleep()$ to each node $l$ in subregion;}\\
+\hspace*{1.2cm}\emph{Update $RE_k $;}\\
+\hspace*{0.6cm}  {\bf end}\\
+\hspace*{0.6cm}  {\bf else}\\
+\hspace*{1.2cm}\emph{$s_k.status$ = LISTENING;}\\
+\hspace*{1.2cm}\emph{Wait $ActiveSleep()$ packet from the Leader;}\\
+\hspace*{1.2cm}\emph{Update $RE_k $;}\\
+\hspace*{0.6cm}  {\bf end}\\
+{\bf end}\\
+{\bf else}\\
+\hspace*{0.6cm} \emph{Exclude $s_k$ from entering in the current sensing stage;}\\
+{\bf end}\\
 \label{alg:PeCO}
 \end{algorithm}
-\fi
+
+
 
 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
@@ -522,9 +466,6 @@ 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.
 
 \section{Perimeter-based Coverage Problem Formulation}
 \label{cp}
@@ -550,12 +491,9 @@ a^j_{ik} = \left \{
   	&	\mbox{coverage interval $i$ of sensor $j$}, \\
   0 & \mbox{otherwise.}\\
 \end{array} \right.
-%\label{eq12} 
-%\notag
 \end{equation}
 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.
-%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
@@ -578,51 +516,30 @@ 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. 
-
-%\noindent In this paper, let us define some parameters, which are used in our protocol.
-%the set of segment points is denoted by $I$, the set of all sensors in the network by $J$, and the set of alive sensors within $J$ by $K$.
-
 
-%\noindent \begin{equation}
-%X_{k} = \left \{ 
-%\begin{array}{l l}
- % 1& \mbox{if sensor $k$  is active,} \\
-%  0 &  \mbox{otherwise.}\\
-%\end{array} \right.
-%\label{eq11} 
-%\notag
-%\end{equation}
 
-%\noindent $M^j_i (undercoverage): $ 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 $j$.
 
 Our coverage optimization problem can then be mathematically expressed as follows: 
-%Objective:
-\begin{equation} %\label{eq:ip2r}
+
+\begin{equation} 
 \left \{
 \begin{array}{ll}
 \min \sum_{j \in S} \sum_{i \in I_j} (\alpha^j_i ~ M^j_i + \beta^j_i ~ V^j_i )&\\
 \textrm{subject to :}&\\
 \sum_{k \in A} ( a^j_{ik} ~ X_{k}) + M^j_i  \geq l \quad \forall i \in I_j, \forall j \in S\\
-%\label{c1} 
 \sum_{k \in A} ( a^j_{ik} ~ X_{k}) - V^j_i  \leq l \quad \forall i \in I_j, \forall j \in S\\
-% \label{c2}
-% \Theta_{p}\in \mathbb{N}, &\forall p \in P\\
-% U_{p} \in \{0,1\}, &\forall p \in P\\
 X_{k} \in \{0,1\}, \forall k \in A
 \end{array}
 \right.
-%\notag
 \end{equation}
+
 $\alpha^j_i$ and $\beta^j_i$  are nonnegative weights selected  according to the
 relative importance of satisfying the associated level of coverage. For example,
 weights associated with  coverage intervals of a specified part  of a region may
 be  given by a  relatively larger  magnitude than  weights associated  with another
 region. This  kind of integer program  is inspired from the  model developed for
 brachytherapy treatment planning  for optimizing dose  distribution
-\cite{0031-9155-44-1-012}. The integer  program must be solved by  the leader in
+\citep{0031-9155-44-1-012}. The integer  program must be solved by  the leader in
 each subregion at the beginning of  each sensing phase, whenever the environment
 has  changed (new  leader,  death of  some  sensors). Note  that  the number  of
 constraints in the model is constant  (constraints of coverage expressed for all
@@ -632,22 +549,22 @@ 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}
+
 
 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}.
+and we use the same energy consumption than in our previous work~\citep{Idrees2}.
 Table~\ref{table3} gives the chosen parameters settings.
 
 \begin{table}[ht]
 \tbl{Relevant parameters for network initialization \label{table3}}{
-% title of Table
+
 \centering
-% used for centering table
+
 \begin{tabular}{c|c}
-% centered columns (4 columns)
+
 \hline
 Parameter & Value  \\ [0.5ex]
    
@@ -656,21 +573,20 @@ Parameter & Value  \\ [0.5ex]
 Sensing field & $(50 \times 25)~m^2 $   \\
 
 WSN size &  100, 150, 200, 250, and 300~nodes   \\
-%\hline
+
 Initial energy  & in range 500-700~Joules  \\  
-%\hline
+
 Sensing period & duration of 60 minutes \\
 $E_{th}$ & 36~Joules\\
 $R_s$ & 5~m   \\     
-%\hline
+
 $\alpha^j_i$ & 0.6   \\
-% [1ex] adds vertical space
-%\hline
+
 $\beta^j_i$ & 0.4
-%inserts single line
+
 \end{tabular}}
 
-% is used to refer this table in the text
+
 \end{table}
 To  obtain  experimental  results  which are  relevant,  simulations  with  five
 different node densities going from  100 to 300~nodes were performed considering
@@ -697,7 +613,7 @@ in covering the interval.
 We introduce the following performance metrics to evaluate the efficiency of our
 approach.
 
-%\begin{enumerate}[i)]
+
 \begin{itemize}
 \item {\bf Network Lifetime}: the lifetime  is defined as the time elapsed until
   the  coverage  ratio  falls  below a  fixed  threshold.   $Lifetime_{95}$  and
@@ -711,12 +627,12 @@ approach.
   observe the area of interest. In our  case, we discretized the sensor field as
   a regular grid, which yields the following equation:
   
-%\begin{equation*}
+
 \[
     \scriptsize
     \mbox{CR}(\%) = \frac{\mbox{$n$}}{\mbox{$N$}} \times 100
 \]
-%  \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
@@ -726,12 +642,12 @@ approach.
   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.
@@ -739,13 +655,13 @@ approach.
   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
@@ -757,31 +673,31 @@ approach.
   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}
 
 In  order  to  assess and  analyze  the  performance  of  our protocol  we  have
-implemented PeCO protocol in  OMNeT++~\cite{varga} simulator.  Besides PeCO, two
+implemented PeCO protocol in  OMNeT++~\citep{varga} simulator.  Besides PeCO, two
 other  protocols,  described  in  the  next paragraph,  will  be  evaluated  for
 comparison purposes.   The simulations were run  on a DELL laptop  with an Intel
-Core~i3~2370~M (2.4~GHz)  processor (2  cores) whose MIPS  (Million Instructions
+Core~i3~2370~M (1.8~GHz)  processor (2  cores) whose MIPS  (Million Instructions
 Per Second) rate  is equal to 35330. To  be consistent with the use  of a sensor
 node based on  Atmels AVR ATmega103L microcontroller (6~MHz) having  a MIPS rate
 equal to 6,  the original execution time  on the laptop is  multiplied by 2944.2
 $\left(\frac{35330}{2} \times  \frac{1}{6} \right)$.  The modeling  language for
-Mathematical Programming (AMPL)~\cite{AMPL} is  employed to generate the integer
+Mathematical Programming (AMPL)~\citep{AMPL} is  employed to generate the integer
 program instance  in a  standard format, which  is then read  and solved  by the
 optimization solver  GLPK (GNU  linear Programming Kit  available in  the public
-domain) \cite{glpk} through a Branch-and-Bound method.
+domain) \citep{glpk} through a Branch-and-Bound method.
 
 As said previously, the PeCO is  compared to three other approaches. The first
 one,  called  DESK,  is  a  fully distributed  coverage  algorithm  proposed  by
-\cite{ChinhVu}. The second one,  called GAF~\cite{xu2001geography}, consists in
+\citep{ChinhVu}. The second one,  called GAF~\citep{xu2001geography}, consists in
 dividing  the monitoring  area into  fixed  squares. Then,  during the  decision
 phase, in each square, one sensor is  chosen to remain active during the sensing
-phase. The last  one, the DiLCO protocol~\cite{Idrees2}, is  an improved version
-of a research work we presented in~\cite{idrees2014coverage}. Let us notice that
+phase. The last  one, the DiLCO protocol~\citep{Idrees2}, is  an improved version
+of a research work we presented in~\citep{idrees2014coverage}. Let us notice that
 PeCO and  DiLCO protocols are  based on the  same framework. In  particular, the
 choice for the simulations of a partitioning in 16~subregions was made because
 it corresponds to the configuration producing  the best results for DiLCO. The
@@ -794,7 +710,7 @@ one ($l=1$).
 
 \subsubsection{\bf Coverage Ratio}
 
-Figure~\ref{fig333}  shows the  average coverage  ratio for  200 deployed  nodes
+Figure~\ref{figure5}  shows the  average coverage  ratio for  200 deployed  nodes
 obtained with the  four protocols. DESK, GAF, and DiLCO  provide a slightly better
 coverage ratio with respectively 99.99\%,  99.91\%, and 99.02\%, compared to the 98.76\%
 produced by  PeCO for the  first periods. This  is due to  the fact that  at the
@@ -811,38 +727,36 @@ substantial increase of the coverage performance.
 \centering
  \includegraphics[scale=0.5] {figure5.eps} 
 \caption{Coverage ratio for 200 deployed nodes.}
-\label{fig333}
+\label{figure5}
 \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 PeCO protocol. The coverage ratio of PeCO 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. 
 
 
 \subsubsection{\bf Active Sensors Ratio}
 
 Having the less active sensor nodes in  each period is essential to minimize the
-energy consumption  and thus to  maximize the network  lifetime.  Figure~\ref{fig444}
+energy consumption  and thus to  maximize the network  lifetime.  Figure~\ref{figure6}
 shows the  average active nodes ratio  for 200 deployed nodes.   We observe that
 DESK and  GAF have 30.36  \% and  34.96 \% active  nodes for the  first fourteen
 rounds and  DiLCO and PeCO  protocols compete perfectly  with only 17.92~\% and
 20.16~\% active  nodes during the same  time interval. As the  number of periods
 increases, PeCO protocol  has a lower number of active  nodes in comparison with
 the three other approaches, while keeping a greater coverage ratio as shown in
-Figure \ref{fig333}.
+figure \ref{figure5}.
 
 \begin{figure}[h!]
 \centering
 \includegraphics[scale=0.5]{figure6.eps}  
 \caption{Active sensors ratio for 200 deployed nodes.}
-\label{fig444}
+\label{figure6}
 \end{figure} 
 
 \subsubsection{\bf Energy Consumption}
 
 We studied the effect of the energy  consumed by the WSN during the communication,
 computation, listening, active, and sleep status for different network densities
-and  compared  it for  the  four  approaches.  Figures~\ref{fig3EC}(a)  and  (b)
+and  compared  it for  the  four  approaches.  Figures~\ref{figure7}(a)  and  (b)
 illustrate  the  energy   consumption  for  different  network   sizes  and  for
 $Lifetime95$ and  $Lifetime50$. The results show  that our PeCO protocol  is the
 most competitive  from the energy  consumption point of  view. As shown  in both
@@ -860,28 +774,23 @@ while keeping a good coverage level.
     \includegraphics[scale=0.475]{figure7b.eps} & \raisebox{2.75cm}{(b)}
   \end{tabular}
   \caption{Energy consumption per period for (a)~$Lifetime_{95}$ and (b)~$Lifetime_{50}$.}
-  \label{fig3EC}
+  \label{figure7}
 \end{figure} 
 
-%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}
-
 \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
+Figures~\ref{figure8}(a)  and (b),  $Lifetime95$ and  $Lifetime50$ are  shown for
 different  network  sizes.   As  highlighted  by  these  figures,  the  lifetime
 increases with the size  of the network, and it is clearly   largest for DiLCO
 and PeCO  protocols.  For instance,  for a  network of 300~sensors  and coverage
-ratio greater than 50\%, we can  see on Figure~\ref{fig3LT}(b) that the lifetime
+ratio greater than 50\%, we can  see on figure~\ref{figure8}(b) that the lifetime
 is about twice longer with  PeCO compared to DESK protocol.  The performance
-difference    is    more    obvious   in    Figure~\ref{fig3LT}(b)    than    in
-Figure~\ref{fig3LT}(a) because the gain induced  by our protocols increases with
+difference    is    more    obvious   in    figure~\ref{figure8}(b)    than    in
+figure~\ref{figure8}(a) because the gain induced  by our protocols increases with
  time, and the lifetime with a coverage  of 50\% is far  longer than with
 95\%.
 
@@ -893,12 +802,12 @@ Figure~\ref{fig3LT}(a) because the gain induced  by our protocols increases with
   \end{tabular}
   \caption{Network Lifetime for (a)~$Lifetime_{95}$ \\
     and (b)~$Lifetime_{50}$.}
-  \label{fig3LT}
+  \label{figure8}
 \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, 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
+
+Figure~\ref{figure9}  compares  the  lifetime  coverage of  our  protocols  for
 different coverage  ratios. We denote by  Protocol/50, Protocol/80, Protocol/85,
 Protocol/90, and  Protocol/95 the amount  of time  during which the  network can
 satisfy an area coverage greater than $50\%$, $80\%$, $85\%$, $90\%$, and $95\%$
@@ -913,10 +822,10 @@ not ineffective for the smallest network sizes.
 \begin{figure}[h!]
 \centering \includegraphics[scale=0.5]{figure9.eps}
 \caption{Network lifetime for different coverage ratios.}
-\label{figLTALL}
+\label{figure9}
 \end{figure} 
 
-%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}
@@ -934,24 +843,18 @@ 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.
+
 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;
+
 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;
+
 Finally,  it   would  be   interesting  to  implement   our  protocol   using  a
 sensor-testbed to evaluate it in real world applications.
 
