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@@ -1,237 +1,207 @@
-\documentclass[a4paper,twoside]{article}
+\documentclass[a4,12pt]{article}

 
 

+
+\usepackage[paper=a4paper,dvips,top=1.5cm,left=1.5cm,right=1.5cm,foot=1cm,bottom=1.5cm]{geometry}

 \usepackage{epsfig}
 \usepackage{subfigure}
 \usepackage{epsfig}
 \usepackage{subfigure}

-\usepackage{calc}
+%\usepackage{calc}

 \usepackage{amssymb}
 \usepackage{amssymb}

-\usepackage{amstext}
-\usepackage{amsmath}
-\usepackage{amsthm}
-\usepackage{multicol}
-\usepackage{pslatex}
-\usepackage{apalike}
-\usepackage{SCITEPRESS}
+%\usepackage{amstext}
+%\usepackage{amsmath}
+%\usepackage{amsthm}
+%\usepackage{multicol}
+%\usepackage{pslatex}
+%\usepackage{apalike}
+%\usepackage{SCITEPRESS}

 \usepackage[small]{caption}
 \usepackage[small]{caption}

-
+\usepackage{color}

 \usepackage[linesnumbered,ruled,vlined,commentsnumbered]{algorithm2e}
 \usepackage{mathtools}  
 
 \usepackage[linesnumbered,ruled,vlined,commentsnumbered]{algorithm2e}
 \usepackage{mathtools}  
 

-\subfigtopskip=0pt
-\subfigcapskip=0pt
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+%\subfigtopskip=0pt
+%\subfigcapskip=0pt
+%\subfigbottomskip=0pt
+

 
 

-\begin{document}

 
 %\title{Authors' Instructions  \subtitle{Preparation of Camera-Ready Contributions to SCITEPRESS Proceedings} }
 
 
 %\title{Authors' Instructions  \subtitle{Preparation of Camera-Ready Contributions to SCITEPRESS Proceedings} }
 

-\title{Distributed Lifetime Coverage Optimization Protocol \\in Wireless Sensor Networks}
+\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}
+\author{Ali Kadhum Idrees, Karine Deschinkel,\\ Michel Salomon, and Rapha\"el Couturier\\
+%\affiliation{
+FEMTO-ST Institute, UMR 6174 CNRS, University of Franche-Comt\'e,\\
+ Belfort, France\\
+%}

 %\affiliation{\sup{2}Department of Computing, Main University, MySecondTown, MyCountry}
 %\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: 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}
 %\email{\{f\_author, s\_author\}@ips.xyz.edu, t\_author@dc.mu.edu}

-}

 
 

-\keywords{Wireless   Sensor   Networks,   Area   Coverage,   Network   lifetime,
-Optimization, Scheduling.}
+\begin{document}
+ \maketitle 
+%\keywords{Wireless   Sensor   Networks,   Area   Coverage,   Network   lifetime,Optimization, Scheduling.}

 
 \abstract{ One of the main research challenges faced in Wireless Sensor Networks
   (WSNs) is to preserve continuously and effectively the coverage of an area (or
   region) of interest  to be monitored, while simultaneously  preventing as much
   as possible a network failure due to battery-depleted nodes.  In this paper we
   propose a protocol, called Distributed Lifetime Coverage Optimization protocol
 
 \abstract{ One of the main research challenges faced in Wireless Sensor Networks
   (WSNs) is to preserve continuously and effectively the coverage of an area (or
   region) of interest  to be monitored, while simultaneously  preventing as much
   as possible a network failure due to battery-depleted nodes.  In this paper we
   propose a protocol, called Distributed Lifetime Coverage Optimization protocol

-  (DiLCO), which maintains the coverage  and improves the lifetime of a wireless
-  sensor  network. As  a  first step  we  partition the  area  of interest  into
-  subregions using a classical  divide-and-conquer method. Our DiLCO protocol is
-  then distributed  on the sensor nodes in  each subregion in a  second step. To
-  fulfill  our   objective,  the   proposed  protocol  combines   two  effective
-  techniques:   a  leader   election   in  each   subregion,   followed  by   an
-  optimization-based node activity scheduling  performed by each elected leader.
-  This two-step process takes place periodically, in order to choose a small set
-  of nodes remaining  active for sensing during a time slot.   Each set is built
-  to ensure  coverage at  a low  energy cost, allowing  to optimize  the network
-  lifetime. More  precisely, a period  consists of four  phases: (i)~Information
-  Exchange,  (ii)~Leader   Election,  (iii)~Decision,  and   (iv)~Sensing.   The
-  decision process,  which result in  an activity scheduling vector,  is carried
-  out by a leader node through  the solving of an integer program. In comparison
-  with  some other  protocols, the  simulations  done using  the discrete  event
-  simulator OMNeT++ show that our approach  is able to increase the WSN lifetime
-  and provides improved coverage performance. }
-
-\onecolumn \maketitle \normalsize \vfill
+  (DiLCO), which maintains the coverage and  improves the lifetime of a wireless
+  sensor network. First, we partition the area of interest into subregions using
+  a classical divide-and-conquer method.  Our DiLCO protocol is then distributed
+  on  the sensor  nodes in  each subregion  in a  second step.   To fulfill  our
+  objective, the proposed  protocol combines two effective  techniques: a leader
+  election in  each subregion, followed  by an optimization-based  node activity
+  scheduling  performed by  each elected  leader.  This  two-step process  takes
+  place periodically, in  order to choose a small set  of nodes remaining active
+  for sensing during a time slot.  Each set is built to ensure coverage at a low
+  energy cost,  allowing to optimize  the network lifetime.  %More  precisely, a
+  %period  consists  of  four   phases:  (i)~Information  Exchange,  (ii)~Leader
+  %Election,  (iii)~Decision, and  (iv)~Sensing.   The  decision process,  which
+  results in  an activity  scheduling vector,  is carried out  by a  leader node
+  through the solving of an integer program.
+% MODIF - BEGIN
+  Simulations are conducted using the discret event simulator
+  OMNET++.  We  refer to the characterictics  of a Medusa II  sensor for
+  the energy consumption  and the computation time.   In comparison with
+  two other existing  methods, our approach is able to  increase the WSN
+  lifetime and provides improved coverage performance. }
+% MODIF - END
+
+%\onecolumn
+
+
+%\normalsize \vfill

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

+

 \noindent 
 Energy efficiency is  a crucial issue in wireless  sensor networks since sensory
 \noindent 
 Energy efficiency is  a crucial issue in wireless  sensor networks since sensory

-consumption,  in order  to maximize  the network  lifetime, represent  the major
+consumption, in  order to  maximize the network  lifetime, represents  the major

 difficulty when designing WSNs. As a consequence, one of the 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
 difficulty when designing WSNs. As a consequence, one of the 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. On the one  hand we want to monitor the area  of interest in the most
-efficient way~\cite{Nayak04}. On the other hand we want to use as less energy as
-possible.  Sensor nodes  are  battery-powered  with no  means  of recharging  or
-replacing, usually due to environmental (hostile or unpractical environments) or
-cost reasons.  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.
+sensor  field is  monitored. On  the one  hand we  want to  monitor the  area of
+interest in the most efficient way~\cite{Nayak04}.  On the other hand we want to
+use  as little energy  as possible.   Sensor nodes  are battery-powered  with no
+means  of recharging  or replacing,  usually  due to  environmental (hostile  or
+unpractical environments)  or cost reasons.   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.

 
 In this  paper we design  a protocol that  focuses on the area  coverage problem
 with  the objective  of maximizing  the network  lifetime. Our  proposition, the
 
 In this  paper we design  a protocol that  focuses on the area  coverage problem
 with  the objective  of maximizing  the network  lifetime. Our  proposition, the

-DiLCO protocol,  maintains the coverage and  improves the lifetime  in WSNs. The
-area of  interest is  first divided into  subregions using  a divide-and-conquer
-algorithm and  an activity scheduling  for sensor nodes  is then 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 Distributed Lifetime
-Coverage Optimization (DILCO) protocol  considers periods, where a period starts
-with  a  discovery phase  to  exchange information  between  sensors  of a  same
-subregion, in order to choose in a suitable manner a sensor node (the leader) to
-carry out the coverage strategy. In each subregion the activation of the sensors
-for the  sensing phase of the current  period is obtained by  solving an integer
-program.
+Distributed  Lifetime  Coverage  Optimization  (DILCO) protocol,  maintains  the
+coverage  and improves  the lifetime  in  WSNs. The  area of  interest is  first
+divided  into subregions using  a divide-and-conquer  algorithm and  an activity
+scheduling  for sensor  nodes is  then  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 periods, where a period
+starts with  a discovery  phase to exchange  information between sensors  of the
+same  subregion, in order  to choose  in a  suitable manner  a sensor  node (the
+leader) to carry out the coverage  strategy. In each subregion the activation of
+the sensors for  the sensing phase of the current period  is obtained by solving
+an integer program.  The resulting activation vector is  broadcast by a leader
+to every node of its subregion. 
+
+% MODIF - BEGIN
+Our previous  paper ~\cite{idrees2014coverage} relies almost  exclusively on the
+framework of the  DiLCO approach and the coverage problem  formulation.  In this
+paper  we   made  more  realistic   simulations  by  taking  into   account  the
+characteristics of  a Medusa II sensor  ~\cite{raghunathan2002energy} to measure
+the energy consumption and the computation  time.  We have implemented two other
+existing approaches (a distributed one,  DESK ~\cite{ChinhVu}, and a centralized
+one called GAF  ~\cite{xu2001geography}) in order to  compare their performances
+with our approach.  We also focus on performance analysis based on the number of
+subregions. 
+% MODIF - END

 
 The remainder  of the  paper continues with  Section~\ref{sec:Literature Review}
 where a  review of some related  works is presented. The  next section describes
 the  DiLCO  protocol,  followed   in  Section~\ref{cp}  by  the  coverage  model
 formulation    which    is    used     to    schedule    the    activation    of
 sensors. Section~\ref{sec:Simulation Results  and Analysis} shows the simulation
 
 The remainder  of the  paper continues with  Section~\ref{sec:Literature Review}
 where a  review of some related  works is presented. The  next section describes
 the  DiLCO  protocol,  followed   in  Section~\ref{cp}  by  the  coverage  model
 formulation    which    is    used     to    schedule    the    activation    of
 sensors. Section~\ref{sec:Simulation Results  and Analysis} shows the simulation

-results. The paper  ends with conclusions and some  suggestions for further work
+results. The paper ends with a  conclusion and some suggestions for further work

 in Section~\ref{sec:Conclusion and Future Works}.
 
 \section{\uppercase{Literature Review}}
 \label{sec:Literature Review}
 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 problem , and distinguish our DiLCO protocol from the works presented in the literature.\\
-The most discussed coverage  problems in literature
-can  be classified into  three types  \cite{li2013survey}: area  coverage (where
-every point inside an area is  to be monitored), target coverage (where the main
-objective is to  cover only a finite number of  discrete points called targets),
-and  barrier coverage (to  prevent intruders  from entering  into the  region of
-interest). 
-{\it In DiLCO protocol, the area coverage, ie the coverage
-of every point in the sensing region, is transformed to the coverage of a fraction of points called primary points. }
-
-The major approach to extend network lifetime while preserving coverage is to divide/organize the sensors into a suitable number of set covers (disjoint or non-disjoint) where each set completely covers an interest region and to activate these set covers successively. The network activity can be planned in advance and scheduled for the entire network lifetime  or organized in periods, and the set of
-active sensor nodes is decided at the beginning of each period.
-Active node selection is determined based on the problem
-requirements (e.g. area monitoring, connectivity, power
-efficiency). Different methods has been proposed in literature.
-
-{\it DiLCO protocol works in periods, each period contains a preliminary phase for information exchange and decisions, followed by a sensing phase  where 
-one  cover  set  is in charge  of  the  sensing  task.}
-
-Various approaches, including centralised, distributed and localized algorithms, have been proposed to extend the network lifetime. 
-%For instance, in order to hide the occurrence of faults, or the sudden unavailability of
-%sensor nodes, some distributed algorithms have been developed in~\cite{Gallais06,Tian02,Ye03,Zhang05,HeinzelmanCB02}. 
-In distributed algorithms, information is disseminated throughout the network and sensors decide cooperatively by communicating with their neighbours which of them will remain in sleep mode for a certain period of time. 
-The centralized algorithms always provide nearly
-or close  to optimal solution since the  algorithm has global view  of the whole
-network, but such a method has the disadvantage of requiring 
-high communication costs,  since the  node (located at the base station) making the decision  needs information from all the  sensor nodes in the area. 
-
-{\it In DiLCO protocol, the area coverage is divided into several smaller subregions, and in each of which, a node called the leader is on charge for selecting the active sensors for the current period.} 
-
-A large variety of coverage scheduling algorithms have been proposed in the literature. Many of the existing algorithms, dealing with the maximisation of the number of cover sets, are heuristics. These heuristics involve the construction of a cover set by including in priority the sensor nodes which cover critical targets, that is to say targets that are covered by the smallest number of sensors. Other approaches are based on mathematical programming formulations and dedicated techniques (solving with a branch-and-bound algorithms available in optimization solver). The problem is formulated as an optimization problem (maximization of the lifetime, of the number of cover sets) under target coverage and energy constraints. Column  generation techniques,  well-known and widely practiced techniques for solving linear programs with too many variables, have been also used~\cite{castano2013column,rossi2012exact,deschinkel2012column}.
-
-
-{\it In DiLCO protocol, each leader, in each subregion, solves an integer program with a double objective consisting in minimizing the overcoverage and limiting the undercoverage. This program is inspired from the work of \cite{} where the objective is to maximize the number of cover sets.} 
- 
-
-\iffalse
-
-Some algorithms have been developed in ~\cite{yang2014energy,ChinhVu,vashistha2007energy,deschinkel2012column,shi2009,qu2013distributed,ling2009energy,xin2009area,cheng2014achieving,ling2009energy} to solve the area coverage problem so as to preserve coverage and prolong the network lifetime.
-
-
-Yang et al.~\cite{yang2014energy} investigated full area coverage problem
-under the probabilistic sensing model in the sensor networks. They have studied the relationship between the
-coverage of two adjacent points mathematically and then convert the problem of full area coverage into point coverage problem. They proposed $\varepsilon$-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.

 
 

-
-Vu et al.~\cite{ChinhVu} proposed a localized and distributed greedy algorithm named DESK for generating non-disjoint cover sets which provide the k-area coverage for the whole network. 
-
- 
-Qu et al.~\cite{qu2013distributed} developed a distributed algorithm using  adjustable sensing sensors
-for maintaining the full coverage of such sensor networks. The
-algorithm contains two major parts: the first part aims at
-providing $100\%$ coverage and the second part aims at saving
-energy by decreasing the sensing radius.
-
-Shi et al.~\cite{shi2009} modeled the Area Coverage Problem (ACP), which will be changed into a set coverage
-problem. By using this model, they are proposed  an  Energy-Efficient central-Scheduling greedy algorithm, which can reduces energy consumption and increases network lifetime, by selecting a appropriate subset of sensor nodes to support the networks periodically. 
-
-The work in~\cite{cheng2014achieving} 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.
-
- In~\cite{ling2009energy}, the lifetime of
-a sensor node is divided into epochs. At each epoch, the
-base station deduces the current sensing coverage requirement
-from application or user request. It then applies the heuristic algorithm in order to produce the set of active nodes which take the mission of sensing during the current epoch.  After that, the produced schedule is sent to the sensor nodes in the network. 
-\fi
-
-\iffalse
-
-The work in ~\cite{vu2009delaunay} considered the area coverage problem for variable sensing radii in WSNs by improving the energy balancing heuristic proposed in ~\cite{wang2007energy} so that  the area of interest can be full covered using Delaunay triangulation structure.
-
-Diongue and Thiare~\cite{diongue2013alarm} proposed an energy aware sleep scheduling algorithm for lifetime maximization in wireless sensor networks (ALARM).  The proposed approach permits to schedule redundant nodes according to the weibull distribution. This work did not analyze the ALARM scheme under the coverage problem. 
- 
-
-In~\cite{xin2009area}, the authors proposed a circle intersection localized coverage algorithm
-to maintain connectivity  based  on loose connectivity critical condition
-. By using the connected coverage node set, it can maintain network
-connection in the case which loose condition is not meet.
-The authors in ~\cite{vashistha2007energy} addressed the full area coverage problem using information
-coverage. They are proposed a low-complexity heuristic algorithm to obtain full area information covers (FAIC), which they refer to as Grid Based FAIC (GB-FAIC) algorithm. Using these FAICs, they are obtained the optimal schedule for applying the sensing activity of sensor nodes  in order to
-achieve increased sensing lifetime of the network. 
-
-
-
-  
-
-
-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 period 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, and (5) The improved energy consumption model.
-\fi
-\iffalse
-The work presented in~\cite{luo2014parameterized,tian2014distributed} tries 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.
-%Je ne comprends pas la phrase ci-dessus
-The work proposed in~\cite{kim2013maximum} considers the barrier-coverage problem in WSNs. The final goal is to maximize the network lifetime such that any penetration of the intruder is detected.
-%inutile de parler de ce papier car il concerne barrier coverage
-In \cite{ChinhVu},  the authors propose 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} proposes 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} considers the coverage problem in WSNs where each sensor has variable sensing radius. The final objective is to maximize the network coverage lifetime in WSNs.
-
-
-
-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.
-
-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.
-
-\fi
+\noindent  In  this section,  we  summarize  some  related works  regarding  the
+coverage problem and distinguish our  DiLCO protocol from the works presented in
+the literature.
+
+The most discussed coverage problems  in literature can be classified into three
+types \cite{li2013survey}:  area coverage \cite{Misra} where  every point inside
+an area is to be  monitored, target coverage \cite{yang2014novel} where the main
+objective is  to cover only a  finite number of discrete  points called targets,
+and barrier coverage \cite{Kumar:2005}\cite{kim2013maximum} to prevent intruders
+from entering into the region  of interest. In \cite{Deng2012} authors transform
+the area coverage problem to the target coverage problem taking into account the
+intersection points among disks of sensors nodes or between disk of sensor nodes
+and boundaries.  {\it In DiLCO protocol, the area coverage, i.e. the coverage of
+  every  point in  the  sensing region,  is  transformed to  the  coverage of  a
+  fraction of points called primary points. }
+
+The major  approach to extend network  lifetime while preserving  coverage is to
+divide/organize the  sensors into a suitable  number of set  covers (disjoint or
+non-disjoint), where  each set  completely covers a  region of interest,  and to
+activate these set  covers successively. The network activity  can be planned in
+advance and scheduled  for the entire network lifetime  or organized in periods,
+and the set  of active sensor nodes  is decided at the beginning  of each period
+\cite{ling2009energy}.  Active node selection is determined based on the problem
+requirements  (e.g.  area   monitoring,  connectivity,  power  efficiency).  For
+instance,  Jaggi  et al.  \cite{jaggi2006}  address  the  problem of  maximizing
+network lifetime by dividing sensors into the maximum number of disjoint subsets
+such  that each  subset  can ensure  both  coverage and  connectivity. A  greedy
+algorithm  is applied  once to  solve  this problem  and the  computed sets  are
+activated  in   succession  to  achieve   the  desired  network   lifetime.   Vu
+\cite{chin2007}, Padmatvathy et al. \cite{pc10}, propose algorithms working in a
+periodic fashion where a cover set  is computed at the beginning of each period.
+{\it  Motivated by  these works,  DiLCO protocol  works in  periods,  where each
+  period contains  a preliminary phase  for information exchange  and decisions,
+  followed by a  sensing phase where one  cover set is in charge  of the sensing
+  task.}
+
+Various approaches, including centralized,  or distributed algorithms, have been
+proposed     to    extend    the     network    lifetime.      In    distributed
+algorithms~\cite{yangnovel,ChinhVu,qu2013distributed},       information      is
+disseminated  throughout  the  network   and  sensors  decide  cooperatively  by
+communicating with their neighbors which of them will remain in sleep mode for a
+certain         period         of         time.          The         centralized
+algorithms~\cite{cardei2005improving,zorbas2010solving,pujari2011high}     always
+provide nearly or close to optimal  solution since the algorithm has global view
+of the whole  network. But such a method has the  disadvantage of requiring high
+communication costs,  since the  node (located at  the base station)  making the
+decision needs information from all the  sensor nodes in the area and the amount
+of  information can  be huge.   {\it  In order  to be  suitable for  large-scale
+  network,  in the DiLCO  protocol, the  area coverage  is divided  into several
+  smaller subregions, and in each one, a node called the leader is in charge for
+  selecting the active sensors for the current period.}
+
+A large  variety of coverage scheduling  algorithms has been  developed. Many of
+the existing  algorithms, dealing with the  maximization of the  number of cover
+sets, are heuristics.  These heuristics  involve the construction of a cover set
+by including in priority the sensor  nodes which cover critical targets, that is
+to  say   targets  that   are  covered  by   the  smallest  number   of  sensors
+\cite{berman04,zorbas2010solving}.  Other  approaches are based  on mathematical
+programming formulations~\cite{cardei2005energy,5714480,pujari2011high,Yang2014}
+and dedicated  techniques (solving with a  branch-and-bound algorithms available
+in optimization solver).   The problem is formulated as  an optimization problem
+(maximization of the lifetime or number of cover sets) under target coverage and
+energy  constraints.   Column   generation  techniques,  well-known  and  widely
+practiced techniques for  solving linear programs with too  many variables, have
+also                                                                        been
+used~\cite{castano2013column,rossi2012exact,deschinkel2012column}. {\it In DiLCO
+  protocol, each  leader, in  each subregion, solves  an integer program  with a
+  double objective  consisting in minimizing  the overcoverage and  limiting the
+  undercoverage.  This  program is inspired from the  work of \cite{pedraza2006}
+  where the objective is to maximize the number of cover sets.}

 
 \section{\uppercase{Description of the DiLCO protocol}}
 \label{sec:The DiLCO Protocol Description}
 
 \section{\uppercase{Description of the DiLCO protocol}}
 \label{sec:The DiLCO Protocol Description}


@@ -241,27 +211,12 @@ 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,  applied  periodically  to  efficiently
 maximize the lifetime in the network.
 techniques: network leader election  and sensor activity scheduling for coverage
 preservation  and  energy  conservation,  applied  periodically  to  efficiently
 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 sensor  network composed  of static  nodes distributed
 independently and uniformly at random.  A high density deployment ensures a high
 
 \subsection{Assumptions and models}
 
 \noindent  We consider  a sensor  network composed  of static  nodes distributed
 independently and uniformly at random.  A high density deployment ensures a high

-coverage ratio of the interested area at the starting. The nodes are supposed to
+coverage ratio of the interested area at the start. The nodes are supposed to

 have homogeneous characteristics from a  communication and a processing point of
 view, whereas they  have heterogeneous energy provisions.  Each  node has access
 to its location thanks,  either to a hardware component (like a  GPS unit), or a
 have homogeneous characteristics from a  communication and a processing point of
 view, whereas they  have heterogeneous energy provisions.  Each  node has access
 to its location thanks,  either to a hardware component (like a  GPS unit), or a


@@ -272,7 +227,7 @@ sensor coverage  model in the  literature. Thus, since  a sensor has  a constant
 sensing range $R_s$, every space points  within a disk centered at a 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
 sensing range $R_s$, every space points  within a disk centered at a 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
+Hou~\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.
 
 hypothesis, a complete coverage of  a convex area implies connectivity among the
 working nodes in the active mode.
 


@@ -283,53 +238,9 @@ corresponding to  a sensor node is covered  by its neighboring nodes  if all its
 primary points are covered. Obviously,  the approximation of coverage is more or
 less accurate according to the number of primary points.
 
 primary points are covered. Obviously,  the approximation of coverage is more or
 less accurate according to the number of primary points.
 

-\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}
+\subsection{Main idea}

 \label{main_idea}
 \label{main_idea}

-

 \noindent We start  by applying a divide-and-conquer algorithm  to partition the
 area of interest  into smaller areas called subregions and  then our protocol is
 executed   simultaneously  in   each   subregion.
 \noindent We start  by applying a divide-and-conquer algorithm  to partition the
 area of interest  into smaller areas called subregions and  then our protocol is
 executed   simultaneously  in   each   subregion.


@@ -343,27 +254,27 @@ executed   simultaneously  in   each   subregion.
 
 As  shown  in Figure~\ref{fig2},  the  proposed  DiLCO  protocol is  a  periodic
 protocol where  each period is  decomposed into 4~phases:  Information Exchange,
 
 As  shown  in Figure~\ref{fig2},  the  proposed  DiLCO  protocol is  a  periodic
 protocol where  each period is  decomposed into 4~phases:  Information Exchange,

-Leader Election ,  Decision, and Sensing. For each period  there will be exactly
+Leader Election,  Decision, and Sensing. For  each period there  will be exactly

 one  cover  set  in charge  of  the  sensing  task.   A periodic  scheduling  is
 interesting  because it  enhances the  robustness  of the  network against  node
 failures. First,  a node  that has not  enough energy  to complete a  period, or
 which fails before  the decision is taken, will be  excluded from the scheduling
 process. Second,  if a node  fails later, whereas  it was supposed to  sense the
 one  cover  set  in charge  of  the  sensing  task.   A periodic  scheduling  is
 interesting  because it  enhances the  robustness  of the  network against  node
 failures. First,  a node  that has not  enough energy  to complete a  period, or
 which fails before  the decision is taken, will be  excluded from the scheduling
 process. Second,  if a node  fails later, whereas  it was supposed to  sense the

-region  of interest,  it will  only  affect the  quality of  coverage until  the
-definition of a new cover set  in the next period.  Constraints, like the energy
+region of  interest, it will only affect  the quality of the  coverage until the
+definition of  a new  cover set  in the next  period.  Constraints,  like energy

 consumption, can be easily taken into consideration since the sensors can update
 and exchange their  information during the first phase.  Let  us notice that the
 phases  before  the sensing  one  (Information  Exchange,  Leader Election,  and
 Decision) are  energy consuming for all the  nodes, even nodes that  will not be
 retained by the leader to keep watch over the corresponding area.
 
 consumption, can be easily taken into consideration since the sensors can update
 and exchange their  information during the first phase.  Let  us notice that the
 phases  before  the sensing  one  (Information  Exchange,  Leader Election,  and
 Decision) are  energy consuming for all the  nodes, even nodes that  will not be
 retained by the leader to keep watch over the corresponding area.
 

-During the execution of the DiLCO protocol, two kinds of packets will be used:
+During the execution of the DiLCO protocol, two kinds of packet will be used:

 %\begin{enumerate}[(a)]
 \begin{itemize} 
 \item INFO  packet: sent  by each  sensor node to  all the  nodes inside  a same
   subregion for information exchange.
 \item ActiveSleep packet:  sent by the leader to all the  nodes in its subregion
 %\begin{enumerate}[(a)]
 \begin{itemize} 
 \item INFO  packet: sent  by each  sensor node to  all the  nodes inside  a same
   subregion for information exchange.
 \item ActiveSleep packet:  sent by the leader to all the  nodes in its subregion

-  to inform them to be stay Active or to go Sleep during the sensing phase.
+  to inform them to stay Active or to go Sleep during the sensing phase.

 \end{itemize}
 %\end{enumerate}
 and each sensor node will have five possible status in the network:
 \end{itemize}
 %\end{enumerate}
 and each sensor node will have five possible status in the network:


@@ -394,57 +305,9 @@ to each sensor  in the same subregion to  indicate it if it has to  be active or
 not.  Alternately, if  the  sensor  is not  the  leader, it  will  wait for  the
 Active-Sleep packet to know its state for the coming sensing phase.
 
 not.  Alternately, if  the  sensor  is not  the  leader, it  will  wait for  the
 Active-Sleep packet to know its state for the coming sensing phase.
 

-\iffalse
-\subsubsection{Information Exchange Phase}
-
-Each sensor node $j$ sends its position, remaining energy $RE_j$, and
-the number of neighbors  $NBR_j$ 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 neighbors,  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!]                
 
 \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} \; 
   
   \BlankLine
   %\emph{Initialize the sensor node and determine it's position and subregion} \; 
   


@@ -468,7 +331,7 @@ sensor in the subregion and then describe it in more detail.  \fi
       \Else{
         \emph{$s_j.status$ = LISTENING}\;
         \emph{Wait $ActiveSleep()$ packet from the Leader}\;
       \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 $}\;
       }  
       %  }
         \emph{Update $RE_j $}\;
       }  
       %  }


@@ -481,24 +344,77 @@ sensor in the subregion and then describe it in more detail.  \fi
 
 \end{algorithm}
 
 
 \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{\uppercase{Coverage problem formulation}}
 \label{cp}
 
 \section{\uppercase{Coverage problem formulation}}
 \label{cp}
 

+% MODIF - BEGIN
+We formulate the coverage optimization problem with an integer program.
+The objective function consists in minimizing the undercoverage and the overcoverage of the area as suggested in \cite{pedraza2006}. 
+The area coverage problem is expressed as the coverage of a fraction of points called primary points. 
+Details on the choice and the number of primary points can be found in \cite{idrees2014coverage}. The set of primary points is denoted by $P$
+and the set of sensors by $J$. As we consider a boolean disk coverage model, we use the boolean indicator $\alpha_{jp}$ which is equal to 1 if the primary point $p$ is in the sensing range of the sensor $j$. The binary variable $X_j$ represents the activation or not of the sensor $j$. So we can express the number of  active sensors  that cover  the primary  point $p$ by $\sum_{j \in J} \alpha_{jp} * X_{j}$. We deduce the overcoverage denoted by $\Theta_p$ of the primary point $p$ :
+\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}
+More  precisely, $\Theta_{p}$ represents  the number of  active sensor
+nodes minus  one that  cover the primary  point~$p$.
+In the same way, we define the  undercoverage variable
+$U_{p}$ of the primary point $p$ as:
+\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}
+There is, of course, a relationship between the three variables $X_j$, $\Theta_p$, and $U_p$ which can be formulated as follows :
+\begin{equation}
+\sum_{j \in J}  \alpha_{jp} X_{j} - \Theta_{p}+ U_{p} =1, \forall p \in P
+\end{equation}
+If the point $p$ is not covered, $U_p=1$,  $\sum_{j \in J}  \alpha_{jp} X_{j}=0$ and $\Theta_{p}=0$ by definition, so the equality is satisfied.
+On the contrary, if the point $p$ is covered, $U_p=0$, and $\Theta_{p}=\left( \sum_{j \in J} \alpha_{jp}  X_{j} \right)- 1$. 
+\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}
+The objective function is a weighted sum of overcoverage and undercoverage. The goal is to limit the overcoverage in order to activate a minimal number of sensors while simultaneously preventing undercoverage. Both  weights $w_\theta$  and $w_U$ must  be carefully  chosen in
+order to  guarantee that the  maximum number of  points are covered  during each
+period.
+% MODIF - END
+
+
+
+
+
+
+
+\iffalse 
+

 \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,  the 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
 \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,  the 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  variable $X_{j}$ which  determine the  activation of
+model, we consider that the binary variable $X_{j}$ determines the activation of

 sensor $j$  in the sensing  phase. We also  consider primary points  as targets.
 The set of primary points is denoted by $P$ and the set of sensors by $J$.
 
 sensor $j$  in the sensing  phase. We also  consider primary points  as targets.
 The set of primary points is denoted by $P$ and the set of sensors by $J$.
 


@@ -533,10 +449,9 @@ We define the Overcoverage variable $\Theta_{p}$ as:
 \end{array} \right.
 \label{eq13} 
 \end{equation}
 \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:
+\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}
 \begin{equation}
 U_{p} = \left \{ 
 \begin{array}{l l}


@@ -556,7 +471,7 @@ U_{p} = \left \{
 %\label{c1} 
 %\sum_{t \in T} X_{j,t} \leq \frac{RE_j}{e_t} &\forall j \in J \\
 %\label{c2}
 %\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\\
+\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}
 U_{p} \in \{0,1\}, &\forall p \in P \\
 X_{j} \in \{0,1\}, &\forall j \in J
 \end{array}


@@ -582,6 +497,8 @@ undercoverage. Both  weights $w_\theta$  and $w_U$ must  be carefully  chosen in
 order to  guarantee that the  maximum number of  points are covered  during each
 period.
 
 order to  guarantee that the  maximum number of  points are covered  during each
 period.
 

+\fi
+

 \section{\uppercase{Protocol evaluation}}  
 \label{sec:Simulation Results and Analysis}
 \noindent \subsection{Simulation framework}
 \section{\uppercase{Protocol evaluation}}  
 \label{sec:Simulation Results and Analysis}
 \noindent \subsection{Simulation framework}


@@ -642,7 +559,7 @@ node typically  consists of  four units: a  MicroController Unit, an  Atmels AVR
 ATmega103L in  case of Medusa II,  to perform the  computations; a communication
 (radio) unit able to send and  receive messages; a sensing unit to collect data;
 a power supply  which provides the energy consumed by  node. Except the battery,
 ATmega103L in  case of Medusa II,  to perform the  computations; a communication
 (radio) unit able to send and  receive messages; a sensing unit to collect data;
 a power supply  which provides the energy consumed by  node. Except the battery,

-all the other unit  can be be switched off to save  energy according to the node
+all the other unit  can be switched off to save  energy according to the node

 status.   Table~\ref{table4} summarizes  the energy  consumed (in  milliWatt per
 second) by a node for each of its possible status.
 
 status.   Table~\ref{table4} summarizes  the energy  consumed (in  milliWatt per
 second) by a node for each of its possible status.
 


@@ -687,22 +604,34 @@ ActiveSleep  packet. To  compute the  energy  needed by  a node  to transmit  or
 receive such  packets, we  use the equation  giving the  energy spent to  send a
 1-bit-content   message  defined   in~\cite{raghunathan2002energy}   (we  assume
 symmetric  communication costs), and  we set  their respective  size to  112 and
 receive such  packets, we  use the equation  giving the  energy spent to  send a
 1-bit-content   message  defined   in~\cite{raghunathan2002energy}   (we  assume
 symmetric  communication costs), and  we set  their respective  size to  112 and

-24~bits. The energy required to send or receive a 1-bit is equal to $0.2575 mW$.
+24~bits. The energy required to send  or receive a 1-bit-content message is thus
+ equal to 0.2575~mW.

 
 

-Each node has an initial energy level, in Joules, which is randomly drawn in the
-interval  $[500-700]$.   If  it's  energy   provision  reaches  a   value  below
+Each node  has an initial  energy level, in  Joules, which is randomly  drawn in
+$[500-700]$.   If its  energy  provision  reaches a  value  below the  threshold

 $E_{th}=36$~Joules, the minimum  energy needed for a node  to stay active during
 $E_{th}=36$~Joules, the minimum  energy needed for a node  to stay active during

-one period,  it will no  more participate in  the coverage task. This  value has
-been computed  by multiplying the energy  consumed in active state  (9.72 mW) by
-the time in  second for one round (3600 seconds).  According  to the interval of
-initial energy, a sensor may be active during at most 20 rounds.
+one  period, it  will  no longer  take part  in  the coverage  task. This  value
+corresponds to the  energy needed by the sensing  phase, obtained by multiplying
+the energy  consumed in active state  (9.72 mW) by  the time in seconds  for one
+period  (3,600 seconds),  and  adding  the energy  for  the pre-sensing  phases.
+According to  the interval of initial energy,  a sensor may be  active during at
+most 20 periods.

 
 In the simulations,  we introduce the following performance  metrics to evaluate
 the efficiency of our approach:
 
 %\begin{enumerate}[i)]
 \begin{itemize}
 
 In the simulations,  we introduce the following performance  metrics to evaluate
 the efficiency of our approach:
 
 %\begin{enumerate}[i)]
 \begin{itemize}

-  
+\item {{\bf Network Lifetime}:} we define the network lifetime as the time until
+  the  coverage  ratio  drops  below  a  predefined  threshold.   We  denote  by
+  $Lifetime_{95}$ (respectively $Lifetime_{50}$) the amount of time during which
+  the  network can  satisfy an  area coverage  greater than  $95\%$ (respectively
+  $50\%$). We assume that the sensor  network can fulfill its task until all its
+  nodes have  been drained of their  energy or it  becomes disconnected. Network
+  connectivity  is crucial because  an active  sensor node  without connectivity
+  towards a base  station cannot transmit any information  regarding an observed
+  event in the area that it monitors.
+     

 \item {{\bf Coverage Ratio (CR)}:} it measures how well the WSN is able to 
   observe the area of interest. In our case, we discretized the sensor field
   as a regular grid, which yields the following equation to compute the
 \item {{\bf Coverage Ratio (CR)}:} it measures how well the WSN is able to 
   observe the area of interest. In our case, we discretized the sensor field
   as a regular grid, which yields the following equation to compute the


@@ -712,30 +641,13 @@ the efficiency of our approach:
 \mbox{CR}(\%) = \frac{\mbox{$n$}}{\mbox{$N$}} \times 100.
 \end{equation*}
 where  $n$ is  the number  of covered  grid points  by active  sensors  of every
 \mbox{CR}(\%) = \frac{\mbox{$n$}}{\mbox{$N$}} \times 100.
 \end{equation*}
 where  $n$ is  the number  of covered  grid points  by active  sensors  of every

-subregions during  the current  sensing phase  and $N$ is  total number  of grid
+subregions during  the current  sensing phase  and $N$ is the total number  of grid

 points in  the sensing field. In  our simulations, we have  a layout of  $N = 51
 \times 26 = 1326$ grid points.
 points in  the sensing field. In  our simulations, we have  a layout of  $N = 51
 \times 26 = 1326$ 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  Energy Consumption}:}  energy consumption (EC)  can be seen  as the
 
 \item {{\bf  Energy Consumption}:}  energy consumption (EC)  can be seen  as the

-  total   energy   consumed   by   the   sensors   during   $Lifetime_{95}$   or
-  $Lifetime_{50}$, divided  by the number of periods.  Formally, the computation
+  total amount of  energy   consumed   by   the   sensors   during   $Lifetime_{95}$   
+  or $Lifetime_{50}$, divided  by the number of periods.  Formally, the computation

   of EC can be expressed as follows:
   \begin{equation*}
     \scriptsize
   of EC can be expressed as follows:
   \begin{equation*}
     \scriptsize


@@ -743,43 +655,21 @@ Where: $A_r^t$ is the number of active sensors in the subregion $r$ during round
       + E^{a}_m+E^{s}_m \right)}{M},
   \end{equation*}
 
       + E^{a}_m+E^{s}_m \right)}{M},
   \end{equation*}
 

-where $M$  corresponds to the number  of periods.  The total  energy consumed by
-the  sensors (EC)  comes  through  taking into  consideration  four main  energy
-factors. The  first one , denoted $E^{\scriptsize  \mbox{com}}_m$, represent the
-energy consumption  spent by  all the nodes  for wireless  communications during
-period $m$.   $E^{\scriptsize \mbox{list}}_m$,  the next factor,  corresponds to
-the  energy consumed by  the sensors  in LISTENING  status before  receiving the
-decision to  go active or  sleep in period $m$.  $E^{\scriptsize \mbox{comp}}_m$
-refers to the energy needed by all the leader nodes to solve the integer program
-during a period.  Finally, $E^a_{m}$ and $E^s_{m}$ indicate  the energy consumed
-by the whole network in the sensing phase (active and sleeping nodes).
-
-\item {{\bf Network Lifetime}:} we define the network lifetime as the time until
-  the  coverage  ratio  drops  below  a  predefined  threshold.   We  denote  by
-  $Lifetime_{95}$ (respectively $Lifetime_{50}$) the amount of time during which
-  the  network can  satisfy an  area coverage  greater than  $95\%$ (respectively
-  $50\%$). We assume that the sensor  network can fulfill its task until all its
-  nodes have  been drained of their  energy or it  becomes disconnected. Network
-  connectivity  is crucial because  an active  sensor node  without connectivity
-  towards a base  station cannot transmit any information  regarding an observed
-  event in the area that it monitors.
-
-\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
+where $M$  corresponds to  the number  of periods.  The  total amount  of energy
+consumed by the  sensors (EC) comes through taking  into consideration four main
+energy   factors.  The  first   one,  denoted   $E^{\scriptsize  \mbox{com}}_m$,
+represents  the  energy  consumption  spent   by  all  the  nodes  for  wireless
+communications  during period  $m$.  $E^{\scriptsize  \mbox{list}}_m$,  the next
+factor, corresponds  to the energy consumed  by the sensors  in LISTENING status
+before  receiving   the  decision  to  go   active  or  sleep   in  period  $m$.
+$E^{\scriptsize \mbox{comp}}_m$  refers to the  energy needed by all  the leader
+nodes  to solve the  integer program  during a  period.  Finally,  $E^a_{m}$ and
+$E^s_{m}$ indicate the energy consumed by the whole network in the sensing phase
+(active and sleeping nodes).

 
 \end{itemize}
 %\end{enumerate}
 
 
 \end{itemize}
 %\end{enumerate}
 

-

 %\subsection{Performance Analysis for different subregions}
 \subsection{Performance analysis}
 \label{sub1}
 %\subsection{Performance Analysis for different subregions}
 \subsection{Performance analysis}
 \label{sub1}


@@ -788,7 +678,7 @@ In this subsection, we first focus  on the performance of our DiLCO protocol for
 different numbers  of subregions.  We consider partitions  of the WSN  area into
 $2$, $4$, $8$, $16$, and $32$ subregions. Thus the DiLCO protocol is declined in
 five versions:  DiLCO-2, DiLCO-4,  DiLCO-8, DiLCO-16, and  DiLCO-32. Simulations
 different numbers  of subregions.  We consider partitions  of the WSN  area into
 $2$, $4$, $8$, $16$, and $32$ subregions. Thus the DiLCO protocol is declined in
 five versions:  DiLCO-2, DiLCO-4,  DiLCO-8, DiLCO-16, and  DiLCO-32. Simulations

-without  partitioning  the  area  of  interest,  case  which  corresponds  to  a
+without  partitioning  the  area  of  interest,  cases  which  correspond  to  a

 centralized  approach, are  not presented  because they  require  high execution
 times to solve the integer program and therefore consume too much energy.
 
 centralized  approach, are  not presented  because they  require  high execution
 times to solve the integer program and therefore consume too much energy.
 


@@ -801,23 +691,23 @@ chosen to remain active during the sensing phase.
 \subsubsection{Coverage ratio} 
 
 Figure~\ref{fig3} shows  the average coverage  ratio for 150 deployed  nodes. It
 \subsubsection{Coverage ratio} 
 
 Figure~\ref{fig3} shows  the average coverage  ratio for 150 deployed  nodes. It

-can  be seen  that both  DESK and  GAF provide  a little  better  coverage ratio
-compared to DiLCO  in the first thirty periods. This can  be easily explained by
-the number of  active nodes: the optimization process  of our protocol activates
-less nodes  than DESK  or GAF, resulting  in a  slight decrease of  the coverage
-ratio. In case of DiLCO-2  (respectively DiLCO-4), the coverage ratio exhibits a
-fast decrease with  the number of periods and reaches zero  value in period {\bf
-  X} (respectively {\bf Y}), whereas the  other versions of DiLCO, DESK, and GAF
-ensure a coverage  ratio above 50\% for subsequent periods.  We believe that the
-results obtained with  these two methods can be explained  by a high consumption
-of energy and we will check this assumption in the next subsection.
+can be seen  that both DESK and  GAF provide a coverage ratio  which is slightly
+better  compared to  DiLCO  in the  first  thirty periods.  This  can be  easily
+explained  by  the number  of  active nodes:  the  optimization  process of  our
+protocol activates less  nodes than DESK or GAF, resulting  in a slight decrease
+of the coverage  ratio. In case of DiLCO-2  (respectively DiLCO-4), the coverage
+ratio exhibits a fast decrease with the number of periods and reaches zero value
+in period~18 (respectively  46), whereas the other versions  of DiLCO, DESK, and
+GAF ensure a coverage ratio above  50\% for subsequent periods.  We believe that
+the  results  obtained  with these  two  methods  can  be  explained by  a  high
+consumption of energy and we will check this assumption in the next subsection.

 
 Concerning  DiLCO-8, DiLCO-16,  and  DiLCO-32,  these methods  seem  to be  more
 efficient than DESK  and GAF, since they can provide the  same level of coverage
 (except in the first periods where  DESK and GAF slightly outperform them) for a
 greater number  of periods. In fact, when  our protocol is applied  with a large
 number of subregions (from 8 to 32~regions), it activates a restricted number of
 
 Concerning  DiLCO-8, DiLCO-16,  and  DiLCO-32,  these methods  seem  to be  more
 efficient than DESK  and GAF, since they can provide the  same level of coverage
 (except in the first periods where  DESK and GAF slightly outperform them) for a
 greater number  of periods. In fact, when  our protocol is applied  with a large
 number of subregions (from 8 to 32~regions), it activates a restricted number of

-nodes, and thus allow to extend the network lifetime.
+nodes, and thus enables the extension of the network lifetime.

 
 \parskip 0pt    
 \begin{figure}[t!]
 
 \parskip 0pt    
 \begin{figure}[t!]


@@ -827,10 +717,6 @@ nodes, and thus allow to extend the network lifetime.
 \label{fig3}
 \end{figure} 
 
 \label{fig3}
 \end{figure} 
 

-%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 periods. Coverage ratio decreases when the number of periods 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{Energy consumption}
 
 
 \subsubsection{Energy consumption}
 


@@ -848,7 +734,7 @@ used for the different performance metrics.
 \begin{figure}[h!]
 \centering
 \includegraphics[scale=0.45]{R/EC.pdf} 
 \begin{figure}[h!]
 \centering
 \includegraphics[scale=0.45]{R/EC.pdf} 

-\caption{Energy consumption}
+\caption{Energy consumption per period}

 \label{fig95}
 \end{figure} 
 
 \label{fig95}
 \end{figure} 
 


@@ -856,11 +742,16 @@ The  results  depict the  good  performance of  the  different  versions of  our
 protocol.   Indeed,  the protocols  DiLCO-16/50,  DiLCO-32/50, DiLCO-16/95,  and
 DiLCO-32/95  consume less  energy than  their DESK  and GAF  counterparts  for a
 similar level of area coverage.   This observation reflects the larger number of
 protocol.   Indeed,  the protocols  DiLCO-16/50,  DiLCO-32/50, DiLCO-16/95,  and
 DiLCO-32/95  consume less  energy than  their DESK  and GAF  counterparts  for a
 similar level of area coverage.   This observation reflects the larger number of

-nodes set active by DESK and GAF.
-
+nodes set active  by DESK and GAF. 

 
 

-%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.  
+Now, if we consider a same  protocol, we can notice that the average consumption
+per  period increases slightly  for our  protocol when  increasing the  level of
+coverage and the number of node,  whereas it increases more largely for DESK and
+GAF.  In case of DiLCO, it means that even if a larger network allows to improve
+the number of periods with a  minimum coverage level value, this improvement has
+a  higher energy  cost  per period  due  to communication  overhead  and a  more
+difficult optimization problem.   However, in comparison with DESK  and GAF, our
+approach has a reasonable energy overcost.

 
 \subsubsection{Execution time}
 
 
 \subsubsection{Execution time}
 


@@ -890,13 +781,11 @@ limited number  of variables and  constraints.  Conversely, DiLCO-2  requires to
 solve an optimization problem with half of the network nodes and thus presents a
 high execution time.  Nevertheless if  we refer to Figure~\ref{fig3}, we observe
 that DiLCO-32  is slightly less efficient  than DilCO-16 to maintain  as long as
 solve an optimization problem with half of the network nodes and thus presents a
 high execution time.  Nevertheless if  we refer to Figure~\ref{fig3}, we observe
 that DiLCO-32  is slightly less efficient  than DilCO-16 to maintain  as long as

-possible high  coverage. In fact excessive  subdivision of the  area of interest
-prevents   to  ensure   good  coverage   especially  on   the  borders   of  the
+possible high  coverage. In fact an excessive  subdivision of the  area of interest
+prevents it  to  ensure a  good  coverage   especially  on   the  borders   of  the

 subregions. Thus,  the optimal number of  subregions can be seen  as a trade-off
 between execution time and coverage performance.
 
 subregions. Thus,  the optimal number of  subregions can be seen  as a trade-off
 between execution time and coverage performance.
 

-%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{Network lifetime}
 
 In the next figure, the network lifetime is illustrated. Obviously, the lifetime
 \subsubsection{Network lifetime}
 
 In the next figure, the network lifetime is illustrated. Obviously, the lifetime


@@ -915,22 +804,17 @@ network lifetime.
 As  highlighted by  Figure~\ref{figLT95},  when the  coverage  level is  relaxed
 ($50\%$) the network lifetime also  improves. This observation reflects the fact
 that  the higher  the coverage  performance, the  more nodes  must be  active to
 As  highlighted by  Figure~\ref{figLT95},  when the  coverage  level is  relaxed
 ($50\%$) the network lifetime also  improves. This observation reflects the fact
 that  the higher  the coverage  performance, the  more nodes  must be  active to

-ensure the  wider monitoring.  For a  same level of  coverage, DiLCO outperforms
+ensure the  wider monitoring.  For a  similar level of  coverage, DiLCO outperforms

 DESK and GAF for the lifetime of  the network. More specifically, if we focus on
 DESK and GAF for the lifetime of  the network. More specifically, if we focus on

-the larger level  of coverage ($95\%$) in case of  our protocol, the subdivision
+the larger level  of coverage ($95\%$) in the case of  our protocol, the subdivision

 in $16$~subregions seems to be the most appropriate.
 
 in $16$~subregions seems to be the most appropriate.
 

-% 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 work}}
 \label{sec:Conclusion and Future Works} 
 
 A crucial problem in WSN is  to schedule the sensing activities of the different
 
 \section{\uppercase{Conclusion and future work}}
 \label{sec:Conclusion and Future Works} 
 
 A crucial problem in WSN is  to schedule the sensing activities of the different

-nodes  in order to  ensure both  coverage of  the area  of interest  and longest
+nodes  in order to  ensure both  coverage of  the area  of interest  and longer

 network lifetime. The inherent limitations of sensor nodes, in energy provision,
 communication and computing capacities,  require protocols that optimize the use
 of  the  available resources  to  fulfill the  sensing  task.   To address  this
 network lifetime. The inherent limitations of sensor nodes, in energy provision,
 communication and computing capacities,  require protocols that optimize the use
 of  the  available resources  to  fulfill the  sensing  task.   To address  this


@@ -938,60 +822,29 @@ problem, this paper proposes a  two-step approach. Firstly, the field of sensing
 is  divided into  smaller  subregions using  the  concept of  divide-and-conquer
 method. Secondly,  a distributed  protocol called Distributed  Lifetime Coverage
 Optimization is applied in each  subregion to optimize the coverage and lifetime
 is  divided into  smaller  subregions using  the  concept of  divide-and-conquer
 method. Secondly,  a distributed  protocol called Distributed  Lifetime Coverage
 Optimization is applied in each  subregion to optimize the coverage and lifetime

-performances.   In a subregion,  our protocol  consists to  elect a  leader node
+performances.   In a subregion,  our protocol  consists in  electing a  leader node

 which will then perform a sensor activity scheduling. The challenges include how
 to  select   the  most  efficient  leader   in  each  subregion   and  the  best
 representative set of active nodes to ensure a high level of coverage. To assess
 the performance of our approach, we  compared it with two other approaches using
 many performance metrics  like coverage ratio or network  lifetime. We have also
 which will then perform a sensor activity scheduling. The challenges include how
 to  select   the  most  efficient  leader   in  each  subregion   and  the  best
 representative set of active nodes to ensure a high level of coverage. To assess
 the performance of our approach, we  compared it with two other approaches using
 many performance metrics  like coverage ratio or network  lifetime. We have also

-study the  impact of the  number of subregions  chosen to subdivide the  area of
+studied the  impact of the  number of subregions  chosen to subdivide the  area of

 interest,  considering  different  network  sizes.  The  experiments  show  that
 interest,  considering  different  network  sizes.  The  experiments  show  that

-increasing the  number of subregions allows  to improves the  lifetime. The more
-there  are   subregions,  the  more   the  network  is  robust   against  random
-disconnection resulting from dead nodes.  However, for a given sensing field and
-network size  there is an optimal  number of subregions.  Therefore,  in case of
-our simulation  context a  subdivision in $16$~subregions  seems to be  the most
-relevant. The optimal number of subregions will be investigated in the future.
-
-\iffalse
-\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
-\fi
+increasing the  number of subregions improves  the lifetime. The  more subregions there are,  the  more robust  the  network  is   against  random  disconnection
+resulting from dead nodes.  However, for  a given sensing field and network size
+there is an optimal number of  subregions.  Therefore, in case of our simulation
+context  a subdivision in  $16$~subregions seems  to be  the most  relevant. The
+optimal number of subregions will be investigated in the future.

 
 \section*{\uppercase{Acknowledgements}}
 
 
 \section*{\uppercase{Acknowledgements}}
 

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

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

-Campus France for the received support.
+Campus France for  the received support. This paper is  also partially funded by
+the Labex ACTION program (contract ANR-11-LABX-01-01).

 
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+\bibliographystyle{plain}

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