Michel : Abstract + Intro (en cours)

[LiCO.git] / LiCO_Journal.tex

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@@ -1,12 +1,9 @@
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-\title{Lifetime Coverage Optimization Protocol in Wireless Sensor Networks}  %LiCO Protocol
-
- 
+\title{Lifetime Coverage Optimization Protocol \\
+  in Wireless Sensor Networks}  %LiCO Protocol 

 
 \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, Belfort, France. Email: ali.idness@edu.univ-fcomte.fr, $\lbrace$karine.deschinkel, michel.salomon, raphael.couturier$\rbrace$@univ-fcomte.fr}}
-%\thanks{J. Doe and J. Doe are with Anonymous University.}% <-this % stops a space
-%\thanks{Manuscript received April 19, 2005; revised December 27, 2012.}}
- 
-\markboth{IEEE Communications Letters,~Vol.~11, No.~4, December~2014}%
-{Shell \MakeLowercase{\textit{et al.}}: Bare Demo of IEEEtran.cls for Journals}
+        \thanks{The authors are with FEMTO-ST Institute, UMR 6174 CNRS, University of Franche-Comt\'e,
+          Belfort, France. Email: ali.idness@edu.univ-fcomte.fr, $\lbrace$karine.deschinkel,
+          michel.salomon, raphael.couturier$\rbrace$@univ-fcomte.fr}}

 
 

+\markboth{IEEE Communications Letters,~Vol.~XX, No.~Y, January 2015}%
+{Shell \MakeLowercase{\textit{et al.}}: Bare Demo of IEEEtran.cls for Journals}

 
 \maketitle
 
 
 \maketitle
 

-

 \begin{abstract}
 \begin{abstract}

-
-
- One fundamental issue in Wireless Sensor Networks (WSNs) is the lifetime coverage optimization, which reflects how well a WSN is covered by a wireless sensors so that the network lifetime can be maximized. In this paper, a Lifetime Coverage Optimization Protocol (LiCO) in WSNs is proposed. The surveillance region is divided into subregions and LiCO protocol is distributed among sensor nodes in each subregion. LiC0 protocols works into periods, each period is divided into four stages: Information exchange, Leader Election, Optimization Decision, and Sensing. Schedules node activities (wakeup and sleep of sensors) is performed in each subregion by a leader whose selection is the result of cooperation between nodes within the same subregion. The novelty of the approach lies essentially in the formulation of a new mathematical optimization model based on perimeter coverage level to schedule sensors activities. Extensive simulation experiments have been performed using OMNeT++, the discrete event simulator, to demonstrate that LiCO is capable to extend the lifetime coverage of WSN as longer time as possible in comparison with some other protocols.
-
-\end{abstract}
-
+The most important problem in Wireless Sensor Networks (WSNs) is to optimize the
+use of its limited energy provision, so  that it can fulfill its monitoring task
+as  long as  possible. Among  known  available approaches  that can  be used  to
+improve  power  management,  lifetime coverage  optimization  provides  activity
+scheduling which ensures  sensing coverage while minimizing the  energy cost. In
+this paper,  we propose  a such approach  called Lifetime  Coverage Optimization
+protocol (LiCO).   It is a  hybrid of  centralized and distributed  methods: the
+region of interest is first subdivided  into subregions and our protocol is then
+distributed among sensor nodes in each  subregion. A sensor node which runs LiCO
+protocol  repeats   periodically  four  stages:  information   exchange,  leader
+election, optimization decision, and sensing.  More precisely, the scheduling of
+nodes activities (sleep/wakeup  duty cycles) is achieved in each  subregion by a
+leader selected after  cooperation between nodes within the  same subregion. The
+novelty of  approach lies essentially in  the formulation of a  new mathematical
+optimization  model  based  on  perimeter coverage  level  to  schedule  sensors
+activities.  Extensive simulation experiments have been performed using OMNeT++,
+the  discrete event  simulator, to  demonstrate that  LiCO is  capable to  offer
+longer lifetime coverage for WSNs in comparison with some other protols.
+\end{abstract} 

 
 % Note that keywords are not normally used for peerreview papers.
 \begin{IEEEkeywords}
 Wireless Sensor Networks, Area Coverage, Network lifetime, Optimization, Scheduling.
 \end{IEEEkeywords}
 
 
 % Note that keywords are not normally used for peerreview papers.
 \begin{IEEEkeywords}
 Wireless Sensor Networks, Area Coverage, Network lifetime, Optimization, Scheduling.
 \end{IEEEkeywords}
 

-

 \IEEEpeerreviewmaketitle
 
 \IEEEpeerreviewmaketitle
 

-
-
-
-

 \section{\uppercase{Introduction}}
 \label{sec:introduction}
 \section{\uppercase{Introduction}}
 \label{sec:introduction}

-\noindent The great development in  Micro Electro-Mechanical Systems (MEMS) and wireless communication hardware are being led to emerge networks of tiny distributed sensors called WSN~\cite{akyildiz2002wireless,puccinelli2005wireless}. WSN comprises of small, low-powered sensors working together for perform a typical mission by communicating with one another through multihop wireless connections. They can send the sensed measurements based on local decisions to the user by means of sink nodes. WSN has been used in many applications such as Military, Habitat, Environment, Health, industrial, and Business~\cite{yick2008wireless}.Typically, a sensor node contains three main parts~\cite{anastasi2009energy}: a sensing subsystem, for sense, measure, and gather the measurements from the real environment; processing subsystem, for measurements processing and storage; a communication subsystem, for data transmission and receiving. Moreover,  the energy needed by the sensor node is supplied by a power supply, to accomplish the scheduled task. This power supply is composed of a battery with a limited lifetime. And it maybe be unsuitable or impossible to replace or recharge the batteries in most applications. It is then necessary to deploy the WSN with high density so as to increase the reliability and to exploit redundancy by using energy-efficient activity scheduling approaches. So, the main question is: how to extend the lifetime coverage of WSN as long time as possible while ensuring a high level of coverage? Many energy-efficient mechanisms have been suggested to retain energy and extend the lifetime of the WSNs~\cite{rault2014energy}. 
+
+\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
+tasks.   A  WSN  consists  of  small low-powered  sensors  working  together  by
+communicating with one another through  multihop 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  son~\cite{yick2008wireless}.  Typically,  a sensor  node contains
+three main components~\cite{anastasi2009energy}: a  sensing unit able to measure
+physical,  chemical, or  biological  phenomena observed  in  the environment;  a
+processing  unit  which  will  process  and store  the  measurements  which  are
+collected; a radio communication unit for data transmission and receiving.
+
+The energy needed  by an active sensor node to  perform sensing, processing, and
+communication is supplied by a power supply which is a battery. This battery has
+a limited energy provision and it may  be unsuitable or impossible to replace or
+recharge it in  most applications. Therefore it is necessary  to deploy WSN with
+high density in order to increase the reliability and to exploit node redundancy
+thanks to energy-efficient activity  scheduling approaches.  Indeed, the overlap
+of sensing  areas can be exploited  to schedule alternatively some  sensors in a
+low power sleep mode and thus save  energy. Overall, the main question that must
+be answered is: how to extend the lifetime coverage of a WSN as long as possible
+while  ensuring   a  high  level   of  coverage?   So,  this  last   years  many
+energy-efficient mechanisms have been suggested  to retain energy and extend the
+lifetime of the WSNs~\cite{rault2014energy}.

 
 %The sensor system ought to have a lifetime long enough to satisfy the application necessities. The lifetime coverage maximization is one of the fundamental requirements of any area coverage protocol in WSN implementation~\cite{nayak2010wireless}. In order to increase the reliability and prevent the possession of coverage holes (some parts are not covered in the area of interest) in the WSN, it is necessary to deploy the WSN with high density so as to increase the reliability and to exploit redundancy by using energy-efficient activity scheduling approaches.
 
 %From a certain standpoint, the high coverage ratio is required by many applications such as military and health-care. Therefore, a suitable number of sensors are being chosen so as to cover the area of interest, is the first challenge. Meanwhile, the sensor nodes have a limited capabilities in terms of memory, processing, communication, and battery power being the most important and critical one.  So, the main question is: how to extend the lifetime coverage of WSN as long time as possible?. There are many energy-efficient mechanisms have been suggested to retain energy and extend the lifetime of the WSNs~\cite{rault2014energy}.
 
 
 %The sensor system ought to have a lifetime long enough to satisfy the application necessities. The lifetime coverage maximization is one of the fundamental requirements of any area coverage protocol in WSN implementation~\cite{nayak2010wireless}. In order to increase the reliability and prevent the possession of coverage holes (some parts are not covered in the area of interest) in the WSN, it is necessary to deploy the WSN with high density so as to increase the reliability and to exploit redundancy by using energy-efficient activity scheduling approaches.
 
 %From a certain standpoint, the high coverage ratio is required by many applications such as military and health-care. Therefore, a suitable number of sensors are being chosen so as to cover the area of interest, is the first challenge. Meanwhile, the sensor nodes have a limited capabilities in terms of memory, processing, communication, and battery power being the most important and critical one.  So, the main question is: how to extend the lifetime coverage of WSN as long time as possible?. There are many energy-efficient mechanisms have been suggested to retain energy and extend the lifetime of the WSNs~\cite{rault2014energy}.
 

-%\uppercase{\textbf{Our contributions.}} 
-This paper makes the following contributions.\\
+%\uppercase{\textbf{Our contributions.}}
+
+% MICHEL - TO CONTINUED FROM HERE
+This paper makes the following contributions.

 \begin{enumerate}
 \begin{enumerate}

-\item We devise a framework to schedules nodes to be activated alternatively, such that the network lifetime may be prolonged ans certain coverage reuirement can still be met. 
-This framework is based on the division of the area of interest into several smaller subregions; on the division of timeline into periods of equal length. 
-One leader 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
-\item We propose a new mathematical optimization model. Instead of trying to cover a set of specified points/targets as in most of the methods proposed in the literature, 
-we formulate an integer program based on perimeter coverage of each sensor. The model involves integer variables to capture the deviations between the 
-actual level of coverage and the required level. And a weighted sum of these deviations is minimized. 
-\item We conducted extensive simulation experiments using the discrete event simulator OMNeT++, to demonstrate the efficiency of our protocol, compared to two approaches found in the literature, DESK \ref{} and  GAF \ref{}, and compared to our previous work using another optimization model for sensor scheduling. 
+\item  We  devise a  framework  to  schedules  nodes to  be  activated
+  alternatively, such that  the network lifetime may  be prolonged ans
+  certain coverage  requirement can still  be met.  This  framework is
+  based on the  division of the area of interest  into several smaller
+  subregions;  on  the division  of  timeline  into periods  of  equal
+  length.  One leader is elected for each subregion in an independent,
+  distributed,  and  simultaneous way  by  the  cooperation among  the
+  sensor nodes within  each subregion, and this is  similar to cluster
+  architecture
+\item We  propose a  new mathematical  optimization model.  Instead of
+  trying to cover a set of  specified points/targets as in most of the
+  methods proposed in the literature,  we formulate an integer program
+  based  on perimeter  coverage  of each  sensor.  The model  involves
+  integer variables to capture the deviations between the actual level
+  of coverage  and the  required level.  And a  weighted sum  of these
+  deviations is minimized.
+\item We conducted extensive simulation experiments using the discrete
+  event  simulator  OMNeT++,  to  demonstrate the  efficiency  of  our
+  protocol, compared to  two approaches found in  the literature, DESK
+  \cite{ChinhVu} and  GAF \cite{xu2001geography}, and compared  to our
+  previous work using another optimization model for sensor scheduling
+  \cite{Idrees2}.

 \end{enumerate}
 
 
 \end{enumerate}
 
 


@@ -103,9 +149,13 @@ actual level of coverage and the required level. And a weighted sum of these dev
 % the second, activity scheduling based new optimization model has been used to provide the optimal cover set that will take the mission of sensing during current period. This optimization algorithm is based on a perimeter-coverage model so as to optimize the shared perimeter among the sensors in each subregion, and this represents as a energu-efficient control topology mechanism in WSN.
 
 
 % the second, activity scheduling based new optimization model has been used to provide the optimal cover set that will take the mission of sensing during current period. This optimization algorithm is based on a perimeter-coverage model so as to optimize the shared perimeter among the sensors in each subregion, and this represents as a energu-efficient control topology mechanism in WSN.
 
 

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

 future works in Section~\ref{sec:Conclusion and Future Works}.
 
 % that show that our protocol outperforms others protocols.
 future works in Section~\ref{sec:Conclusion and Future Works}.
 
 % that show that our protocol outperforms others protocols.


@@ -118,14 +168,14 @@ coverage problem and distinguish our  LiCO protocol from the works presented in
 the literature.
 
 The most discussed coverage problems  in literature can be classified into three
 the literature.
 
 The most discussed coverage problems  in literature can be classified into three

-types \cite{li2013survey}:  area coverage \cite{Misra} where  every point inside
+types \cite{li2013survey}: area coverage \cite{Misra} where every point inside

 an area is to be  monitored, target coverage \cite{yang2014novel} where the main
 objective is  to cover only a  finite number of discrete  points called targets,
 an area is to be  monitored, target coverage \cite{yang2014novel} where the main
 objective is  to cover only a  finite number of discrete  points called targets,

-and barrier coverage \cite{Kumar:2005}\cite{kim2013maximum} to prevent intruders
+and barrier coverage \cite{HeShibo}\cite{kim2013maximum} to prevent intruders

 from entering into the region  of interest. In \cite{Deng2012} authors transform
 the area coverage problem to the target coverage problem taking into account the
 intersection points among disks of sensors nodes or between disk of sensor nodes
 from entering into the region  of interest. In \cite{Deng2012} authors transform
 the area coverage problem to the target coverage problem taking into account the
 intersection points among disks of sensors nodes or between disk of sensor nodes

-and boundaries. In \cite{Huang:2003:CPW:941350.941367} authors prove that if the perimeters of sensors are sufficiently covered, the whole area is sufficiently covered and they provide an algorithm in $O(n d \quad log d)$ time to compute the perimeter-coverage of each sensor ($d$ the maixmum number of sensors that are neighboring to a sensor, $n$ the total number of sensors in teh network). {\it In LiCO protocol, rather than 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.}
+and boundaries. In \cite{Huang:2003:CPW:941350.941367} authors prove that if the perimeters of sensors are sufficiently covered, the whole area is sufficiently covered and they provide an algorithm in $O(nd~log~d)$ time to compute the perimeter-coverage of each sensor ($d$ the maximum number of sensors that are neighboring to a sensor, $n$ the total number of sensors in the network). {\it In LiCO protocol, instead of determining the level of coverage of a set of discrete points, our optimization model is based on checking the perimeter-coverage of each sensor to activate a minimal number of sensors.}

 
 The major  approach to extend network  lifetime while preserving  coverage is to
 divide/organize the  sensors into a suitable  number of set  covers (disjoint or
 
 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


@@ -232,20 +282,20 @@ the double objective  consisting in minimizing  the overcoverage and the
 \subsection{ Assumptions and Models}
 \noindent A WSN consisting of $J$ stationary sensor nodes randomly and uniformly distributed in a bounded sensor field is considered. The  wireless sensors  are deployed in high density to ensure initially a high coverage ratio of the interested area. We assume that all the sensor nodes are homogeneous in terms of  communication, sensing, and processing capabilities and heterogeneous in term of energy supply. The  location  information is available to the  sensor node  either through hardware such as embedded GPS or through location discovery algorithms. We assume that each sensor node can directly transmit its measurements to a mobile sink node. For example, a sink can be an unmanned aerial vehicle (UAV) flying regularly over the sensor field to collect measurements from sensor nodes. A mobile sink node collects the measurements and transmits them to the base station.  We consider a boolean  disk coverage model which is the most widely used sensor coverage model in the literature. Each sensor has a constant sensing range $R_s$. All space points within a disk centered at the sensor with the radius of the sensing range is said to be covered by this sensor. We also assume that the communication range $R_c \geq 2R_s$. In  fact,   Zhang  and Zhou~\cite{Zhang05} proved that if the transmission range fulfills the previous hypothesis, a complete coverage of a convex area implies connectivity among the working nodes in the active mode.
 
 \subsection{ Assumptions and Models}
 \noindent A WSN consisting of $J$ stationary sensor nodes randomly and uniformly distributed in a bounded sensor field is considered. The  wireless sensors  are deployed in high density to ensure initially a high coverage ratio of the interested area. We assume that all the sensor nodes are homogeneous in terms of  communication, sensing, and processing capabilities and heterogeneous in term of energy supply. The  location  information is available to the  sensor node  either through hardware such as embedded GPS or through location discovery algorithms. We assume that each sensor node can directly transmit its measurements to a mobile sink node. For example, a sink can be an unmanned aerial vehicle (UAV) flying regularly over the sensor field to collect measurements from sensor nodes. A mobile sink node collects the measurements and transmits them to the base station.  We consider a boolean  disk coverage model which is the most widely used sensor coverage model in the literature. Each sensor has a constant sensing range $R_s$. All space points within a disk centered at the sensor with the radius of the sensing range is said to be covered by this sensor. We also assume that the communication range $R_c \geq 2R_s$. In  fact,   Zhang  and Zhou~\cite{Zhang05} proved that if the transmission range fulfills the previous hypothesis, a complete coverage of a convex area implies connectivity among the working nodes in the active mode.
 

-\indent LiCO protocol uses the perimeter-coverage model which states in ~\cite{huang2005coverage} as following: The sensor is said to be perimeter covered if all the points on its perimeter are covered by at least one sensor other than itself. Huang and Tseng in \cite{huang2005coverage} proves that a network area is $k-covered$ if and only if each sensor in the network is $k-perimeter-covered$.
+\indent LiCO protocol uses the perimeter-coverage model which states in ~\cite{huang2005coverage} as following: The sensor is said to be perimeter covered if all the points on its perimeter are covered by at least one sensor other than itself. Huang and Tseng in \cite{huang2005coverage} proves that a network area is $k$-covered if and only if each sensor in the network is $k$-perimeter-covered.

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

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

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

-\includegraphics[width=75mm]{pcm.pdf}  
+\includegraphics[width=75mm]{pcm.jpg}  

 \caption{Perimeter coverage of sensor node 0}
 \label{pcmfig}
 \end{figure} 
 
 \caption{Perimeter coverage of sensor node 0}
 \label{pcmfig}
 \end{figure} 
 

-Figure~\ref{twosensors} demonstrates the way of locating the left and right points of a segment for a sensor node $u$ covered by a sensor node $v$. This figure supposed that the neighbor sensor node $v$ is located on the west of a sensor $u$. It is assumed  that the two sensor nodes $v$ and $u$ are located in the positions $(v_x,v_y)$ and $(u_x,u_y)$, respectively. The distance between $v$ and $u$ is computed by $Dist(u,v) = \sqrt{\vert u_x - v_x \vert^2 + \vert u_y - v_y \vert^2}$ . The angle $\alpha$ is computed through the formula $\alpha = arccos \left(\dfrac{Dist(u,v)}{2R_s} \right) $. So, the arch of sensor $u$ falling in the angle $[\pi - \alpha,\pi + \alpha]$, is said to be perimeter-covered by sensor node $v$. 
+Figure~\ref{twosensors} demonstrates the way of locating the left and right points of a segment for a sensor node $u$ covered by a sensor node $v$. This figure assumes that the neighbor sensor node $v$ is located on the west of a sensor $u$. It is assumed  that the two sensor nodes $v$ and $u$ are located in the positions $(v_x,v_y)$ and $(u_x,u_y)$, respectively. The distance between $v$ and $u$ is computed by $Dist(u,v) = \sqrt{\vert u_x - v_x \vert^2 + \vert u_y - v_y \vert^2}$. The angle $\alpha$ is computed through the formula $\alpha = arccos \left(\dfrac{Dist(u,v)}{2R_s} \right)$. So, the arch of sensor $u$ falling in the angle $[\pi - \alpha,\pi + \alpha]$, is said to be perimeter-covered by sensor node $v$. 

 
 

-The left and right points of each segment are placed on the line segment $[0,2\pi]$. Figure~\ref{pcmfig} illustrates the segments for the 9 neighbors of sensor $0$. The points reported on the line segment separates it in intervals. For each interval, we sump 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. The table in figure~\ref{expcm} summarizes the level of coverage for each interval and the sensors involved in.  
+The left and right points of each segment are placed on the line segment $[0,2\pi]$. Figure~\ref{pcmfig} illustrates the segments for the 9 neighbors of sensor $0$. The points reported on the line segment $[0,2\pi]$ separates it in intervals as shown in figure~\ref{expcm}. For example, for each neighboring sensor of sensor 0, place the points  $\alpha^ 1_L$, $\alpha^ 1_R$, $\alpha^ 2_L$, $\alpha^ 2_R$, $\alpha^ 3_L$, $\alpha^ 3_R$, $\alpha^ 4_L$, $\alpha^ 4_R$, $\alpha^ 5_L$, $\alpha^ 5_R$, $\alpha^ 6_L$, $\alpha^ 6_R$, $\alpha^ 7_L$, $\alpha^ 7_R$, $\alpha^ 8_L$, $\alpha^ 8_R$, $\alpha^ 9_L$, and $\alpha^ 9_R$; on the line segment $[0,2\pi]$, and then sort all these points in an ascending order into a list.  Traverse the line segment $[0,2\pi]$ by visiting each point in the sorted list from left to right and determine the coverage level of each interval of the sensor 0 (see figure \ref{expcm}). For each interval, we sum up the number of parts of segments, and we deduce a level of coverage for each interval. For instance, the interval delimited by the points $5L$ and $6L$ contains three parts of segments. That means that this part of the perimeter of the sensor $0$ may be covered by three sensors, sensor $0$ itself and sensors $2$ and $5$. The level of coverage of this interval may reach $3$ if all previously mentioned sensors are active. Let say that sensors $0$, $2$ and $5$ are involved in the coverage of this interval. Table~\ref{my-label} summarizes the level of coverage for each interval and the sensors involved in for sensor node 0 in figure~\ref{pcmfig}. 

 % to determine the level of the perimeter coverage for each left and right point of a segment.
 \begin{figure}[ht!]
 \centering
 % to determine the level of the perimeter coverage for each left and right point of a segment.
 \begin{figure}[ht!]
 \centering


@@ -254,6 +304,7 @@ The left and right points of each segment are placed on the line segment $[0,2\p
 \label{twosensors}
 \end{figure} 
 
 \label{twosensors}
 \end{figure} 
 

+

 \begin{figure}[ht!]
 \centering
 \includegraphics[width=75mm]{expcm.pdf}  
 \begin{figure}[ht!]
 \centering
 \includegraphics[width=75mm]{expcm.pdf}  


@@ -261,8 +312,18 @@ The left and right points of each segment are placed on the line segment $[0,2\p
 \label{expcm}
 \end{figure} 
 
 \label{expcm}
 \end{figure} 
 

+
+
+
+
+
+
+
+

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

+\iffalse
+

 \begin{figure}[ht!]
 \centering
 \includegraphics[width=90mm]{ex2pcm.jpg}  
 \begin{figure}[ht!]
 \centering
 \includegraphics[width=90mm]{ex2pcm.jpg}  


@@ -270,6 +331,37 @@ The left and right points of each segment are placed on the line segment $[0,2\p
 \label{ex2pcm}
 \end{figure} 
 
 \label{ex2pcm}
 \end{figure} 
 

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

 %The optimization algorithm that used by LiCO protocol based on the perimeter coverage levels of the left and right points of the segments and worked to minimize the number of sensor nodes for each left or right point of the segments within each sensor node. The algorithm minimize the perimeter coverage level of the left and right points of the segments, while, it assures that every perimeter coverage level of the left and right points of the segments greater than or equal to 1.
 
 In LiCO protocol, scheduling of sensor nodes'activities is formulated with an integer program based on coverage intervals and is detailed in section~\ref{cp}.
 %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.
 
 In LiCO protocol, scheduling of sensor nodes'activities is formulated with an integer program based on coverage intervals and is detailed in section~\ref{cp}.


@@ -281,13 +373,13 @@ In the case of sensor node, which has a part of its sensing range outside the bo
 \caption{Part of sensing range outside the the border of WSN sensing field.}
 \label{ex4pcm}
 \end{figure} 
 \caption{Part of sensing range outside the the border of WSN sensing field.}
 \label{ex4pcm}
 \end{figure} 

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


@@ -374,8 +466,8 @@ The pseudo-code for LiCO Protocol is illustrated as follows:
 
 \end{algorithm}
 
 
 \end{algorithm}
 

-\noindent Algorithm 1 gives a brief description of the protocol applied by each sensor node (denoted by $s_k$ for a sensor node indexed by $k$). In this algorithm, the K.CurrentSize and K.PreviousSize refer to the current size and the previous size of sensor nodes in the subregion respectively.
-Initially, the sensor node checks its remaining energy in order to participate in the current period. Each sensor node determines its position and its subregion based Embedded GPS  or Location Discovery Algorithm. After that, all the sensors collect position coordinates, remaining energy $RE_k$, sensor node id, and the number of its one-hop live neighbors during the information exchange. The sensors inside a same region cooperates to elect a leader. The selection criteria for the leader in order  of priority  are: larger number of neighbors,  larger remaining  energy, and  then in  case of equality, larger index. Thereafter the leader collects information to formulate and solve the integer program which allows to construct the set of active sensors in the sensing stage.  
+\noindent Algorithm 1 gives a brief description of the protocol applied by each sensor node (denoted by $s_k$ for a sensor node indexed by $k$). In this algorithm, the K.CurrentSize and K.PreviousSize refer to the current size and the previous size of sensor nodes still alive in the subregion respectively.
+Initially, the sensor node checks its remaining energy $RE_k$, which must be greater than a threshold $E_{th}$ in order to participate in the current period. Each sensor node determines its position and its subregion based Embedded GPS  or Location Discovery Algorithm. After that, all the sensors collect position coordinates, remaining energy, sensor node id, and the number of its one-hop live neighbors during the information exchange. The sensors inside a same region cooperate to elect a leader. The selection criteria for the leader in order  of priority  are: larger number of neighbors,  larger remaining  energy, and  then in  case of equality, larger index. Thereafter the leader collects information to formulate and solve the integer program which allows to construct the set of active sensors in the sensing stage.  

 
 
 %After the cooperation among the sensor nodes in the same subregion, the leader will be elected in distributed way, where each sensor node and based on it's information decide who is the leader. The selection criteria for the leader in order  of priority  are: larger number of neighbors,  larger remaining  energy, and  then in  case of equality, larger index. Thereafter,  if the sensor node is leader, it will execute the perimeter-coverage model for each sensor in the subregion in order to determine the segment points which would be used in the next stage by the optimization algorithm of the LiCO protocol. Every sensor node is selected as a leader, it is executed the perimeter coverage model only one time during it's life in the network.
 
 
 %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.


@@ -392,7 +484,7 @@ For convenience, the notations are described first.
 \noindent $A :$ the set of alive sensors within $S$.\\
 %\noindent $I :$ the set of segment points.\\
 \noindent $I_j :$ the set of coverage intervals (CI)  for sensor $j$.\\
 \noindent $A :$ the set of alive sensors within $S$.\\
 %\noindent $I :$ the set of segment points.\\
 \noindent $I_j :$ the set of coverage intervals (CI)  for sensor $j$.\\

-
+\noindent $I_j$ refers to the set of intervals which have been defined for each sensor $j$ in section~\ref{sec:The LiCO Protocol Description}.

 \noindent For a coverage interval  $i$,  let  $a^j_{ik}$ denote the indicator function of whether the sensor $k$ is involved in the coverage interval $i$ of sensor $j$, that is:
 
 \begin{equation}
 \noindent For a coverage interval  $i$,  let  $a^j_{ik}$ denote the indicator function of whether the sensor $k$ is involved in the coverage interval $i$ of sensor $j$, that is:
 
 \begin{equation}


@@ -405,9 +497,10 @@ a^j_{ik} = \left \{
 %\label{eq12} 
 \notag
 \end{equation}
 %\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 $k$. .   
 %, 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 $k$. .   

-We  consider binary variables $X_{k}$ ($X_k=1$ if the sensor $k$ is active or 0 otherwise), which determine the activation of sensor $k$ in the sensing phase. We define the integer variable $M^j_i$ which measures the undercoverage for the coverage interval $i$ for sensor $j$. In the same way, we define the integer variable $V^j_i$, which measures the overcoverage for the coverage interval $i$ for sensor $j$. If we decide to sustain a level of coverage equal to $l$ all along the perimeter of the sensor $j$, we have to ensure that at least $l$ sensors involved in each coverage interval $i$ ($i \in I_j$) of sensor $j$ are active. According to the previous notations, the number of active sensors in the coverage interval $i$ of sensor $j$ is given by $\sum_{k \in K} a^j_{ik} X_k$. To extend the network lifetime, the objective is to active a minimal number of sensors in each period to ensure the desired coverage level. As the number of alive sensors decreases, it becomes impossible to satisfy the level of coverage for all covergae intervals. We uses variables $M^j_i$ and $V^j_i$ as a measure of the deviation between the desired number of active sensors in a coverage interval and the effective number of active sensors. And we try to minimize these deviations, first to force the activation of a minimal number of sensors to ensure the desired coverage level, and if the desired level can not be completely  satisfied, to reach a coverage level as close as possible that the desired one.
+\noindent We  consider binary variables $X_{k}$ ($X_k=1$ if the sensor $k$ is active or 0 otherwise), which determine the activation of sensor $k$ in the sensing phase. We define the integer variable $M^j_i$ which measures the undercoverage for the coverage interval $i$ for sensor $j$. In the same way, we define the integer variable $V^j_i$, which measures the overcoverage for the coverage interval $i$ for sensor $j$. If we decide to sustain a level of coverage equal to $l$ all along the perimeter of the sensor $j$, we have to ensure that at least $l$ sensors involved in each coverage interval $i$ ($i \in I_j$) of sensor $j$ are active. According to the previous notations, the number of active sensors in the coverage interval $i$ of sensor $j$ is given by $\sum_{k \in K} a^j_{ik} X_k$. To extend the network lifetime, the objective is to active a minimal number of sensors in each period to ensure the desired coverage level. As the number of alive sensors decreases, it becomes impossible to satisfy the level of coverage for all covergae intervals. We uses variables $M^j_i$ and $V^j_i$ as a measure of the deviation between the desired number of active sensors in a coverage interval and the effective number of active sensors. And we try to minimize these deviations, first to force the activation of a minimal number of sensors to ensure the desired coverage level, and if the desired level can not be completely  satisfied, to reach a coverage level as close as possible that the desired one.

 
 
 
 
 
 


@@ -460,7 +553,7 @@ 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
 level of coverage. For example, weights associated with coverage intervals of a specified part of a region
 may be given a relatively
 larger magnitude than weights associated

-with another region. This kind of integer program is inspired from the model developed for brachytherapy treatment planning for optimizing dose distribution \ref{0031-9155-44-1-012}. The integer program must be solved by the leader in each subregion at the beginning of each sensing phase, whenever the environment has changed (new leader, death of some sensors). Note that the number of constraints in the model is constant (constraints of coverage expressed for all sensors), whereas the number of variables $X_k$ decreases over periods, since we consider only alive sensors (sensors with enough energy to be alive during one sensing phase) in the model. 
+with another region. This kind of integer program is inspired from the model developed for brachytherapy treatment planning for optimizing dose distribution \cite{0031-9155-44-1-012}. The integer program must be solved by the leader in each subregion at the beginning of each sensing phase, whenever the environment has changed (new leader, death of some sensors). Note that the number of constraints in the model is constant (constraints of coverage expressed for all sensors), whereas the number of variables $X_k$ decreases over periods, since we consider only alive sensors (sensors with enough energy to be alive during one sensing phase) in the model. 

 
 
 \section{\uppercase{PERFORMANCE EVALUATION AND ANALYSIS}}  
 
 
 \section{\uppercase{PERFORMANCE EVALUATION AND ANALYSIS}}  


@@ -469,7 +562,7 @@ with another region. This kind of integer program is inspired from the model dev
 
 \subsection{Simulation Settings}
 %\label{sub1}
 
 \subsection{Simulation Settings}
 %\label{sub1}

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

 
 \begin{table}[ht]
 \caption{Relevant parameters for network initializing.}
 
 \begin{table}[ht]
 \caption{Relevant parameters for network initializing.}


@@ -516,6 +609,8 @@ for one period (3600 seconds), and  adding the energy for the pre-sensing phases
 According to  the interval of initial energy,  a sensor may be  active during at
 most 20 rounds.
 
 According to  the interval of initial energy,  a sensor may be  active during at
 most 20 rounds.
 

+The values of $\alpha^j_i$ and $\beta^j_i$ have been chosen in a way that ensuring a good network coverage and for a longer time during the lifetime of the WSN.  We have given a higher priority for the undercoverage ( by setting the $\alpha^j_i$ with a larger value than $\beta^j_i$) so as to prevent the non-coverage for the interval i of the sensor j. On the other hand, we have given a little bit lower value for $\beta^j_i$ so as to minimize the number of active sensor nodes that contribute in covering the interval i in sensor j.
+

 In the simulations,  we introduce the following performance  metrics to evaluate
 the efficiency of our approach:
 
 In the simulations,  we introduce the following performance  metrics to evaluate
 the efficiency of our approach:
 


@@ -582,11 +677,11 @@ by the whole network in the sensing phase (active and sleeping nodes).
 %\end{enumerate}
 
 \subsection{Simulation Results}
 %\end{enumerate}
 
 \subsection{Simulation Results}

-In this section, we present the simulation results of LiCO protocol and the other protocols using a discrete event simulator OMNeT++ \cite{varga} to run different series of simulations. We implemented all protocols precisely on a laptop DELL with Intel Core~i3~2370~M (2.4 GHz)  processor (2 cores) and the MIPS (Million Instructions  Per Second) rate equal to 35330. To be consistent  with the use of a sensor node with Atmels AVR ATmega103L microcontroller (6 MHz) and  a MIPS rate  equal to 6,  the original execution time on the laptop is multiplied by  2944.2 $\left(\frac{35330}{2} \times  \frac{1}{6} \right)$  so as to use it by the energy consumption model especially, after the computation and listening. Employing the modeling language ????\ref{}, the associated integer program instance is generated in a standard format, which is then read and solved by the optimization solver GLPK (GNU linear Programming Kit available in the public domain) \cite{glpk} through a  Branch-and-Bound method. 
+In this section, we present the simulation results of LiCO protocol and the other protocols using a discrete event simulator OMNeT++ \cite{varga} to run different series of simulations. We implemented all protocols precisely on a laptop DELL with Intel Core~i3~2370~M (2.4 GHz)  processor (2 cores) and the MIPS (Million Instructions  Per Second) rate equal to 35330. To be consistent  with the use of a sensor node with Atmels AVR ATmega103L microcontroller (6 MHz) and  a MIPS rate  equal to 6,  the original execution time on the laptop is multiplied by  2944.2 $\left(\frac{35330}{2} \times  \frac{1}{6} \right)$  so as to use it by the energy consumption model especially, after the computation and listening. Employing the modeling language for Mathematical Programming (AMPL)~\cite{AMPL}, the associated integer program instance is generated in a standard format, which is then read and solved by the optimization solver GLPK (GNU linear Programming Kit available in the public domain) \cite{glpk} through a Branch-and-Bound method. 

  
 We compared LiCO protocol to three other approaches: the first, called DESK and proposed  by ~\cite{ChinhVu}  is a fully distributed  coverage  algorithm;  the second, called GAF  ~\cite{xu2001geography}, consists in dividing the region
 into fixed  squares.  During the decision  phase, in each square,  one sensor is
  
 We compared LiCO protocol to three other approaches: the first, called DESK and proposed  by ~\cite{ChinhVu}  is a fully distributed  coverage  algorithm;  the second, called GAF  ~\cite{xu2001geography}, consists in dividing the region
 into fixed  squares.  During the decision  phase, in each square,  one sensor is

-chosen to remain active during the sensing phase; the third, DiLCO protocol~\cite{Idrees2} is an improved version on the work presented in ~\cite{idrees2014coverage}.  DNote that the LiCO protocol is based on the same framework as that of DiLCO. For thes two protocols, the division of the region of interest in 16 subregions was chosen since it produces the best results. The difference between the two protocols relies on the use of the integer programming to provide the set of sensors that have to be actived in each sensing phase. Whereas DilCO protocol tries to satisfy the coverage of a set of primary points, LiCO protocol tries to reach a desired level of coverage $l$ for each sensor's perimeter. In the experimentations, we chose a level of coverage equal to 1 ($l=1$).
+chosen to remain active during the sensing phase; the third, DiLCO protocol~\cite{Idrees2} is an improved version on the work presented in ~\cite{idrees2014coverage}. Note that the LiCO protocol is based on the same framework as that of DiLCO. For these two protocols, the division of the region of interest in 16 subregions was chosen since it produces the best results. The difference between the two protocols relies on the use of the integer programming to provide the set of sensors that have to be activated in each sensing phase. Whereas DiLCO protocol tries to satisfy the coverage of a set of primary points, LiCO protocol tries to reach a desired level of coverage $l$ for each sensor's perimeter. In the experimentations, we chose a level of coverage equal to 1 ($l=1$).

 
 \subsubsection{\textbf{Coverage Ratio}}
 Figure~\ref{fig333} shows the average coverage ratio for 200 deployed nodes obtained with the four methods.
 
 \subsubsection{\textbf{Coverage Ratio}}
 Figure~\ref{fig333} shows the average coverage ratio for 200 deployed nodes obtained with the four methods.


@@ -599,7 +694,7 @@ Figure~\ref{fig333} shows the average coverage ratio for 200 deployed nodes obta
 \label{fig333}
 \end{figure} 
 
 \label{fig333}
 \end{figure} 
 

-DESK,  GAF, and DiLCO provides a little better coverage ratio with 99.99\%, 99.91\%, and 99.02\% against 98.76\% produced by LiCO for the lowest number of periods. This is due to the fact that DiLCO protocol put in sleep mode redundant sensors using optimization (which lightly decreases the coverage ratio) while there are more active nodes in the case of others methods. But when the number of periods exceeds 70 periods, it clearly appears that LiCO provides a better coverage ratio and keeps a coverage ratio greater than 50\% for longer periods (15 more compared to DiLCO, 40 more compared to DESK).
+DESK,  GAF, and DiLCO provide a little better coverage ratio with 99.99\%, 99.91\%, and 99.02\% against 98.76\% produced by LiCO for the first periods. This is due to the fact that DiLCO protocol put in sleep mode redundant sensors using optimization (which lightly decreases the coverage ratio) while there are more active nodes in the case of others methods. But when the number of periods exceeds 70 periods, it clearly appears that LiCO provides a better coverage ratio and keeps a coverage ratio greater than 50\% for longer periods (15 more compared to DiLCO, 40 more compared to DESK).

 
 %When the number of periods increases, coverage ratio produced by DESK and GAF protocols decreases. This is due to dead nodes. However, DiLCO protocol maintains almost a good coverage from the round 31 to the round 63 and it is close to 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 LiCO protocol. The coverage ratio of LiCO protocol is better than other approaches from the period 64.
 


@@ -619,7 +714,7 @@ Having active nodes as few as possible in each period is essential in order to m
 We observe that DESK and GAF have 30.36 \% and 34.96 \% active nodes for the first fourteen rounds and DiLCO and LiCO protocols compete perfectly with only 17.92 \% and 20.16 \% active nodes during the same time interval. As the number of periods increases, LiCO protocol has a lower number of active nodes in comparison with the three other approaches, while keeping of greater coverage ratio as shown in figure \ref{fig333}.
 
 \subsubsection{\textbf{The Energy Consumption}}
 We observe that DESK and GAF have 30.36 \% and 34.96 \% active nodes for the first fourteen rounds and DiLCO and LiCO protocols compete perfectly with only 17.92 \% and 20.16 \% active nodes during the same time interval. As the number of periods increases, LiCO protocol has a lower number of active nodes in comparison with the three other approaches, while keeping of greater coverage ratio as shown in figure \ref{fig333}.
 
 \subsubsection{\textbf{The Energy Consumption}}

-We study the effect of the energy consumed by the WSN during the communication, computation, listening, active, and sleep modes for different network densities and compare it for the four approaches. Figures~\ref{fig3EC95} and ~\ref{fig3EC50} illustrate the energy consumption for different network sizes and for $Lifetime95$ and $Lifetime50$. 
+We study the effect of the energy consumed by the WSN during the communication, computation, listening, active, and sleep modes for different network densities and compare it for the four approaches. Figures~\ref{fig3EC95} and \ref{fig3EC50} illustrate the energy consumption for different network sizes and for $Lifetime95$ and $Lifetime50$. 

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


@@ -635,7 +730,7 @@ We study the effect of the energy consumed by the WSN during the communication,
 \label{fig3EC50}
 \end{figure} 
 
 \label{fig3EC50}
 \end{figure} 
 

-The results show that our LiCO protocol is the most competitive from the energy consumption point of view. As shown in figures~\ref{fig3EC95} and ~\ref{fig3EC50}, LiCO consumes much less energy  than the three other methods. One might think that the resolution of the integer program is too costly in energy, but the results show that it is very beneficial to lose a bit of time in the selection of sensors to activate. Indeed this optimization program allows to reduce significantly the number of active sensors and so the energy consumption while keeping a good coverage level.
+The results show that our LiCO protocol is the most competitive from the energy consumption point of view. As shown in figures~\ref{fig3EC95} and \ref{fig3EC50}, LiCO consumes much less energy  than the three other methods. One might think that the resolution of the integer program is too costly in energy, but the results show that it is very beneficial to lose a bit of time in the selection of sensors to activate. Indeed this optimization program allows to reduce significantly the number of active sensors and so the energy consumption while keeping a good coverage level.

 %The optimization algorithm, which used by LiCO protocol,  was improved the lifetime coverage efficiently based on the perimeter coverage model.
 
  %The 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 optimization algorithm, which used by LiCO 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.