+\documentclass[a4paper,twoside]{article}
+
+\usepackage{epsfig}
+\usepackage{subfigure}
+\usepackage{calc}
+\usepackage{amssymb}
+\usepackage{amstext}
+\usepackage{amsmath}
+\usepackage{amsthm}
+\usepackage{multicol}
+\usepackage{pslatex}
+\usepackage{apalike}
+\usepackage{SCITEPRESS}
+\usepackage[small]{caption}
+
+\usepackage[linesnumbered,ruled,vlined,commentsnumbered]{algorithm2e}
+\usepackage{mathtools}
+
+\subfigtopskip=0pt
+\subfigcapskip=0pt
+\subfigbottomskip=0pt
+
+\begin{document}
+
+%\title{Authors' Instructions \subtitle{Preparation of Camera-Ready Contributions to SCITEPRESS Proceedings} }
+
+\title{Distributed Lifetime Coverage Optimization Protocol \\in Wireless Sensor Networks}
+
+\author{\authorname{Ali Kadhum Idrees, Karine Deschinkel, Michel Salomon, and Rapha\"el Couturier}
+\affiliation{FEMTO-ST Institute, UMR 6174 CNRS, University of Franche-Comte, Belfort, France}
+%\affiliation{\sup{2}Department of Computing, Main University, MySecondTown, MyCountry}
+\email{ali.idness@edu.univ-fcomte.fr, $\lbrace$karine.deschinkel, michel.salomon, raphael.couturier$\rbrace$@univ-fcomte.fr}
+%\email{\{f\_author, s\_author\}@ips.xyz.edu, t\_author@dc.mu.edu}
+}
+
+\keywords{Wireless Sensor Networks, Area Coverage, Network lifetime,
+Optimization, Scheduling.}
+
+\abstract{One of the fundamental challenges in Wireless Sensor Networks (WSNs) is the
+coverage preservation and the extension of the network lifetime continuously and
+effectively when monitoring a certain area (or region) of interest. In this
+paper, a Distributed Lifetime Coverage Optimization protocol (DiLCO) to maintain
+the coverage and to improve the lifetime in wireless sensor networks is
+proposed. The area of interest is first divided into subregions using a
+divide-and-conquer method and then the DiLCO protocol is distributed on the
+sensor nodes in each subregion. The DiLCO combines two efficient techniques:
+leader election for each subregion, followed by an optimization-based planning
+of activity scheduling decisions for each subregion. The proposed DiLCO works
+into rounds during which a small number of nodes, remaining active for sensing,
+is selected to ensure coverage so as to maximize the lifetime of wireless sensor
+network. Each round consists of four phases: (i)~Information Exchange,
+(ii)~Leader Election, (iii)~Decision, and (iv)~Sensing. The decision process is
+carried out by a leader node, which solves an integer program. Compared with
+some existing protocols, simulation results show that the proposed protocol can
+prolong the network lifetime and improve the coverage performance effectively.}
+
+\onecolumn \maketitle \normalsize \vfill
+
+\section{\uppercase{Introduction}}
+\label{sec:introduction}
+\noindent
+Energy efficiency is very important issue in WSNs since sensors are powered by batteries. Therefore, reducing energy consumption and extending network lifetime are the main challenges in the design of WSNs. One of the major scientific research challenges in WSNs, which has been addressed by a large amount of literature during the last few years, is the design of energy efficient approaches for coverage and connectivity~\cite{conti2014mobile}.
+Coverage reflects how well a sensor field is monitored, is one of the most important performance metrics to measure WSNs. The most discussed coverage problems in literature can be classified
+into three types \cite{li2013survey}: area (blanket) coverage (where every
+point inside an area is to be monitored), target (sweep) coverage (where the main objective is to cover only a finite number of discrete
+points called targets), and barrier coverage (The problem of preventing an intruder from entering a region of interest is referred to as the barrier coverage).
+ It is required to monitor the area of interest efficiently~\cite{Nayak04}, but in the same time the power consumption should be minimized. Since sensor nodes have a limited batteries life~\cite{Sudip03} and since it is impossible, difficult or expensive to be recharged and /or replaced after they are deployed in remote, hostile, or unpractical environments, Therefore, it is desired that the WSNs are deployed with high densities so as to exploit the overlapping sensing regions of some sensor nodes to save energy by turning off some of them during the sensing phase to prolong the network lifetime by elaborate managing the duty cycle of nodes in WSN.
+
+In this paper we concentrate on the area coverage problem with the objective of
+maximizing the network lifetime by using DiLCO protocol to maintain the coverage and to improve the lifetime in WSNs. The area of interest is divided into subregions using divide-and-conquer method and an activity scheduling based optimization for sensor nodes is planned by the elected leader in each subregion. In fact, the nodes in a subregion can be seen as a cluster where each node sends sensing data to the cluster head or the sink node. Furthermore, the activities in a subregion/cluster can continue even if another cluster stops due to too many node failures. Our DiLCO protocol considers rounds, where a round starts with a discovery phase to exchange information between sensors of the subregion, in order to choose in a suitable manner a sensor node to carry out a coverage strategy. Our DiLCO protocol involves solving an integer program, which provides the activation of the sensors for the sensing phase of the current round.
+
+The remainder of the paper is organized as follows. The next section reviews the related work in the field. Section~\ref{sec:The DiLCO Protocol Description} is devoted to the DiLCO 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} shows the simulation results. Finally, we give concluding remarks and some suggestions for
+future works in Section~\ref{sec:Conclusion and Future Works}.
+
+\section{\uppercase{Literature Review}}
+\label{sec:Literature Review}
+\noindent In this section, we summarize some related works regarding coverage lifetime maximization and scheduling, and distinguish our DiLCO protocol from the works presented in the literature.
+
+The work presented in~\cite{luo2014parameterized,tian2014distributed} try to solve the target coverage problem so as to extend the network lifetime since it is easy to verify the coverage status of discreet target.
+The work proposed in~\cite{kim2013maximum} considered the barrier-coverage problem in WSNs. The final goal is to maximize the network lifetime such that any penetration of the intruder is detected.
+In \cite{ChinhVu}, the authors are proposed a localized and distributed greedy algorithm named DESK for generating non-disjoint cover sets which provide the k-coverage for the whole network.
+Our Work in~\cite{idrees2014coverage} is proposed a coverage optimization protocol to improve the lifetime in heterogeneous energy wireless sensor networks. In this work, the coverage protocol distributed in each sensor node in the subregion but the optimization take place over the the whole subregion. We are considered only distributing the coverage protocol over two subregions.
+The work presented in ~\cite{Zhang} focuses on a distributed clustering method, which aims to extend the network lifetime, while the coverage is ensured.
+
+The work proposed by \cite{qu2013distributed} considered the coverage problem in WSNs where each sensor has variable sensing radius. The final objective is to maximize the network coverage lifetime in WSNs.
+
+
+\iffalse
+Casta{\~n}o et al.~\cite{castano2013column} proposed a multilevel approach based on column generation (CG) to extend the network lifetime with connectivity and coverage constraints. They are included two heuristic methods within the CG framework so as to accelerate the solution process.
+In \cite{diongue2013alarm}, diongue is proposed an energy Aware sLeep scheduling AlgoRithm for lifetime maximization in WSNs (ALARM) algorithm for coverage lifetime maximization in wireless sensor networks. ALARM is sensor node scheduling approach for lifetime maximization in WSNs in which it schedule redundant nodes according to the weibull distribution taking into consideration frequent nodes failure.
+Yu et al.~\cite{yu2013cwsc} presented a connected k-coverage working sets construction
+approach (CWSC) to maintain k-coverage and connectivity. This approach try to select the minimum number of connected sensor nodes that can provide k-coverage ($k \geq 1$).
+In~\cite{cheng2014achieving}, the authors are presented a unified sensing architecture for duty cycled sensor networks, called uSense, which comprises three ideas: Asymmetric Architecture, Generic Switching and Global Scheduling. The objective is to provide a flexible and efficient coverage in sensor networks.
+\fi
+In~\cite{yang2013energy}, the authors are investigated full area coverage problem
+under the probabilistic sensing model in the sensor networks. %They are designed $\varepsilon-$full area coverage optimization (FCO) algorithm to select a subset of sensors to provide probabilistic area coverage dynamically so as to extend the network lifetime.
+In \cite{xu2001geography}, Xu et al. proposed a Geographical Adaptive Fidelity (GAF) algorithm, which uses geographic location information to divide the area of interest into fixed square grids. Within each grid, it keeps only one node staying awake to take the responsibility of sensing and communication.
+
+The main contributions of our DiLCO Protocol can be summarized as follows:
+(1) The distributed optimization over the subregions in the area of interest,
+(2) The distributed dynamic leader election at each round by each sensor node in the subregion,
+(3) The primary point coverage model to represent each sensor node in the network,
+(4) The activity scheduling based optimization on the subregion, which are based on the primary point coverage model to activate as less number as possible of sensor nodes to take the mission of the coverage in each subregion,
+(5) The improved energy consumption model.
+
+
+
+\section{ The DiLCO Protocol Description}
+\label{sec:The DiLCO Protocol Description}
+
+\noindent In this section, we introduce a Distributed Lifetime Coverage Optimization protocol, which is called DiLCO. It is distributed on each subregion in the area of interest. It is based on two efficient techniques: network leader election and sensor activity scheduling for coverage preservation and energy conservation continuously and efficiently to maximize the lifetime in the network.
+\iffalse The main features of our DiLCO protocol:
+i)It divides the area of interest into subregions by using divide-and-conquer concept, ii)It requires only the information of the nodes within the subregion, iii) it divides the network lifetime into rounds, iv)It based on the autonomous distributed decision by the nodes in the subregion to elect the Leader, v)It apply the activity scheduling based optimization on the subregion, vi) it achieves an energy consumption balancing among the nodes in the subregion by selecting different nodes as a leader during the network lifetime, vii) It uses the optimization to select the best representative set of sensors in the subregion by optimize the coverage and the lifetime over the area of interest, viii)It uses our proposed primary point coverage model, which represent the sensing range of the sensor as a set of points, which are used by the our optimization algorithm, ix) It uses a simple energy model that takes communication, sensing and computation energy consumptions into account to evaluate the performance of our protocol.
+\fi
+\subsection{ Assumptions and Models}
+\noindent We consider a randomly and uniformly deployed network consisting of
+static wireless sensors. The wireless sensors are deployed in high
+density to ensure initially a high coverage ratio of the interested area. We
+assume that all nodes are homogeneous in terms of communication and
+processing capabilities and heterogeneous in term of energy provision.
+The location information is available to the sensor node either
+through hardware such as embedded GPS or through location discovery
+algorithms. 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 Instead of working with the coverage area, we consider for each
+sensor a set of points called primary points~\cite{idrees2014coverage}. We also assume that the
+sensing disk defined by a sensor is covered if all the primary points of
+this sensor are covered.
+
+\iffalse
+By knowing the position (point center: ($p_x,p_y$)) of a wireless
+sensor node and its $R_s$, we calculate the primary points directly
+based on the proposed model. We use these primary points (that can be
+increased or decreased if necessary) as references to ensure that the
+monitored region of interest is covered by the selected set of
+sensors, instead of using all the points in the area.
+
+\indent We can calculate the positions of the selected primary
+points in the circle disk of the sensing range of a wireless sensor
+node (see figure~\ref{fig1}) as follows:\\
+$(p_x,p_y)$ = point center of wireless sensor node\\
+$X_1=(p_x,p_y)$ \\
+$X_2=( p_x + R_s * (1), p_y + R_s * (0) )$\\
+$X_3=( p_x + R_s * (-1), p_y + R_s * (0)) $\\
+$X_4=( p_x + R_s * (0), p_y + R_s * (1) )$\\
+$X_5=( p_x + R_s * (0), p_y + R_s * (-1 )) $\\
+$X_6= ( p_x + R_s * (\frac{-\sqrt{2}}{2}), p_y + R_s * (0)) $\\
+$X_7=( p_x + R_s * (\frac{\sqrt{2}}{2}), p_y + R_s * (0))$\\
+$X_8=( p_x + R_s * (\frac{-\sqrt{2}}{2}), p_y + R_s * (\frac{-\sqrt{2}}{2})) $\\
+$X_9=( p_x + R_s * (\frac{\sqrt{2}}{2}), p_y + R_s * (\frac{-\sqrt{2}}{2})) $\\
+$X_{10}=( p_x + R_s * (\frac{-\sqrt{2}}{2}), p_y + R_s * (\frac{\sqrt{2}}{2})) $\\
+$X_{11}=( p_x + R_s * (\frac{\sqrt{2}}{2}), p_y + R_s * (\frac{\sqrt{2}}{2})) $\\
+$X_{12}=( p_x + R_s * (0), p_y + R_s * (\frac{\sqrt{2}}{2})) $\\
+$X_{13}=( p_x + R_s * (0), p_y + R_s * (\frac{-\sqrt{2}}{2})) $.
+
+ \begin{figure}[h!]
+\centering
+ \begin{multicols}{3}
+\centering
+%\includegraphics[scale=0.20]{fig21.pdf}\\~ ~ ~ ~ ~(a)
+%\includegraphics[scale=0.20]{fig22.pdf}\\~ ~ ~ ~ ~(b)
+\includegraphics[scale=0.25]{principles13.pdf}%\\~ ~ ~ ~ ~(c)
+%\includegraphics[scale=0.10]{fig25.pdf}\\~ ~ ~(d)
+%\includegraphics[scale=0.10]{fig26.pdf}\\~ ~ ~(e)
+%\includegraphics[scale=0.10]{fig27.pdf}\\~ ~ ~(f)
+\end{multicols}
+\caption{Wireless Sensor Node represented by 13 primary points}
+%\caption{Wireless Sensor Node represented by (a)5, (b)9 and (c)13 primary points respectively}
+\label{fig1}
+\end{figure}
+
+\fi
+
+\subsection{The Main Idea}
+\noindent The area of interest can be divided using the
+divide-and-conquer strategy into smaller areas called subregions and
+then our coverage protocol will be implemented in each subregion
+simultaneously. Our DiLCO protocol works in rounds fashion as shown in figure~\ref{fig2}.
+\begin{figure}[ht!]
+\centering
+\includegraphics[width=75mm]{FirstModel.pdf} % 70mm
+\caption{DiLCO protocol}
+\label{fig2}
+\end{figure}
+
+Each round is divided into 4 phases : Information (INFO) Exchange,
+Leader Election, Decision, and Sensing. For each round there is
+exactly one set cover responsible for the sensing task. This protocol is
+more reliable against an unexpected node failure because it works
+in rounds. On the one hand, if a node failure is detected before
+making the decision, the node will not participate to this phase, and,
+on the other hand, if the node failure occurs after the decision, the
+sensing task of the network will be temporarily affected: only during
+the period of sensing until a new round starts, since a new set cover
+will take charge of the sensing task in the next round. The energy
+consumption and some other constraints can easily be taken into
+account since the sensors can update and then exchange their
+information (including their residual energy) at the beginning of each
+round. However, the pre-sensing phases (INFO Exchange, Leader
+Election, Decision) are energy consuming for some nodes, even when
+they do not join the network to monitor the area.
+We define two types of packets to be used by our DiLCO protocol.
+%\begin{enumerate}[(a)]
+\begin{itemize}
+\item INFO packet: sent by each sensor node to all the nodes of it's subregion for information exchange.
+\item ActiveSleep packet: sent by the leader to all the nodes in the same of it's subregion to inform them to be Active or Sleep during the sensing phase.
+\end{itemize}
+%\end{enumerate}
+
+There are four status for each sensor node in the network
+%\begin{enumerate}[(a)]
+\begin{itemize}
+\item LISTENING: Sensor is waiting for a decision (to be active or not)
+\item COMPUTATION: Sensor applies the optimization process as leader
+\item ACTIVE: Sensor is active
+\item SLEEP: Sensor is turned off
+\item COMMUNICATION: Sensor is transmitting or receiving packet
+\end{itemize}
+%\end{enumerate}
+%Below, we describe each phase in more details.
+In Algorithm 1, Initially, the sensor node check it's remaining energy in order to participate in the current round. Each sensor node determines it's position and it's subregion based Embedded GPS or Location Discovery Algorithm. After that, all the sensors collect position coordinates, remaining energy $RE_j$, sensor node id, and the number of its one-hop live neighbors during the information exchange. The sensor node enter in listening mode waiting to receive ActiveSleep packet from the leader to take the decision. The selection criteria for the leader in order of priority are: larger number of neighbours, larger remaining energy, and then in case of
+equality, larger index. After that, if the sensor node is leader, It will execute the integer program algorithm ( see section~\ref{cp}) to optimize the coverage and the lifetime in it's subregion. After the decision, the optimization approach will select the set of sensor nodes to take the mission of coverage during the sensing phase.
+
+
+
+
+\iffalse
+\subsubsection{Information Exchange Phase}
+
+Each sensor node $j$ sends its position, remaining energy $RE_j$, and
+the number of neighbours $NBR_j$ to all wireless sensor nodes in
+its subregion by using an INFO packet and then listens to the packets
+sent from other nodes. After that, each node will have information
+about all the sensor nodes in the subregion. In our model, the
+remaining energy corresponds to the time that a sensor can live in the
+active mode.
+
+\subsubsection{Leader Election Phase}
+This step includes choosing the Wireless Sensor Node Leader (WSNL),
+which will be responsible for executing the coverage algorithm. Each
+subregion in the area of interest will select its own WSNL
+independently for each round. All the sensor nodes cooperate to
+select WSNL. The nodes in the same subregion will select the leader
+based on the received information from all other nodes in the same
+subregion. The selection criteria in order of priority are: larger
+number of neighbours, larger remaining energy, and then in case of
+equality, larger index.
+
+\subsubsection{Decision phase}
+The WSNL will solve an integer program (see section~\ref{cp}) to
+select which sensors will be activated in the following sensing phase
+to cover the subregion. WSNL will send Active-Sleep packet to each
+sensor in the subregion based on the algorithm's results.
+
+
+\subsubsection{Sensing phase}
+Active sensors in the round will execute their sensing task to
+preserve maximal coverage in the region of interest. We will assume
+that the cost of keeping a node awake (or asleep) for sensing task is
+the same for all wireless sensor nodes in the network. Each sensor
+will receive an Active-Sleep packet from WSNL informing it to stay
+awake or to go to sleep for a time equal to the period of sensing until
+starting a new round. Algorithm 1, which
+will be executed by each node at the beginning of a round, explains how the
+Active-Sleep packet is obtained.
+
+\fi
+
+
+\iffalse
+\subsection{DiLCO protocol Algorithm}
+we first show the pseudo-code of DiLCO protocol, which is executed by each sensor in the subregion and then describe it in more detail.
+\fi
+
+\begin{algorithm}[h!]
+ % \KwIn{all the parameters related to information exchange}
+% \KwOut{$winer-node$ (: the id of the winner sensor node, which is the leader of current round)}
+ \BlankLine
+ %\emph{Initialize the sensor node and determine it's position and subregion} \;
+
+ \If{ $RE_j \geq E_{R}$ }{
+ \emph{$s_j.status$ = COMMUNICATION}\;
+ \emph{Send $INFO()$ packet to other nodes in the subregion}\;
+ \emph{Wait $INFO()$ packet from other nodes in the subregion}\;
+ %\emph{UPDATE $RE_j$ for every sent or received INFO Packet}\;
+ %\emph{ Collect information and construct the list L for all nodes in the subregion}\;
+
+ %\If{ the received INFO Packet = No. of nodes in it's subregion -1 }{
+ \emph{LeaderID = Leader election}\;
+ \If{$ s_j.ID = LeaderID $}{
+ \emph{$s_j.status$ = COMPUTATION}\;
+ \emph{$\left\{\left(X_{1},\dots,X_{k},\dots,X_{J}\right)\right\}$ =
+ Execute Integer Program Algorithm($J$)}\;
+ \emph{$s_j.status$ = COMMUNICATION}\;
+ \emph{Send $ActiveSleep()$ to each node $k$ in subregion} \;
+ \emph{Update $RE_j $}\;
+ }
+ \Else{
+ \emph{$s_j.status$ = LISTENING}\;
+ \emph{Wait $ActiveSleep()$ packet from the Leader}\;
+ % \emph{After receiving Packet, Retrieve the schedule and the $T$ rounds}\;
+ \emph{Update $RE_j $}\;
+ }
+ % }
+ }
+ \Else { Exclude $s_j$ from entering in the current sensing phase}
+
+ % \emph{return X} \;
+\caption{DiLCO($s_j$)}
+\label{alg:DiLCO}
+
+\end{algorithm}
+
+\iffalse
+The DiLCO protocol work in rounds and executed at each sensor node in the network , each sensor node can still sense data while being in
+LISTENING mode. Thus, by entering the LISTENING mode at the beginning of each round,
+sensor nodes still executing sensing task while participating in the leader election and decision phases. More specifically, The DiLCO protocol algorithm works as follow:
+Initially, the sensor node check it's remaining energy in order to participate in the current round. Each sensor node determines it's position and it's subregion based Embedded GPS or Location Discovery Algorithm. After that, All the sensors collect position coordinates, current remaining energy, sensor node id, and the number of its one-hop live neighbors during the information exchange. It stores this information into a list L.
+The sensor node enter in listening mode waiting to receive ActiveSleep packet from the leader to take the decision. Each sensor node will execute the Algorithm~1 to know who is the leader. After that, if the sensor node is leader, It will execute the integer program algorithm ( see section~\ref{cp}) to optimize the coverage and the lifetime in it's subregion. After the decision, the optimization approach will select the set of sensor nodes to take the mission of coverage during the sensing phase. The leader will send ActiveSleep packet to each sensor node in the subregion to inform him to it's status during the period of sensing, either Active or sleep until the starting of next round. Based on the decision, the leader as other nodes in subregion, either go to be active or go to be sleep during current sensing phase. the other nodes in the same subregion will stay in listening mode waiting the ActiveSleep packet from the leader. After finishing the time period for sensing, all the sensor nodes in the same subregion will start new round by executing the DiLCO protocol and the lifetime in the subregion will continue until all the sensor nodes are died or the network becomes disconnected in the subregion.
+\fi
+
+
+\section{Coverage problem formulation}
+\label{cp}
+
+\indent Our model is based on the model proposed by
+\cite{pedraza2006} where the objective is to find a maximum number of
+disjoint cover sets. To accomplish this goal, authors proposed an
+integer program, which forces undercoverage and overcoverage of targets
+to become minimal at the same time. They use binary variables
+$x_{jl}$ to indicate if sensor $j$ belongs to cover set $l$. In our
+model, we consider binary variables $X_{j}$, which determine the
+activation of sensor $j$ in the sensing phase of the round. We also
+consider primary points as targets. The set of primary points is
+denoted by $P$ and the set of sensors by $J$.
+
+\noindent For a primary point $p$, let $\alpha_{jp}$ denote the
+indicator function of whether the point $p$ is covered, that is:
+\begin{equation}
+\alpha_{jp} = \left \{
+\begin{array}{l l}
+ 1 & \mbox{if the primary point $p$ is covered} \\
+ & \mbox{by sensor node $j$}, \\
+ 0 & \mbox{otherwise.}\\
+\end{array} \right.
+%\label{eq12}
+\end{equation}
+The number of active sensors that cover the primary point $p$ is equal
+to $\sum_{j \in J} \alpha_{jp} * X_{j}$ where:
+\begin{equation}
+X_{j} = \left \{
+\begin{array}{l l}
+ 1& \mbox{if sensor $j$ is active,} \\
+ 0 & \mbox{otherwise.}\\
+\end{array} \right.
+%\label{eq11}
+\end{equation}
+We define the Overcoverage variable $\Theta_{p}$ as:
+\begin{equation}
+ \Theta_{p} = \left \{
+\begin{array}{l l}
+ 0 & \mbox{if the primary point}\\
+ & \mbox{$p$ is not covered,}\\
+ \left( \sum_{j \in J} \alpha_{jp} * X_{j} \right)- 1 & \mbox{otherwise.}\\
+\end{array} \right.
+\label{eq13}
+\end{equation}
+\noindent More precisely, $\Theta_{p}$ represents the number of active
+sensor nodes minus one that cover the primary point $p$.\\
+The Undercoverage variable $U_{p}$ of the primary point $p$ is defined
+by:
+\begin{equation}
+U_{p} = \left \{
+\begin{array}{l l}
+ 1 &\mbox{if the primary point $p$ is not covered,} \\
+ 0 & \mbox{otherwise.}\\
+\end{array} \right.
+\label{eq14}
+\end{equation}
+
+\noindent Our coverage optimization problem can then be formulated as follows
+\begin{equation} \label{eq:ip2r}
+\left \{
+\begin{array}{ll}
+\min \sum_{p \in P} (w_{\theta} \Theta_{p} + w_{U} U_{p})&\\
+\textrm{subject to :}&\\
+\sum_{j \in J} \alpha_{jp} X_{j} - \Theta_{p}+ U_{p} =1, &\forall p \in P\\
+%\label{c1}
+%\sum_{t \in T} X_{j,t} \leq \frac{RE_j}{e_t} &\forall j \in J \\
+%\label{c2}
+\Theta_{p}\in \mathbb{N} , &\forall p \in P\\
+U_{p} \in \{0,1\}, &\forall p \in P \\
+X_{j} \in \{0,1\}, &\forall j \in J
+\end{array}
+\right.
+\end{equation}
+
+
+
+\begin{itemize}
+\item $X_{j}$ : indicates whether or not the sensor $j$ is actively
+ sensing in the round (1 if yes and 0 if not);
+\item $\Theta_{p}$ : {\it overcoverage}, the number of sensors minus
+ one that are covering the primary point $p$;
+\item $U_{p}$ : {\it undercoverage}, indicates whether or not the primary point
+ $p$ is being covered (1 if not covered and 0 if covered).
+\end{itemize}
+
+The first group of constraints indicates that some primary point $p$
+should be covered by at least one sensor and, if it is not always the
+case, overcoverage and undercoverage variables help balancing the
+restriction equations by taking positive values. There are two main
+objectives. First, we limit the overcoverage of primary points in order to
+activate a minimum number of sensors. Second we prevent the absence of monitoring on
+ some parts of the subregion by minimizing the undercoverage. The
+weights $w_\theta$ and $w_U$ must be properly chosen so as to
+guarantee that the maximum number of points are covered during each
+round.
+
+
+
+
+\section{\uppercase{Simulation Results and Analysis}}
+\label{sec:Simulation Results and Analysis}
+\noindent \subsection{Simulation Framework}
+In this subsection, we conducted a series of simulations to evaluate the
+efficiency and the relevance of our DiLCO protocol, using the discrete event
+simulator OMNeT++ \cite{varga}. The simulation parameters are summarized in
+Table~\ref{table3}
+
+\begin{table}[ht]
+\caption{Relevant parameters for network initializing.}
+% title of Table
+\centering
+% used for centering table
+\begin{tabular}{c|c}
+% centered columns (4 columns)
+ \hline
+%inserts double horizontal lines
+Parameter & Value \\ [0.5ex]
+
+%Case & Strategy (with Two Leaders) & Strategy (with One Leader) & Simple Heuristic \\ [0.5ex]
+% inserts table
+%heading
+\hline
+% inserts single horizontal line
+Sensing Field & $(50 \times 25)~m^2 $ \\
+% inserting body of the table
+%\hline
+Nodes Number & 50, 100, 150, 200 and 250~nodes \\
+%\hline
+Initial Energy & 500-700~joules \\
+%\hline
+Sensing Period & 60 Minutes \\
+$E_{thr}$ & 36 Joules\\
+$R_s$ & 5~m \\
+%\hline
+$w_{\Theta}$ & 1 \\
+% [1ex] adds vertical space
+%\hline
+$w_{U}$ & $|P^2|$
+%inserts single line
+\end{tabular}
+\label{table3}
+% is used to refer this table in the text
+\end{table}
+
+25 simulation runs are performed with different network topologies. The results presented hereafter are the average of these 25 runs.
+We performed simulations for five different densities varying from 50 to 250~nodes. Experimental results are obtained from randomly generated networks in which nodes are deployed over a $(50 \times 25)~m^2 $ sensing field. More precisely, the deployment is controlled at a coarse scale in order to ensure that the deployed nodes can cover the sensing field with a high coverage ratio.\\
+
+Our DiLCO protocol is declined into five versions: DiLCO-2, DiLCO-4, DiLCO-8, DiLCO-16, and DiLCO-32, corresponding to $2$, $4$, $8$, $16$ or $32$ subregions (leaders).
+
+We use an energy consumption model proposed by~\cite{ChinhVu} and based on ~\cite{raghunathan2002energy} with slight modifications.
+The energy consumption for sending/receiving the packets is added whereas the part related to the sensing range is removed because we consider a fixed sensing range.
+% We are took into account the energy consumption needed for the high computation during executing the algorithm on the sensor node.
+%The new energy consumption model will take into account the energy consumption for communication (packet transmission/reception), the radio of the sensor node, data sensing, computational energy of Micro-Controller Unit (MCU) and high computation energy of MCU.
+%revoir la phrase
+
+For our energy consumption model, we refer to the sensor node (Medusa II) which uses Atmels AVR ATmega103L microcontroller~\cite{raghunathan2002energy}. The typical architecture of a sensor is composed of four subsystems : the MCU subsystem which is capable of computation, communication subsystem (radio) which is responsible for
+transmitting/receiving messages, sensing subsystem that collects data, and the power supply which powers the complete sensor node ~\cite{raghunathan2002energy}. Each of the first three subsystems can be turned on or off depending on the current status of the sensor. Energy consumption (expressed in milliWatt per second) for the different status of the sensor is summarized in Table~\ref{table4}. The energy needed to send or receive a 1-bit is equal to $0.2575 mW$.
+
+\begin{table}[ht]
+\caption{The Energy Consumption Model}
+% title of Table
+\centering
+% used for centering table
+\begin{tabular}{|c|c|c|c|c|}
+% centered columns (4 columns)
+ \hline
+%inserts double horizontal lines
+Sensor mode & MCU & Radio & Sensing & Power (mWs) \\ [0.5ex]
+\hline
+% inserts single horizontal line
+Listening & ON & ON & ON & 20.05 \\
+% inserting body of the table
+\hline
+Active & ON & OFF & ON & 9.72 \\
+\hline
+Sleep & OFF & OFF & OFF & 0.02 \\
+\hline
+Computation & ON & ON & ON & 26.83 \\
+%\hline
+%\multicolumn{4}{|c|}{Energy needed to send/receive a 1-bit} & 0.2575\\
+ \hline
+\end{tabular}
+
+\label{table4}
+% is used to refer this table in the text
+\end{table}
+
+For sake of simplicity we ignore the energy needed to turn on the
+radio, to start up the sensor node, the transition from mode to another, etc.
+%We also do not consider the need of collecting sensing data. PAS COMPRIS
+Thus, when a sensor becomes active (i.e., it already decides it's status), it can turn its radio off to save battery. DiLCO protocol uses two types of packets for communication. The size of the INFO-Packet and Status-Packet are 112 bits and 24 bits respectively.
+The value of energy spent to send a 1-bit-content message is obtained by using the equation in ~\cite{raghunathan2002energy} to calculate the energy cost for transmitting messages and we propose the same value for receiving the packets.
+
+The initial energy of each node is randomly set in the interval $[500-700]$. Each sensor node will not participate in the next round if its remaining energy is less than $E_{th}=36 Joules$, the minimum energy needed for the node to stay alive during one round. This value has been computed by multiplying the energy consumed in active state (9.72 mWs) by the time in second for one round (3600 seconds). According to the interval of initial energy, a sensor may be alive during at most 20 rounds.\\
+
+
+In the simulations, we introduce the following performance metrics to evaluate the efficiency of our approach:
+
+%\begin{enumerate}[i)]
+\begin{itemize}
+
+\item {{\bf Coverage Ratio (CR)}:} the coverage ratio measures how much the area of a sensor field is covered. In our case, we treated the sensing fields as a grid, and used each grid point as a sample point
+for calculating the coverage. The coverage ratio can be calculated by:
+\begin{equation*}
+\scriptsize
+\mbox{CR}(\%) = \frac{\mbox{$n^t$}}{\mbox{$N$}} \times 100.
+\end{equation*}
+Where: $n^t$ is the number of covered grid points by the active sensors of all subregions during round $t$ in the current sensing phase and $N$ is total number of grid points in the sensing field of the network. In our simulation $N = 51 \times 26 = 1326$ grid points.
+%The accuracy of this method depends on the distance between grids. In our
+%simulations, the sensing field has been divided into 50 by 25 grid points, which means
+%there are $51 \times 26~ = ~ 1326$ points in total.
+% Therefore, for our simulations, the error in the coverage calculation is less than ~ 1 $\% $.
+
+\iffalse
+
+\item{{\bf Number of Active Sensors Ratio(ASR)}:} It is important to have as few active nodes as possible in each round,
+in order to minimize the communication overhead and maximize the
+network lifetime. The Active Sensors Ratio is defined as follows:
+\begin{equation*}
+\scriptsize
+\mbox{ASR}(\%) = \frac{\sum\limits_{r=1}^R \mbox{$A_r^t$}}{\mbox{$S$}} \times 100 .
+\end{equation*}
+Where: $A_r^t$ is the number of active sensors in the subregion $r$ during round $t$ in the current sensing phase, $S$ is the total number of sensors in the network, and $R$ is the total number of the subregions in the network.
+
+\fi
+
+\item {{\bf Network Lifetime}:} we define the network lifetime as the time until the coverage ratio drops below a predefined threshold. We denoted by $Lifetime95$ (respectively $Lifetime50$) as the amount of time during which the network can satisfy an area coverage greater than $95\%$ (repectively $50\%$). We assume that the network
+is alive until all nodes have been drained of their energy or the
+sensor network becomes disconnected . Network connectivity is important because an
+active sensor node without connectivity towards a base station cannot
+transmit information on an event in the area that it monitors.
+
+
+\item {{\bf Energy Consumption}:}
+
+ Energy Consumption (EC) can be seen as the total energy consumed by the sensors during the $Lifetime95$ or $Lifetime50$ divided by the number of rounds. The EC can be computed as follow: \\
+ \begin{equation*}
+\scriptsize
+\mbox{EC} = \frac{\sum\limits_{m=1}^{M_L} \left( E^{\mbox{com}}_m+E^{\mbox{list}}_m+E^{\mbox{comp}}_m \right) +
+ \sum\limits_{t=1}^{T_L} \left( E^{a}_t+E^{s}_t \right)}{T_L},
+\end{equation*}
+
+%\begin{equation*}
+%\scriptsize
+%\mbox{EC} = \frac{\mbox{$\sum\limits_{d=1}^D E^c_d$}}{\mbox{$D$}} + \frac{\mbox{$\sum\limits_{d=1}^D %E^l_d$}}{\mbox{$D$}} + \frac{\mbox{$\sum\limits_{d=1}^D E^a_d$}}{\mbox{$D$}} + %\frac{\mbox{$\sum\limits_{d=1}^D E^s_d$}}{\mbox{$D$}}.
+%\end{equation*}
+
+where $M_L$ and $T_L$ are respectively the number of periods and rounds during
+$Lifetime_{95}$ or $Lifetime_{50}$. The total energy consumed by the sensors
+(EC) comes through taking into consideration four main energy factors. The first
+one , denoted $E^{\scriptsize \mbox{com}}_m$, represent the energy consumption
+spent by all the nodes for wireless communications during period $m$.
+$E^{\scriptsize \mbox{list}}_m$, the next factor, corresponds to the energy
+consumed by the sensors in LISTENING status before receiving the decision to go
+active or sleep in period $m$. $E^{\scriptsize \mbox{comp}}_m$ refers to the
+energy needed by all the leader nodes to solve the integer program during a
+period. Finally, $E^a_t$ and $E^s_t$ indicate the energy consummed by the whole
+network in round $t$.
+
+\iffalse
+\item {{\bf Execution Time}:} a sensor node has limited energy resources and computing power,
+therefore it is important that the proposed algorithm has the shortest
+possible execution time. The energy of a sensor node must be mainly
+used for the sensing phase, not for the pre-sensing ones.
+
+\item {{\bf Stopped simulation runs}:} A simulation
+ends when the sensor network becomes
+disconnected (some nodes are dead and are not able to send information to the base station). We report the number of simulations that are stopped due to network disconnections and for which round it occurs.
+
+\fi
+
+\end{itemize}
+%\end{enumerate}
+
+
+%\subsection{Performance Analysis for differnet subregions}
+\subsection{Performance Analysis}
+\label{sub1}
+In this subsection, we are studied the performance of our DiLCO protocol for a different number of subregions (Leaders).
+The DiLCO-1 protocol is a centralized approach on all the area of the interest, while DiLCO-2, DiLCO-4, DiLCO-8, DiLCO-16 and DiLCO-32 are distributed on two, four, eight, sixteen, and thirty-two subregions respectively. We did not take the DiLCO-1 protocol in our simulation results because it need high execution time to give the decision leading to consume all it's energy before producing the solution for optimization problem. our DiLCO protocol compared with other two approches. The first approach, called DESK that proposed by ~\cite{ChinhVu}, which is a full distributed coverage algorithm. The second approach, 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 on during the sensing phase time.
+
+
+\subsubsection{Coverage Ratio}
+In this experiment, Figure~\ref{fig3} shows the average coverage ratio for 150 deployed nodes.
+\parskip 0pt
+\begin{figure}[h!]
+\centering
+ \includegraphics[scale=0.45] {R/CR.pdf}
+\caption{The Coverage Ratio}
+\label{fig3}
+\end{figure}
+
+It is shown that DESK and GAF provides a
+a little better coverage ratio with 99.99\% and 99.91\% against 98.9\%, 99.1\%, 99.2\%, 99.1\% and 99.4\% produced by DiLCO-2, DiLCO-4, DiLCO-8, DiLCO-16 and DiLCO-32 for the lowest number of rounds. This is due to the fact that our DiLCO protocol versions put in sleep mode redundant sensors using optimization (which lightly decreases the coverage ratio) while there are more nodes are active in the case of DESK and GAF.
+
+As shown in the figure ~\ref{fig3}, as the number of subregions increases, the coverage preservation for area of interest increases for a larger number of rounds. Coverage ratio decreases when the number of rounds increases due to dead nodes. Although some nodes are dead,
+thanks to DiLCO-8, DiLCO-16 and DiLCO-32 protocols, other nodes are preserved to ensure the coverage. Moreover, when we have a dense sensor network, it leads to maintain the coverage for a larger number of rounds. DiLCO-8, DiLCO-16 and DiLCO-32 protocols are
+slightly more efficient than other protocols, because they subdivides
+the area of interest into 8, 16 and 32~subregions if one of the subregions becomes disconnected, the coverage may be still ensured in the remaining subregions.
+
+
+
+\subsubsection{The Energy Consumption}
+Based on the result in figure~\ref{fig3}, we are chose DiLCO-16 and DiLCO-32 protocols to be compared with other approaches. We measure the energy consumed by the sensors during the communication, listening, computation, active, and sleep modes for different network densities and compare it for different approaches. Figure~\ref{fig95} illustrates the energy consumption for different network sizes.
+% for $Lifetime95$ and $Lifetime50$.
+We denoted by $DiLCO-16/50$ (respectively $DiLCO-16/95$) as the amount of energy consumed during which the network can satisfy an area coverage greater than $50\%$ (repectively $95\%$) and we refer the same definition for the other approches.
+\begin{figure}[h!]
+\centering
+\includegraphics[scale=0.45]{R/EC.pdf}
+\caption{The Energy Consumption}
+\label{fig95}
+\end{figure}
+
+The results show that our DiLCO-16/50, DiLCO-32/50, DiLCO-16/95 and DiLCO-32/95 protocols are the most competitive from the energy consumption point of view. The other approaches have a high energy consumption due to activating a larger number of redundant nodes as well as the energy consumed during the different modes of sensor nodes. 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.
+%As shown in Figures~\ref{fig95} and ~\ref{fig50} , DiLCO-2 consumes more energy than the other versions of DiLCO, especially for large sizes of network. This is easy to understand since the bigger the number of sensors involved in the integer program, the larger the time computation to solve the optimization problem as well as the higher energy consumed during the communication.
+
+
+\subsubsection{Execution Time}
+In this experiment, we study the the impact of the size of the network on the excution time of the our distributed optimization approach. Figure~\ref{fig8} gives the average execution times in seconds for the decision phase (solving of the optimization problem) during one round. They are given for the different approaches and various numbers of sensors.
+The original execution time is computed 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 to run the optimization resolution, this time is multiplied by 2944.2 $\left( \frac{35330}{2} \times 6\right)$ and reported on Figure~\ref{fig8} for different network sizes.
+
+\begin{figure}[h!]
+\centering
+\includegraphics[scale=0.45]{R/T.pdf}
+\caption{Execution Time (in seconds)}
+\label{fig8}
+\end{figure}
+
+
+We can see from figure~\ref{fig8}, that the DiLCO-32 has very low execution times in comparison with other DiLCO versions, because it distributed on larger number of small subregions. Conversely, the DiLCO-2 which requires to solve an optimization problem considering half the nodes in each subregion presents high execution times.
+
+The DiLCO-32 has more suitable times in the same time it turn on redundent nodes more. We think that in distributed fashion the solving of the optimization problem in a subregion can be tackled by sensor nodes. Overall, to be able to deal with very large networks, a distributed method is clearly required.
+
+
+\subsubsection{The Network Lifetime}
+In figure~\ref{figLT95}, network lifetime is illustrated for different network sizes. We denoted by $DiLCO-16/50$ (respectively $DiLCO-16/95$) as the amount of time during which the network can satisfy an area coverage greater than $50\%$ ($Lifetime50$)(repectively $95\%$ ($Lifetime95$)) and we refer the same definition for the other approches.
+
+\begin{figure}[h!]
+\centering
+\includegraphics[scale=0.45]{R/LT.pdf}
+\caption{The Network Lifetime}
+\label{figLT95}
+\end{figure}
+
+
+As highlighted by figures~\ref{figLT95}, the network lifetime obviously
+increases when the size of the network increases, with our DiLCO-16/50, DiLCO-32/50, DiLCO-16/95 and DiLCO-32/95 protocols
+that leads to the larger lifetime improvement in comparison with other approaches. By choosing the best
+suited nodes, for each round, to cover the area of interest and by
+letting the other ones sleep in order to be used later in next rounds. Comparison shows that our DiLCO-16/50, DiLCO-32/50, DiLCO-16/95 and DiLCO-32/95 protocols, which are used distributed optimization over the subregions, are the best one because it is robust to network disconnection during the network lifetime as well as it consume less energy in comparison with other approaches. It also means that distributing the protocol in each node and subdividing the sensing field into many subregions, which are managed
+independently and simultaneously, is the most relevant way to maximize the lifetime of a network.
+
+
+
+
+\section{\uppercase{Conclusion and Future Works}}
+\label{sec:Conclusion and Future Works}
+
+\noindent In this paper, we have addressed the problem of the coverage and the lifetime
+optimization in wireless sensor networks. This is a key issue as
+sensor nodes have limited resources in terms of memory, energy and
+computational power. To cope with this problem, the field of sensing
+is divided into smaller subregions using the concept of divide-and-conquer method, and then a DiLCO protocol for optimizing the coverage and lifetime performances in each subregion.
+The proposed protocol combines two efficient techniques: network
+leader election and sensor activity scheduling, where the challenges
+include how to select the most efficient leader in each subregion and
+the best representative active nodes that will optimize the network lifetime
+while taking the responsibility of covering the corresponding
+subregion. The network lifetime in each subregion is divided into
+rounds, each round consists of four phases: (i) Information Exchange,
+(ii) Leader Election, (iii) an optimization-based Decision in order to
+select the nodes remaining active for the last phase, and (iv)
+Sensing. The simulations show the relevance of the proposed DiLCO
+protocol in terms of lifetime, coverage ratio, active sensors ratio, energy consumption, execution time, and the number of stopped simulation runs due to network disconnection. Indeed, when
+dealing with large and dense wireless sensor networks, a distributed
+approach 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.
+
+In future work, we plan to study and propose a coverage optimization protocol, which
+computes all active sensor schedules in one time, using
+optimization methods. \iffalse The round will still consist of 4 phases, but the
+ decision phase will compute the schedules for several sensing phases
+ which, aggregated together, define a kind of meta-sensing phase.
+The computation of all cover sets in one time is far more
+difficult, but will reduce the communication overhead. \fi
+
+\section*{\uppercase{Acknowledgements}}
+\noindent As a Ph.D. student, Ali Kadhum IDREES would like to gratefully acknowledge the University of Babylon - IRAQ for the financial support and Campus France for the received support.
+
+
+
+
+
+%\vfill
+\bibliographystyle{apalike}
+{\small
+\bibliography{Example}}
+
+
+%\vfill
+\end{document}
+
