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@@ -11,7 +11,7 @@
 
 \hyphenation{op-tical net-works semi-conduc-tor}
 
-
+\usepackage{etoolbox}
 \usepackage{float} 
 \usepackage{epsfig}
 \usepackage{calc}
@@ -39,332 +39,183 @@
 \DeclareGraphicsExtensions{.ps}
 \DeclareGraphicsRule{.ps}{pdf}{.pdf}{`ps2pdf -dEPSCrop -dNOSAFER #1 \noexpand\OutputFile}
 
-
 \begin{document}
 %
 % paper title
 % can use linebreaks \\ within to get better formatting as desired
-\title{Coverage and Lifetime Optimization in Heterogeneous Energy Wireless Sensor Networks}
+\title{Coverage and Lifetime Optimization \\
+in Heterogeneous Energy Wireless Sensor Networks}
 
-\author{\IEEEauthorblockN{Ali Kadhum Idrees, Karine Deschinkel, Michel Salomon, and Rapha\"el Couturier}
+\author{\IEEEauthorblockN{Ali Kadhum Idrees, Karine Deschinkel, Michel Salomon, 
+and Rapha\"el Couturier}
 \IEEEauthorblockA{FEMTO-ST Institute, UMR 6174 CNRS \\
 University of Franche-Comt\'e  \\
 Belfort, France\\
-Email: ali.idness@edu.univ-fcomte.fr, $\lbrace$karine.deschinkel, michel.salomon, raphael.couturier$\rbrace$@univ-fcomte.fr}}
+Email: ali.idness@edu.univ-fcomte.fr, $\lbrace$karine.deschinkel, michel.salomon, 
+raphael.couturier$\rbrace$@univ-fcomte.fr}}
 
 \maketitle
 
-
 \begin{abstract}
 One of  the fundamental challenges in Wireless  Sensor Networks (WSNs)
-is  the coverage  preservation  and  the extension  of  the  network  lifetime
+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 coverage optimization protocol to
-improve the lifetime in  heterogeneous energy wireless sensor networks
-is proposed.   The area of  interest is first divided  into subregions
-using a  divide-and-conquer method and then the scheduling  of sensor node
-activity  is  planned for  each  subregion.   The proposed  scheduling
-considers  rounds during  which  a small  number  of nodes,  remaining
-active  for  sensing, is  selected  to  ensure  coverage.  Each  round
-consists  of   four  phases:  (i)~Information   Exchange,  (ii)~Leader
+region) of  interest. In this paper, a  coverage optimization protocol
+to  improve  the  lifetime  in heterogeneous  energy  wireless  sensor
+networks  is proposed.   The area  of interest  is first  divided into
+subregions using  a divide-and-conquer method and  then the scheduling
+of sensor node  activity is planned for each  subregion.  The proposed
+scheduling  considers rounds  during which  a small  number  of nodes,
+remaining active  for sensing, is  selected to ensure  coverage.  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.
+carried  out  by a  leader  node,  which  solves an  integer  program.
 Simulation  results show that  the proposed  approach can  prolong the
 network lifetime and improve the coverage performance.
 \end{abstract}
 
 \begin{IEEEkeywords}
-Area Coverage, Network lifetime, Optimization, Scheduling, Distributed Protocol.
+Wireless   Sensor   Networks,   Area   Coverage,   Network   lifetime,
+Optimization, Scheduling.
 \end{IEEEkeywords}
 %\keywords{Area Coverage, Network lifetime, Optimization, Distributed Protocol}
  
 \IEEEpeerreviewmaketitle
 
-
- 
-
-
-
 \section{Introduction}
 
-\noindent The fast developments in the low-cost sensor devices and wireless communications have allowed the emergence the WSNs. WSN includes a large number of small , limited-power sensors  that can sense, process and transmit
- data over a wireless communication . They communicate with each other by using multi-hop wireless communications , cooperate together to monitor the area of interest, and the measured data can be reported
- to a monitoring center
-called, sink, for analysis it~\cite{Ammari01, Sudip03}. There are several applications used the WSN including health, home, environmental, military,and industrial applications~\cite{Akyildiz02}.
-The coverage  problem is one of the fundamental challenges in WSNs~\cite{Nayak04} that consists in monitoring efficiently and  continuously the area of interest. The limited energy of sensors represents the main challenge in the WSNs design~\cite{Ammari01}, where it is difficult to replace and/or
- recharge their batteries because the the area of interest nature (such as hostile environments) and the cost. So, it is necessary that a WSN deployed with high density  because spatial redundancy can then be exploited to increase the lifetime of the network . However, turn on all the sensor nodes, which monitor the same region at the same time leads to decrease the lifetime of the network. To extend the lifetime of the network, the main idea is to take advantage of the overlapping sensing regions of some sensor nodes to save energy by turning off some of them during the sensing phase~\cite{Misra05}. WSNs require energy-efficient solutions to improve the network lifetime that is constrained by the limited power of each sensor node ~\cite{Akyildiz02}. 
-In  this  paper,  we  concentrate on  the area
-coverage  problem,  with  the  objective  of  maximizing  the  network
-lifetime  by using  an adaptive  scheduling. The  area of  interest is
-divided into subregions and an activity scheduling for sensor nodes is
-planned for  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 scheduling  scheme 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. This  coverage strategy  involves the
-solving of  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
+%\indent  The fast  developments  in the  low-cost  sensor devices  and
+%wireless  communications have  allowed  the emergence  the WSNs.   WSN
+%includes  a large  number  of small,  limited-power  sensors that  can
+%sense, process  and transmit data over a  wireless communication. They
+%communicate   with   each    other   by   using   multi-hop   wireless
+%communications, cooperate  together to  monitor the area  of interest,
+%and the  measured data can be  reported to a  monitoring center called
+%sink  for analysis it~\cite{Sudip03}.  There are  several applications
+%used  the WSN  including  health, home,  environmental, military,  and
+%industrial applications~\cite{Akyildiz02}. The coverage problem is one
+%of the fundamental challenges  in WSNs~\cite{Nayak04} that consists in
+%monitoring    efficiently    and     continuously    the    area    of
+%interest. Thelimited  energy of sensors represents  the main challenge
+%in the  WSNs design~\cite{Sudip03}, where  it is difficult  to replace
+%and/or  recharge their  batteries  because the  the  area of  interest
+%nature  (such  as  hostile  environments)  and the  cost.  So,  it  is
+%necessary  that  a WSN  deployed  with  high  density because  spatial
+%redundancy  can then  be exploited  to  increase the  lifetime of  the
+%network. However, turn on all the sensor nodes, which monitor the same
+%region at the same time leads to decrease the lifetime of the network.
+
+Recent   years  have  witnessed   significant  advances   in  wireless
+communications and embedded micro-sensing MEMS technologies which have
+led to the emergence of Wireless  Sensor Networks (WSNs) as one of the
+most promising  technologies \cite{Akyildiz02}. In  fact, they present
+huge   potential  in   several  domains   ranging  from   health  care
+applications to military applications. A sensor network is composed of
+a  large  number of  tiny  sensing devices  deployed  in  a region  of
+interest.  Each  device  has  processing  and  wireless  communication
+capabilities, which enable it to sense its environment, to compute, to
+store information  and to  deliver report messages  to a  base station
+\cite{Sudip03}.  One of  the main design issues in  WSNs is to prolong
+the network  lifetime, while  achieving acceptable quality  of service
+for  applications. Indeed,  sensors  nodes have  limited resources  in
+terms of memory, energy and computational power.
+
+Since sensor nodes have limited battery life and without being able to
+replace batteries,  especially in remote and  hostile environments, it
+is desirable that  a WSN should be deployed  with high density because
+spatial redundancy can  then be exploited to increase  the lifetime of
+the network. In such a high  density network, if all sensor nodes were
+to be  activated at the same  time, the lifetime would  be reduced. To
+extend the lifetime of the network, the main idea is to take advantage
+of the overlapping sensing regions of some sensor nodes to save energy
+by turning  off some of them during  the sensing phase~\cite{Misra05}.
+Obviously, the deactivation of nodes  is only relevant if the coverage
+of the monitored  area is not affected. In  this paper, we concentrate
+on  the area coverage  problem \cite{Nayak04},  with the  objective of
+maximizing the network lifetime  by using an adaptive scheduling.  The
+area of interest is divided into subregions and an activity scheduling
+for sensor nodes is planned for 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 scheduling scheme 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.  This
+coverage strategy  involves the solving  of 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
 % Section~\ref{rw}
 reviews the related work in the field.  Section~\ref{pd} is devoted to
 the    scheduling     strategy    for    energy-efficient    coverage.
-Section~\ref{cp} gives the coverage model formulation, which is used to
-schedule  the  activation  of  sensors.  Section~\ref{exp}  shows  the
-simulation  results obtained  using  the discrete  event simulator OMNeT++  \cite{varga}. They  fully demonstrate  the usefulness  of the
-proposed  approach.   Finally, we  give  concluding  remarks and  some
-suggestions for future works in Section~\ref{sec:conclusion}.
-
+Section~\ref{cp} gives  the coverage model formulation,  which is used
+to schedule  the activation  of sensors.  Section~\ref{exp}  shows the
+simulation results obtained using the discrete event simulator OMNeT++
+\cite{varga}. They  fully demonstrate  the usefulness of  the proposed
+approach.  Finally,  we give  concluding remarks and  some suggestions
+for future works in Section~\ref{sec:conclusion}.
 
 \section{Related works}
 \label{rw}
-
-\noindent This section is dedicated to the various approaches proposed
-in  the literature  for  the coverage  lifetime maximization  problem,
-where the  objective is to  optimally schedule sensors'  activities in
-order to  extend network lifetime  in a randomly deployed  network. As
-this problem is subject to a wide range of interpretations, we have chosen
-to recall the main definitions and assumptions related to our work.
-
+\indent In this section, we only review some recent works dealing with
+the coverage lifetime maximization  problem, where the objective is to
+optimally  schedule  sensors'  activities  in  order  to  extend  WSNs
+lifetime.
+
+In \cite{chin2007}, the author proposed a novel distributed heuristic,
+called Distributed Energy-efficient  Scheduling for k-coverage (DESK),
+which  ensures  that  the  energy  consumption among  the  sensors  is
+balanced and the lifetime  maximized while the coverage requirement is
+maintained.   This  heuristic works  in  rounds,  requires only  1-hop
+neighbor information,  and each sensor  decides its status  (active or
+sleep)   based   on  the   perimeter   coverage   model  proposed   in
+\cite{Huang:2003:CPW:941350.941367}.    More    recently,   Shibo   et
+al. \cite{Shibo}  expressed the coverage  problem as a  minimum weight
+submodular  set cover  problem  and proposed  a Distributed  Truncated
+Greedy Algorithm (DTGA) to solve it. They take in particular advantage
+from  both temporal and  spatial correlations  between data  sensed by
+different sensors.
+
+The  works  presented  in  \cite{Bang,  Zhixin, Zhang}  focus  on  the
+definition  of  a  coverage-aware,  distributed  energy-efficient  and
+distributed clustering  methods respectively.  They aim  to extend the
+network  lifetime  while ensuring  the  coverage.   S.   Misra et  al.
+\cite{Misra05} proposed a localized algorithm which conserves energy and
+coverage  by  activating  the  subset  of  sensors  with  the  minimum
+overlapping area. It preserves  the network connectivity thanks to the
+formation of the  network backbone. J.~A.~Torkestani \cite{Torkestani}
+designed a Learning  Automata-based Energy-Efficient Coverage protocol
+(LAEEC)  to construct  a Degree-constrained  Connected  Dominating Set
+(DCDS)  in   WSNs.   He  showed   that  the  correct  choice   of  the
+degree-constraint  of DCDS  balances the  network load  on  the active
+nodes and leads to enhance the coverage and network lifetime.
+ 
+The main  contribution of our approach addresses  three main questions
+to build a scheduling strategy.\\
 %\begin{itemize}
-%\item Area Coverage: The main objective is to cover an area. The area coverage requires
-%that the sensing range of working Active nodes cover the whole targeting area, which means any
-%point in target area can be covered~\cite{Mihaela02,Raymond03}.
-
-%\item Target Coverage: The objective is to cover a set of targets. Target coverage means that the discrete target points can be covered in any time. The sensing range of working Active nodes only monitors a finite number of discrete points in targeting area~\cite{Mihaela02,Raymond03}. 
-
-%\item Barrier Coverage An objective to determine the maximal support/breach paths that traverse a sensor field. Barrier coverage is expressed as finding one or more routes with starting position and ending position when the targets pass through the area deployed with sensor nodes~\cite{Santosh04,Ai05}.
-%\end{itemize}
-\subsection{Coverage} 
-%{\bf Coverage}
-
-The most  discussed coverage problems in literature  can be classified
-into two types \cite{ma10}: area coverage (also called full or blanket
-coverage) and target coverage.  An  area coverage problem is to find a
-minimum number of sensors to work, such that each physical point in the
-area is within the sensing range  of at least one working sensor node.
-Target coverage problem  is to cover only a  finite number of discrete
-points  called targets.   This type  of coverage  has  mainly military
-applications. Our work will concentrate on the area coverage by design
-and implementation of a  strategy, which efficiently selects the active
-nodes   that  must   maintain  both   sensing  coverage   and  network
-connectivity and at the same time improve the lifetime of the wireless
-sensor  network.   But,  requiring  that  all physical  points  of  the
-considered region are covered may  be too strict, especially where the
-sensor network is not dense.   Our approach represents an area covered
-by a sensor as a set of primary points and tries to maximize the total
-number  of  primary points  that  are  covered  in each  round,  while
-minimizing  overcoverage (points  covered by  multiple  active sensors
-simultaneously).
-
-\subsection{Lifetime} 
-%{\bf Lifetime}
-
-Various   definitions   exist   for   the   lifetime   of   a   sensor
-network~\cite{die09}.  The main definitions proposed in the literature are
-related to the  remaining energy of the nodes or  to the coverage percentage. 
-The lifetime of the  network is mainly defined as the amount
-of  time during which  the network  can  satisfy its  coverage objective  (the
-amount of  time that the network  can cover a given  percentage of its
-area or targets of interest). In this work, we assume that the network
-is alive  until all  nodes have  been drained of  their energy  or the
-sensor network becomes disconnected, and we measure the coverage ratio
-during the WSN lifetime.  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.
-
-\subsection{Activity scheduling} 
-%{\bf Activity scheduling}
-
-Activity scheduling is to  schedule the activation and deactivation of
-sensor nodes.  The  basic objective is to decide  which sensors are in
-what states (active or sleeping mode)  and for how long, so that the
-application  coverage requirement  can be  guaranteed and  the network
-lifetime can be  prolonged. Various approaches, including centralized,
-distributed, and localized algorithms, have been proposed for activity
-scheduling.  In  distributed algorithms, each node  in the network
-autonomously makes decisions on whether  to turn on or turn off itself
-only using  local neighbor information. In  centralized algorithms, a
-central controller  (a node or  base station) informs every  sensors of
-the time intervals to be activated.
-
-\subsection{Distributed approaches}
-%{\bf Distributed approaches}
-
-Some      distributed     algorithms      have      been     developed
-in~\cite{Gallais06,Tian02,Ye03,Zhang05,HeinzelmanCB02}  to perform the
-scheduling.   Distributed algorithms typically  operate in  rounds for
-a predetermined  duration. At  the  beginning of  each  round, a  sensor
-exchanges information with its neighbors and makes a decision to either
-remain turned  on or to  go to sleep  for the round. This  decision is
-basically made on simple greedy criteria like  the largest uncovered
-area   \cite{Berman05efficientenergy},   maximum   uncovered   targets
-\cite{1240799}.   In \cite{Tian02}, the  scheduling scheme  is divided
-into rounds, where each round  has a self-scheduling phase followed by
-a sensing phase.  Each sensor  broadcasts a message containing the node ID
-and the node location  to its neighbors at the beginning  of each round. A
-sensor determines  its status by  a rule named off-duty  eligible rule,
-which tells  him to  turn off if  its sensing  area is covered  by its
-neighbors. A  back-off scheme is  introduced to let each  sensor delay
-the decision process  with a random period of time,  in order to avoid
-simultaneous conflicting decisions between nodes and  lack of coverage on any area.
-\cite{Prasad:2007:DAL:1782174.1782218}  defines a model  for capturing
-the dependencies  between different cover sets  and proposes localized
-heuristic  based on this  dependency.  The  algorithm consists  of two
-phases, an initial  setup phase during which each  sensor computes and
-prioritizes the  covers and  a sensing phase  during which  each sensor
-first decides  its on/off status, and  then remains on or  off for the
-rest  of the  duration.  Authors  in \cite{chin2007}  propose  a novel
-distributed  heuristic named  Distributed  Energy-efficient Scheduling
-for k-coverage  (DESK) so  that the energy  consumption among  all the
-sensors  is balanced,  and  network lifetime  is  maximized while  the
-coverage requirement  is being  maintained.  This algorithm  works in
-round, requires only  1-sensing-hop-neighbor information, and a sensor
-decides  its status  (active/sleep)  based on  its perimeter  coverage
-computed  through the k-Non-Unit-disk  coverage algorithm  proposed in
-\cite{Huang:2003:CPW:941350.941367}.
-
-Some other approaches do  not consider a synchronized and predetermined
-period  of time  where the  sensors are  active or  not.  Indeed, each
-sensor  maintains its  own timer  and its  wake-up time is randomized
-\cite{Ye03} or regulated \cite{cardei05} over time.
-%A ecrire \cite{Abrams:2004:SKA:984622.984684}p33
-
-%The scheduling information is disseminated throughout the network and only sensors in the active state are responsible
-%for monitoring all targets, while all other nodes are in a low-energy sleep mode. The nodes decide cooperatively which of them will remain in sleep mode for a certain
-%period of time.
-
- %one way of increasing lifeteime is by turning off redundant nodes to sleep mode to conserve energy while active nodes provide essential coverage, which improves fault tolerance. 
-
-%In this paper we focus on centralized algorithms because distributed algorithms are outside the scope of our work. Note that centralized coverage algorithms have the advantage of requiring very low processing power from the sensor nodes which have usually limited processing capabilities. Moreover, a recent study conducted in \cite{pc10} concludes that there is a threshold in terms of network size to switch from a localized to a centralized algorithm. Indeed the exchange of messages in large networks may consume  a considerable amount of energy in a localized approach compared to a centralized one. 
-
-\subsection{Centralized approaches}
-%{\bf Centralized approaches}
-
-Power  efficient  centralized  schemes  differ  according  to  several
-criteria \cite{Cardei:2006:ECP:1646656.1646898},  such as the coverage
-objective  (target coverage  or  area coverage),  the node  deployment
-method (random or deterministic) and the heterogeneity of sensor nodes
-(common sensing range, common battery lifetime). The major approach is
-to divide/organize  the sensors into  a suitable number of  set covers
-where each  set completely covers  an interest region and  to activate
-these set covers successively.
-
-The first algorithms  proposed in the  literature consider that  the cover
-sets  are  disjoint: a  sensor  node appears  in  exactly  one of  the
-generated  cover  sets.    For  instance,  Slijepcevic  and  Potkonjak
-\cite{Slijepcevic01powerefficient}   propose    an   algorithm, which
-allocates sensor nodes in mutually independent sets to monitor an area
-divided into  several fields.  Their algorithm builds  a cover  set by
-including in  priority the sensor  nodes, which cover  critical fields,
-that  is to  say fields  that are  covered by  the smallest  number of
-sensors. The time complexity of  their heuristic is $O(n^2)$ where $n$
-is the number of  sensors. In~\cite{cardei02}, a graph coloring
-technique is described to achieve energy  savings by  organizing the  sensor nodes
-into a maximum number of  disjoint dominating sets, which are activated
-successively. The dominating sets do not guarantee the coverage of the
-whole        region        of        interest.        Abrams        et
-al.~\cite{Abrams:2004:SKA:984622.984684}  design  three  approximation
-algorithms  for a  variation of  the  set k-cover  problem, where  the
-objective is to partition the sensors into covers such that the number
-of covers that  includes an area, summed over  all areas, is maximized.
-Their        work        builds        upon       previous        work
-in~\cite{Slijepcevic01powerefficient} and the  generated cover sets do
-not provide complete coverage of the monitoring zone.
-
-%examine the target coverage problem by disjoint cover sets but relax the requirement that every  cover set monitor all the targets and try to maximize the number of times the targets are covered by the partition. They propose various algorithms and establish approximation ratio.
-
-In~\cite{Cardei:2005:IWS:1160086.1160098},   the  authors   propose  a
-heuristic  to compute  the  disjoint  set covers  (DSC).  In order  to
-compute the maximum number of  covers, they first transform DSC into a
-maximum-flow problem, which  is then formulated  as a  mixed integer
-programming  problem (MIP).  Based on  the solution  of the  MIP, they
-design a heuristic to compute  the final number of covers. The results
-show  a slight  performance  improvement  in terms  of  the number  of
-produced  DSC in comparison  to~\cite{Slijepcevic01powerefficient}, but
-it incurs  higher execution  time due to  the complexity of  the mixed
-integer      programming     solving.       %Cardei      and     Du
-\cite{Cardei:2005:IWS:1160086.1160098} propose a method to efficiently
-compute the maximum  number of disjoint set covers  such that each set
-can  monitor all  targets. They  first  transform the  problem into  a
-maximum  flow   problem, which  is  formulated  as   a  mixed  integer
-programming (MIP). Then their heuristic  uses the output of the MIP to
-compute  disjoint  set  covers.  Results  show  that  this  heuristic
-provides  a   number  of  set  covers  slightly   larger  compared  to
-\cite{Slijepcevic01powerefficient}  but with  a larger  execution time
-due  to the complexity  of the  mixed integer  programming resolution.
-Zorbas  et  al.  \cite{Zorbas2007}  present  B\{GOP\},  a  centralized
-coverage   algorithm  introducing   sensor   candidate  categorization
-depending on their  coverage status and the notion  of critical target
-to  call  targets   that  are  associated  with  a   small  number  of
-sensors. The total running time of their heuristic is $0(m n^2)$ where
-$n$ is the number of sensors,  and $m$ the number of targets. Compared
-to    algorithm's    results     of    Slijepcevic    and    Potkonjak
-\cite{Slijepcevic01powerefficient},  their   heuristic  produces  more
-cover sets with a slight growth rate in execution time.
-%More recently Manju and Pujari\cite{Manju2011}
-
-In the  case of non-disjoint algorithms  \cite{Manju2011}, sensors may
-participate  in more  than  one cover  set.   In some  cases, this  may
-prolong  the lifetime  of the  network in  comparison to  the disjoint
-cover set algorithms, but  designing algorithms for non-disjoint cover
-sets  generally induces a  higher order  of complexity.   Moreover, in
-case of a sensor's  failure, non-disjoint scheduling policies are less
-resilient and less  reliable because a sensor may  be involved in more
-than one  cover sets.  For instance,  Cardei et al.~\cite{cardei05bis}
-present a  linear programming (LP)  solution and a greedy  approach to
-extend the  sensor network lifetime  by organizing the sensors  into a
-maximal  number of  non-disjoint cover  sets. Simulation  results show
-that by allowing sensors to  participate in multiple sets, the network
-lifetime         increases        compared         with        related
-work~\cite{Cardei:2005:IWS:1160086.1160098}.   In~\cite{berman04}, the
-authors  have formulated  the lifetime  problem and  suggested another
-(LP)  technique to  solve this  problem. A  centralized  solution  based      on      the     Garg-K\"{o}nemann
-algorithm~\cite{garg98}, provably near
-the optimal solution,    is also proposed.
-
-\subsection{Our contribution}
-%{\bf Our contribution}
-
-There are  three main questions, which should be addressed  to build a
-scheduling strategy. We  give a brief answer to  these three questions
-to describe our  approach before going into details  in the subsequent
-sections.
-\begin{itemize}
-\item {\bf How must the  phases for information exchange, decision and
-  sensing be planned over time?}   Our algorithm divides the time line
-  into a number  of rounds. Each round contains  4 phases: Information
-  Exchange, Leader Election, Decision, and Sensing.
-
-\item {\bf What are the rules to decide which node has to be turned on
+%\item 
+{\indent \bf  How must the  phases for information  exchange, decision
+  and sensing be  planned over time?}  Our algorithm  divides the time
+line into rounds.  Each round contains 4 phases: Information Exchange,
+Leader Election, Decision, and Sensing.
+
+%\item 
+{\bf What are the rules to decide which node has to be turned on
   or off?}  Our algorithm tends to limit the overcoverage of points of
   interest  to avoid  turning on  too many sensors covering  the same
   areas  at the  same time,  and tries  to prevent  undercoverage. The
   decision  is  a  good   compromise  between  these  two  conflicting
   objectives.
 
-\item {\bf Which  node should make such a  decision?}  As mentioned in
-  \cite{pc10}, both centralized  and distributed algorithms have their
-  own  advantages and  disadvantages. Centralized  coverage algorithms
-  have the advantage  of requiring very low processing  power from the
-  sensor  nodes, which  have usually  limited  processing capabilities.
-  Distributed  algorithms  are  very  adaptable  to  the  dynamic  and
-  scalable nature of sensors network.  Authors in \cite{pc10} conclude
-  that there is a threshold in  terms of network size to switch from a
-  localized  to  a  centralized  algorithm.  Indeed, the  exchange  of
-  messages  in large  networks may  consume a  considerable  amount of
-  energy in a centralized approach  compared to a distributed one. Our
-  work does not  consider only one leader to  compute and to broadcast
-  the scheduling decision  to all the sensors.  When  the network size
-  increases,  the network  is  divided into  many  subregions and  the
-  decision is made by a leader in each subregion.
-\end{itemize}
-
-
+%\item 
+{\bf Which  node should make such  a decision?}  A  leader node should
+make such  a decision. Our work  does not consider only  one leader to
+compute and to  broadcast the scheduling decision to  all the sensors.
+When  the network  size increases,  the network  is divided  into many
+subregions and the decision is made by a leader in each subregion.
+%\end{itemize}
 
 \section{Activity scheduling}
 \label{pd}
@@ -382,8 +233,6 @@ then  our coverage  protocol  will be  implemented  in each  subregion
 simultaneously.   Our protocol  works in  rounds fashion  as  shown in
 figure~\ref{fig1}.
 
-%Given the interested Area $A$, the wireless sensor nodes set $S=\lbrace  s_1,\ldots,s_N \rbrace $ that are deployed randomly and uniformly in this area such that they are ensure a full coverage for A. The Area A is divided into regions $A=\lbrace A^1,\ldots,A^k,\ldots, A^{N_R} \rbrace$. We suppose that each sensor node $s_i$ know its location and its region. We will have a subset $SSET^k =\lbrace s_1,...,s_j,...,s_{N^k} \rbrace $ , where $s_N = s_{N^1} + s_{N^2} +,\ldots,+ s_{N^k} +,\ldots,+s_{N^R}$. Each sensor node $s_i$ has the same initial energy $IE_i$ in the first time and the current residual energy $RE_i$ equal to $IE_i$  in the first time for each $s_i$ in A. \\ 
-
 \begin{figure}[ht!]
 \centering
 \includegraphics[width=85mm]{FirstModel.eps} % 70mm
@@ -460,12 +309,9 @@ starting a new round.
 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 is
-at   least  twice    the size of the   sensing  range.   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.
-%To calculate the coverage ratio for the area of interest, we can propose the following coverage model which is called Wireless Sensor Node Area Coverage Model to ensure that all the area within each node sensing range are covered. We can calculate the positions of the points in the circle disc of the sensing range of wireless sensor node based on the Unit Circle in figure~\ref{fig:cluster1}:
+covered by this sensor. We also assume that the communication range $R_c \geq 2R_s$ ~\cite{Zhang05}. 
+
+
 
 %\begin{figure}[h!]
 %\centering
@@ -530,17 +376,14 @@ $X_{13}=( p_x + R_s * (0), p_y + R_s * (\frac{-\sqrt{2}}{2})) $.
 %\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{Sensor node represented by 13 primary points}
 \label{fig2}
 \end{figure}
 
 \section{Coverage problem formulation}
 \label{cp}
-%We can formulate our optimization problem as energy cost minimization by minimize the number of active sensor nodes and maximizing the coverage rate at the same time in each $A^k$ . This optimization problem can be formulated as follow: Since that we use a homogeneous wireless sensor network, we will assume that the cost of keeping a node awake is the same for all wireless sensor nodes in the network. We can define the decision parameter  $X_j$ as in \eqref{eq11}:\\
 
 
-%To satisfy the coverage requirement, the set of the principal points that will represent all the sensor nodes in the monitored region as $PSET= \lbrace P_1,\ldots ,P_p, \ldots , P_{N_P^k} \rbrace $, where $N_P^k = N_{sp} * N^k $ and according to the proposed model in figure ~\ref{fig:cluster2}. These points can be used by the wireless sensor node leader which will be chosen in each region in A to build a new parameter $\alpha_{jp}$  that represents the coverage possibility for each principal point $P_p$ of each wireless sensor node $s_j$ in $A^k$ as in \eqref{eq12}:\\
-
 \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
@@ -632,31 +475,6 @@ 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.
  
-%In equation \eqref{eq15}, there are two main objectives: the first one using  the Overcoverage parameter to minimize the number of active sensor nodes in the produced final solution vector $X$ which leads to improve the life time of wireless sensor network. The second goal by using the  Undercoverage parameter  to maximize the coverage in the region by means of covering each primary point in $SSET^k$.The two objectives are achieved at the same time. The constraint which represented in equation \eqref{eq16} refer to the coverage function for each primary point $P_p$ in $SSET^k$ , where each $P_p$ should be covered by
-%at least one sensor node in $A^k$. The objective function in \eqref{eq15} involving two main objectives to be optimized simultaneously, where optimal decisions need to be taken in the presence of trade-offs between the two conflicting main objectives in \eqref{eq15} and this refer to that our coverage optimization problem is a multi-objective optimization problem and we can use the BPSO to solve it. The concept of Overcoverage and Undercoverage inspired from ~\cite{Fernan12} but we use it with our model as stated in subsection \ref{Sensing Coverage Model} with some modification to be applied later by BPSO.
-%\subsection{Notations and assumptions}
-
-%\begin{itemize}
-%\item $m$ : the number of targets
-%\item $n$ : the number of sensors
-%\item $K$ : maximal number of cover sets
-%\item $i$ : index of target ($i=1..m$)
-%\item $j$ : index of sensor ($j=1..n$)
-%\item $k$ : index of cover set ($k=1..K$)
-%\item $T_0$ : initial set of targets
-%\item $S_0$ : initial set of sensors
-%\item $T $ : set of targets which are not covered by at least one cover set
-%\item $S$ : set of available sensors
-%\item $S_0(i)$ : set of sensors which cover the target $i$
-%\item $T_0(j)$ : set of targets covered by sensor $j$
-%\item $C_k$ : cover set of index $k$
-%\item $T(C_k)$ : set of targets covered by the cover set $k$
-%\item $NS(i)$ : set of  available sensors which cover the target $i$
-%\item $NC(i)$ : set of cover sets which do not cover the target $i$
-%\item $|.|$ : cardinality of the set
-
-%\end{itemize}
-
 \section{Simulation results}
 \label{exp}
 
@@ -726,7 +544,7 @@ subregion.
 \parskip 0pt 
 \begin{figure}[h!]
 \centering
-\includegraphics[scale=0.5]{TheCoverageRatio150g.eps} %\\~ ~ ~(a)
+\includegraphics[scale=0.37]{CR1.eps} %\\~ ~ ~(a)
 \caption{The impact of the number of rounds on the coverage ratio for 150 deployed nodes}
 \label{fig3}
 \end{figure} 
@@ -748,7 +566,7 @@ for 150 deployed nodes.
 
 \begin{figure}[h!]
 \centering
-\includegraphics[scale=0.5]{TheActiveSensorRatio150g.eps} %\\~ ~ ~(a)
+\includegraphics[scale=0.37]{ASR1.eps} %\\~ ~ ~(a)
 \caption{The impact of the number of rounds on the active sensors ratio for 150 deployed nodes }
 \label{fig4}
 \end{figure} 
@@ -763,7 +581,7 @@ that even if a network is disconnected in one subregion, the other one
 usually  continues  the optimization  process,  and  this extends  the
 lifetime of the network.
 
-\subsection{The impact of the number of rounds on the energy saving ratio} 
+\subsection{Impact of the number of rounds on the energy saving ratio} 
 
 In this experiment, we consider a performance metric linked to energy.
 This metric, called Energy Saving Ratio (ESR), is defined by:
@@ -781,7 +599,7 @@ for all three approaches and for 150 deployed nodes.
 %\centering
 % \begin{multicols}{6}
 \centering
-\includegraphics[scale=0.5]{TheEnergySavingRatio150g.eps} %\\~ ~ ~(a)
+\includegraphics[scale=0.37]{ESR1.eps} %\\~ ~ ~(a)
 \caption{The impact of the number of rounds on the energy saving ratio for 150 deployed nodes}
 \label{fig5}
 \end{figure} 
@@ -812,7 +630,7 @@ optimization participates in extending the network lifetime.
 
 \begin{figure}[h!]
 \centering
-\includegraphics[scale=0.5]{TheNumberofStoppedSimulationRuns150g.eps} 
+\includegraphics[scale=0.36]{SR1.eps} 
 \caption{The percentage of stopped simulation runs compared to the number of rounds for 150 deployed nodes }
 \label{fig6}
 \end{figure} 
@@ -844,7 +662,7 @@ communications have a small impact on the network lifetime.
 
 \begin{figure}[h!]
 \centering
-\includegraphics[scale=0.5]{TheEnergyConsumptiong.eps} 
+\includegraphics[scale=0.37]{EC1.eps} 
 \caption{The energy consumption}
 \label{fig7}
 \end{figure} 
@@ -870,7 +688,7 @@ nodes.   Overall,  to  be  able to  deal  with  very  large  networks,  a
 distributed method is clearly required.
 
 \begin{table}[ht]
-\caption{THE EXECUTION TIME(S) VS THE NUMBER OF SENSORS}
+\caption{EXECUTION TIME(S) VS. NUMBER OF SENSORS}
 % title of Table
 \centering
 
@@ -908,82 +726,65 @@ Sensors number &amp; Strategy~2 &amp; Strategy~1  &amp; Simple heuristic \\ [0.5ex]
 
 Finally, we  have defined the network  lifetime as the  time until all
 nodes  have  been drained  of  their  energy  or each  sensor  network
-monitoring  an area has become  disconnected.  In  figure~\ref{fig8}, the
+monitoring an area has become disconnected.  In figure~\ref{fig8}, the
 network  lifetime for different  network sizes  and for  both strategy
-with two  leaders and the simple  heuristic is illustrated. 
-  We do  not consider  anymore the  centralized strategy  with one
-  leader, because, as shown above, this strategy results  in execution
-  times that quickly become unsuitable for a sensor network.
+with two leaders  and the simple heuristic is  illustrated.  We do not
+consider anymore the centralized strategy with one leader, because, as
+shown  above, this strategy  results in  execution times  that quickly
+become unsuitable for a sensor network.
 
 \begin{figure}[h!]
 %\centering
 % \begin{multicols}{6}
 \centering
-\includegraphics[scale=0.5]{TheNetworkLifetimeg.eps} %\\~ ~ ~(a)
+\includegraphics[scale=0.37]{LT1.eps} %\\~ ~ ~(a)
 \caption{The network lifetime }
 \label{fig8}
 \end{figure} 
 
 As  highlighted by figure~\ref{fig8},  the network  lifetime obviously
-increases when  the size  of the network  increases, with  our approach
-that leads to  the larger lifetime improvement.  By  choosing the  best 
-suited nodes, for each round,  to cover the  region of interest  and by
+increases when  the size of  the network increases, with  our approach
+that leads to  the larger lifetime improvement.  By  choosing the best
+suited nodes, for  each round, to cover the region  of interest and by
 letting the other ones sleep in order to be used later in next rounds,
-our strategy efficiently prolonges the network lifetime. Comparison shows that
-the larger  the sensor number  is, the more our  strategies outperform
-the simple heuristic.  Strategy~2, which uses two leaders, is the best
-one because it is robust to network disconnection in one subregion. It
-also  means   that  distributing  the  algorithm  in   each  node  and
-subdividing the sensing field  into many subregions, which are managed
-independently and simultaneously, is the most relevant way to maximize
-the lifetime of a network.
-
-\section{Conclusion and future works}
+our  strategy efficiently prolonges  the network  lifetime. Comparison
+shows that  the larger the sensor  number is, the  more our strategies
+outperform the simple heuristic.   Strategy~2, which uses two leaders,
+is the best  one because it is robust to  network disconnection in one
+subregion. It also means that  distributing the algorithm in each node
+and  subdividing the  sensing field  into many  subregions,  which are
+managed independently and simultaneously,  is the most relevant way to
+maximize the lifetime of a network.
+
+\section{Conclusion and future work}
 \label{sec:conclusion}
 
-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
+In this paper,  we have addressed the problem of  the coverage and the
+lifetime optimization in WSNs. 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  multi-rounds coverage protocol
 will optimize  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
-protocol in  terms of lifetime, coverage ratio,  active sensors ratio,
-energy saving,  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 propose  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  protocol, which
-computes  all  active  sensor  schedules  in  one time,  using
-optimization  methods  such  as  swarms optimization  or  evolutionary
-algorithms.  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.
+the best  representative active  nodes. Results from  simulations show
+the relevance of the proposed  protocol in terms of lifetime, coverage
+ratio,  active  sensors  ratio,  energy  saving,  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
+propose  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 a  coverage protocol which  computes all  active sensor
+schedules  in one  time,  using optimization  methods  such as  swarms
+optimization or evolutionary algorithms.
 % use section* for acknowledgement
 %\section*{Acknowledgment}
 
-
-
-
 \bibliographystyle{IEEEtran}
 \bibliography{bare_conf}
 
-
 \end{document}
 
 
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