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+\usepackage{etoolbox}
+\usepackage{float} 
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+\usepackage{graphicx,epstopdf}
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+\DeclareGraphicsExtensions{.ps}
+\DeclareGraphicsRule{.ps}{pdf}{.pdf}{`ps2pdf -dEPSCrop -dNOSAFER #1 \noexpand\OutputFile}
 
 \begin{document}
-
-\title{Energy-Efficient Activity Scheduling in Heterogeneous Energy Wireless Sensor Networks}
-
-
-% author names and affiliations
-% use a multiple column layout for up to three different
-% affiliations
-\author{\IEEEauthorblockN{Ali Kadhum Idrees, Karine Deschinkel, Michel Salomon, and Rapha\"el Couturier }
-\IEEEauthorblockA{FEMTO-ST Institute, UMR 6174 CNRS, University of Franche-Comte, Belfort, France \\
-Email: ali.idness@edu.univ-fcomte.fr, $\lbrace$karine.deschinkel, michel.salomon, raphael.couturier$\rbrace$@univ-fcomte.fr}
-%\email{\{ali.idness, karine.deschinkel, michel.salomon, raphael.couturier\}@univ-fcomte.fr}
-%\and
-%\IEEEauthorblockN{Homer Simpson}
-%\IEEEauthorblockA{FEMTO-ST Institute, UMR CNRS, University of Franche-Comte, Belfort, France}
-%\and
-%\IEEEauthorblockN{James Kirk\\ and Montgomery Scott}
-%\IEEEauthorblockA{FEMTO-ST Institute, UMR CNRS, University of Franche-Comte, Belfort, France}
-}
+%
+% paper title
+% can use linebreaks \\ within to get better formatting as desired
+\title{Coverage and Lifetime Optimization \\
+in Heterogeneous Energy Wireless Sensor Networks}
+
+\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}}
 
 \maketitle
 
 \begin{abstract}
 One of  the fundamental challenges in Wireless  Sensor Networks (WSNs)
-is  coverage  preservation  and  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 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  in 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}
 
-%\keywords{Area Coverage, Wireless Sensor Networks, lifetime Optimization, Distributed Protocol.}
+\begin{IEEEkeywords}
+Wireless   Sensor   Networks,   Area   Coverage,   Network   lifetime,
+Optimization, Scheduling.
+\end{IEEEkeywords}
+%\keywords{Area Coverage, Network lifetime, Optimization, Distributed Protocol}
  
 \IEEEpeerreviewmaketitle
 
 \section{Introduction}
-\noindent Recent years have witnessed significant advances in wireless
+
+%\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
-made  emerge wireless  sensor networks  as one  of the  most promising
-technologies~\cite{asc02}.   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 to
-sense its environment, to compute, to store information and to deliver
-report messages to a base station.
-%These sensor nodes run on batteries with limited capacities. To achieve a long life of the network, it is important to conserve battery power. Therefore, lifetime optimisation is one of the most critical issues in wireless sensor networks.
-One of the main design issues in Wireless Sensor Networks (WSNs) is to
-prolong the  network lifetime,  while achieving acceptable  quality of
-service for applications.  Indeed, sensor nodes have limited resources
-in terms of memory, energy and computational power.
-
-Since sensor nodes have limited battery life and without being able to
+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 since it is impossible 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 benefit
-from  the overlapping  sensing regions  of some  sensor nodes  to save
-energy  by  turning  off  some  of  them  during  the  sensing  phase.
+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.  Consequently, future software
-may  need to  adapt  appropriately to  achieve  acceptable quality  of
-service  for  applications.  In  this  paper  we  concentrate on  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.  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  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
+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  on
-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{\uppercase{Related works}}
+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 suggest to
-recall 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  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 
+{\indent \bf  How must the  phases for information  exchange, decision
+  and sensing be  planned over time?}  Our algorithm  divides the timeline into rounds.  Each round contains 4 phases: Information Exchange,
+Leader Election, Decision, and Sensing.
 
-%\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}
-{\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 in 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).
-
-\newpage
-
-{\bf Lifetime}
-
-Various   definitions   exist   for   the   lifetime   of   a   sensor
-network~\cite{die09}.  Main definitions proposed in the literature are
-related to the  remaining energy of the nodes or  to the percentage of
-coverage. The lifetime of the  network is mainly defined as the amount
-of  time that  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.
-
-{\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, such 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  the 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.
-
-{\bf Distributed approaches}
-
-Some      distributed     algorithms      have      been     developed
-in~\cite{Gallais06,Tian02,Ye03,Zhang05,HeinzelmanCB02} to perform the schelduling.     Distributed
-algorithms typically operate in  rounds for predetermined duration. At
-the beginning  of each round,  a sensor exchange 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 based 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 node ID
-and 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
-that nodes  make conflicting decisions simultaneously and  that a part
-of       the       area        is       no       longer       covered.
-\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
-prioritize 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 requirements  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 others approaches do  not consider synchronized and predetermined
-period  of time  where the  sensors are  active or  not.  Indeed, each
-sensor  maintains its  own timer  and its  time wake-up  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. 
-
-{\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.
-
-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.  \cite{cardei02}~describes a graph coloring
-technique  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  include 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  these  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  provably near
-optimal      solution     based      on      the     Garg-K\"{o}nemann
-algorithm~\cite{garg98} is also proposed.
-
-{\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 
+{\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 much  sensors covering  the same
+  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  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 localized approach  compared to a centralized  one. Our
-  work does not  consider only one leader to  compute and to broadcast
-  the  schedule decision  to all  the sensors.  When the  network size
-  increases,  the  network  is  divided  in 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{\uppercase{Activity scheduling}}
+\section{Activity scheduling}
 \label{pd}
 
 We consider  a randomly and  uniformly deployed network  consisting of
@@ -385,8 +232,6 @@ 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
@@ -396,12 +241,12 @@ figure~\ref{fig1}.
 
 Each round  is divided  into 4 phases  : Information  (INFO) Exchange,
 Leader  Election, Decision,  and  Sensing.  For  each  round there  is
-exactly one set cover responsible  for sensing task.  This protocol is
-more reliable  against the unexpectedly node failure  because it works
+exactly one set cover responsible  for the sensing task.  This protocol is
+more reliable  against an unexpected node failure  because it works
 in rounds.   On the  one hand,  if a node  failure is  detected before
-taking the decision, the node will not participate to this phase, and,
+making the decision, the node will not participate to this phase, and,
 on the other hand, if the  node failure occurs after the decision, the
-sensing task of the network  will be affected temporarily: only during
+sensing task of the network  will be temporarily affected: only during
 the period of sensing until a  new round starts, since a new set cover
 will take  charge of the  sensing task in  the next round.  The energy
 consumption  and  some other  constraints  can  easily  be taken  into
@@ -410,12 +255,12 @@ information (including their residual energy) at the beginning of each
 round.  However,   the  pre-sensing  phases   (INFO  Exchange,  Leader
 Election,  Decision) are energy  consuming for  some nodes,  even when
 they do not  join the network to monitor the  area. Below, we describe
-each phase in more detail.
+each phase in more details.
 
-\subsection{\textbf INFOrmation Exchange Phase}
+\subsection{Information exchange phase}
 
 Each sensor node $j$ sends  its position, remaining energy $RE_j$, and
-the number of local neighbors  $NBR_j$ to all wireless sensor nodes in
+the number of local neighbours  $NBR_j$ to all wireless sensor nodes in
 its subregion by using an INFO  packet and then listens to the packets
 sent from  other nodes.  After that, each  node will  have information
 about  all the  sensor  nodes in  the  subregion.  In  our model,  the
@@ -426,32 +271,32 @@ active mode.
 
 %The working phase works in rounding fashion. Each round include 3 steps described as follow :
 
-\subsection{\textbf Leader Election Phase}
-This  step includes choosing  the Wireless  Sensor Node  Leader (WSNL)
-which  will  be  responsible  of executing  coverage  algorithm.  Each
+\subsection{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
+number  of neighbours,  larger remaining  energy, and  then in  case of
 equality, larger index.
 
-\subsection{\textbf Decision Phase}
+\subsection{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 algorithm's results.
+sensor in the subregion based on the algorithm's results.
 %The main goal in this step after choosing the WSNL is to produce the best representative active nodes set that will take the responsibility of covering the whole region $A^k$ with minimum number of sensor nodes to prolong the lifetime in the wireless sensor network. For our problem, in each round we need to select the minimum set of sensor nodes to improve the lifetime of the network and in the same time taking into account covering the region $A^k$ . We need an optimal solution with tradeoff between our two conflicting objectives.
 %The above region coverage problem can be formulated as a Multi-objective optimization problem and we can use the Binary Particle Swarm Optimization technique to solve it. 
 
-\subsection{\textbf Sensing Phase}
+\subsection{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 sleep)  for sensing task is
+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  go sleep  for a time  equal to  the period of  sensing until
+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.
 
 %\subsection{Sensing coverage model}
@@ -459,16 +304,13 @@ starting a new round.
 
 %\noindent We try to produce an adaptive scheduling which allows sensors to operate alternatively so as to prolong the network lifetime. For convenience, the notations and assumptions are described first.
 %The wireless sensor node use the  binary disk sensing model by which each sensor node will has a certain sensing range is reserved within a circular disk called radius $R_s$.
-\noindent We consider a boolean  disk coverage model which is the most
+\indent We consider a boolean  disk coverage model which is the most
 widely used sensor coverage model in the literature. Each sensor has a
 constant sensing range $R_s$. All  space points within a disk centered
 at  the sensor with  the radius  of the  sensing range  is said  to be
-covered by this sensor. We also assume that the communication range is
-at   least  twice   of  the   sensing  range.   In  fact,   Zhang  and
-Zhou~\cite{Zhang05} prove 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
@@ -484,9 +326,9 @@ connectivity among the working nodes in the active mode.
 %We choose to representEach wireless sensor node will be represented into a selected number of primary points by which we can know if the sensor node is covered or not.
 % Figure ~\ref{fig:cluster2} shows the selected primary points that represents the area of the sensor node and according to the sensing range of the wireless sensor node.
 
-\noindent Instead of working with  area coverage, we consider for each
+\indent Instead of working with the coverage area, we consider for each
 sensor a set of points called  primary points. We also assume that the
-sensing disk defined  by a sensor is covered if  all primary points of
+sensing disk defined  by a sensor is covered if  all the primary points of
 this sensor are covered.
 %\begin{figure}[h!]
 %\centering
@@ -502,9 +344,9 @@ 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 points in the area.
+sensors, instead of using all the points in the area.
 
-\noindent  We can  calculate  the positions  of  the selected  primary
+\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{fig2}) as follows:\\
 $(p_x,p_y)$ = point center of wireless sensor node\\  
@@ -533,24 +375,21 @@ $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{\uppercase{Coverage problem formulation}}
+\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}:\\
-
-\noindent   Our   model   is   based   on  the   model   proposed   by
+\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  propose an
-integer program which forces undercoverage and overcoverage of targets
+disjoint  cover sets.   To accomplish  this goal,  authors  proposed an
+integer program, which forces undercoverage and overcoverage of targets
 to  become  minimal at  the  same  time.   They use  binary  variables
 $x_{jl}$ to indicate  if sensor $j$ belongs to cover  set $l$.  In our
-model,  we  consider  binary  variables $X_{j}$  which  determine  the
+model,  we  consider  binary  variables $X_{j}$,  which  determine  the
 activation of  sensor $j$ in the  sensing phase of the  round. We also
 consider  primary points  as targets.   The set  of primary  points is
 denoted by $P$ and the set of sensors by $J$.
@@ -566,8 +405,8 @@ indicator function of whether the point $p$ is covered, that is:
 \end{array} \right.
 %\label{eq12} 
 \end{equation}
-The number of sensors that are covering point $p$ is equal to 
-$\sum_{j \in J} \alpha_{jp} * X_{j}$ where:
+The number of active sensors that cover the primary point $p$ is equal
+to $\sum_{j \in J} \alpha_{jp} * X_{j}$ where:
 \begin{equation}
 X_{j} = \left \{ 
 \begin{array}{l l}
@@ -580,7 +419,8 @@ We define the Overcoverage variable $\Theta_{p}$ as:
 \begin{equation}
  \Theta_{p} = \left \{ 
 \begin{array}{l l}
-  0            & \mbox{if point $p$ is not covered,}\\
+  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} 
@@ -592,7 +432,7 @@ by:
 \begin{equation}
 U_{p} = \left \{ 
 \begin{array}{l l}
-  1 &\mbox{if point $p$ is not covered,} \\
+  1 &\mbox{if the primary point $p$ is not covered,} \\
   0 & \mbox{otherwise.}\\
 \end{array} \right.
 \label{eq14} 
@@ -615,93 +455,71 @@ X_{j} \in \{0,1\}, &\forall j \in J
 \right.
 \end{equation}
 \begin{itemize}
-\item  $X_{j}$ :  indicates  whether  or not  the sensor  $j$ is  actively
+\item $X_{j}$  : indicates whether or  not the sensor  $j$ is actively
   sensing in the round (1 if yes and 0 if not);
 \item $\Theta_{p}$  : {\it overcoverage}, the number  of sensors minus
-  one that are covering point $p$;
-\item $U_{p}$  : {\it undercoverage},  indicates whether or  not point
+  one that are covering the primary point $p$;
+\item $U_{p}$  : {\it undercoverage},  indicates whether or  not the primary point
   $p$ is being covered (1 if not covered and 0 if covered).
 \end{itemize}
 
-The first group of constraints indicates that some point $p$ should be
-covered by  at least  one sensor and,  if it  is not always  the case,
-overcoverage and undercoverage  variables help balance the restriction
-equation  by taking positive  values. There  are two  main objectives.
-First we limit  overcoverage of primary points in  order to activate a
-minimum  number of  sensors.   Second  we prevent  that  parts of  the
-subregion are not monitored  by minimizing undercoverage.  The weights
-$w_\theta$ and $w_U$  must be properly chosen so  as to guarantee that
-the maximum number of points are covered during each round.
+The first group  of constraints indicates that some  primary point $p$
+should be covered by at least one  sensor and, if it is not always the
+case,  overcoverage  and  undercoverage  variables  help  balancing  the
+restriction  equations by taking  positive values.  There are  two main         
+objectives.  First, we limit the overcoverage of primary points in order to
+activate a minimum number of sensors.  Second we prevent the absence of monitoring on
+ some parts of the subregion by  minimizing the undercoverage.   The
+weights  $w_\theta$  and  $w_U$  must  be properly  chosen  so  as  to
+guarantee that  the maximum number  of points are covered  during each
+round.
  
-%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{\uppercase{Simulation Results}}
+\section{Simulation results}
 \label{exp}
 
-In this section, we conducted a series of simulations to evaluate the
-efficiency  and relevance of  our approach,  using the  discrete event
+In this section, we conducted  a series of simulations to evaluate the
+efficiency  and the relevance of  our approach,  using the  discrete event
 simulator  OMNeT++  \cite{varga}. We  performed  simulations for  five
 different densities varying from 50 to 250~nodes. Experimental results
 were  obtained from  randomly generated  networks in  which  nodes are
-deployed over a $(50 \times  25)~m^2 $ sensing field. For each network
-deployment,  we assume  that the  deployed nodes  can fully  cover the
-sensing field  with the given  sensing range.  10 simulation  runs are
-performed  with different  network topologies  for each  node density.
-The results  presented hereafter are the  average of these  10 runs. A
-simulation  ends when all  the nodes  are dead  or the  sensor network
-becomes disconnected  (some nodes may  not be able  to sent to  a base
-station an event they sense).
+deployed over a  $(50 \times 25)~m^2 $ sensing  field. 
+More precisely, the deployment is controlled at a coarse scale in
+  order to ensure that the  deployed nodes can fully cover the sensing
+  field with the given sensing range.
+10~simulation  runs  are performed  with
+different  network  topologies for  each  node  density.  The  results
+presented hereafter  are the  average of these  10 runs.  A simulation
+ends  when  all the  nodes  are dead  or  the  sensor network  becomes
+disconnected (some nodes may not be  able to send, to a base station, an
+event they sense).
 
 Our proposed coverage protocol uses the radio energy dissipation model
 defined by~\cite{HeinzelmanCB02} as  energy consumption model for each
 wireless  sensor node  when  transmitting or  receiving packets.   The
 energy of  each node in a  network is initialized  randomly within the
 range 24-60~joules, and each sensor node will consume 0.2 watts during
-the sensing period which will have  a duration of 60 seconds. Thus, an
-active  node will  consume  12~joules during  sensing  phase, while  a
+the sensing period, which will last 60 seconds. Thus, an
+active  node will  consume  12~joules during the sensing  phase, while  a
 sleeping  node will  use  0.002  joules.  Each  sensor  node will  not
 participate in the next round if its remaining energy is less than 12
-joules.  In  all  experiments  the  parameters  are  set  as  follows:
-$R_s=5m$, $w_{\Theta}=1$, and $w_{U}=|P^2|$.
+joules.  In  all  experiments,  the  parameters  are  set  as  follows:
+$R_s=5~m$, $w_{\Theta}=1$, and $w_{U}=|P^2|$.
 
-We  evaluate the  efficiency of  our approach  using  some performance
+We  evaluate the  efficiency of  our approach by using  some performance
 metrics such as: coverage ratio,  number of active nodes ratio, energy
 saving  ratio, energy consumption,  network lifetime,  execution time,
-and number of stopped simulation runs.  Our approach called Strategy~2
-(with Two Leaders)  works with two subregions, each  one having a size
+and number of stopped simulation runs.  Our approach called strategy~2
+(with two leaders)  works with two subregions, each  one having a size
 of $(25 \times 25)~m^2$.  Our strategy will be compared with two other
-approaches. The first one,  called Strategy~1 (with One Leader), works
-as Strategy~2, but considers only one region of $(50 \times 25)$ $m^2$
+approaches. The first one,  called strategy~1 (with one leader), works
+as strategy~2, but considers only one region of $(50 \times 25)$ $m^2$
 with only  one leader.  The  other approach, called  Simple Heuristic,
-consists in dividing  uniformly the region into squares  of $(5 \times
+consists in uniformly dividing   the region into squares  of $(5 \times
 5)~m^2$.   During the  decision phase,  in  each square,  a sensor  is
 randomly  chosen, it  will remain  turned  on for  the coming  sensing
 phase.
 
-\subsection{The impact of the Number of Rounds on Coverage Ratio} 
+\subsection{The impact of the number of rounds on the coverage ratio} 
 
 In this experiment, the coverage ratio measures how much the area of a
 sensor field is  covered. In our case, the  coverage ratio is regarded
@@ -716,26 +534,26 @@ $90\%$ for five more rounds.  Coverage ratio decreases when the number
 of rounds increases  due to dead nodes. Although  some nodes are dead,
 thanks to  strategy~1 or~2,  other nodes are  preserved to  ensure the
 coverage. Moreover, when  we have a dense sensor  network, it leads to
-maintain the full coverage for  larger number of rounds. Strategy~2 is
-slightly more efficient that strategy 1, because strategy~2 subdivides
+maintain the full coverage for a larger number of rounds. Strategy~2 is
+slightly more efficient than strategy 1, because strategy~2 subdivides
 the region into 2~subregions and  if one of the two subregions becomes
-disconnected,  coverage   may  be  still  ensured   in  the  remaining
+disconnected,  the coverage   may  be  still  ensured   in  the  remaining
 subregion.
 
 \parskip 0pt 
 \begin{figure}[h!]
 \centering
-\includegraphics[scale=0.55]{TheCoverageRatio150.eps} %\\~ ~ ~(a)
-\caption{The impact of the Number of Rounds on Coverage Ratio for 150 deployed nodes}
+\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} 
 
-\subsection{The impact of the Number of Rounds on Active Sensors Ratio} 
+\subsection{The impact of the number of rounds on the active sensors ratio} 
 
 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.  This point is  assessed through the  Active Sensors
-Ratio, which is defined as follows:
+Ratio (ASR), which is defined as follows:
 \begin{equation*}
 \scriptsize
 \mbox{ASR}(\%) = \frac{\mbox{Number of active sensors 
@@ -747,32 +565,32 @@ for 150 deployed nodes.
 
 \begin{figure}[h!]
 \centering
-\includegraphics[scale=0.55]{TheActiveSensorRatio150.eps} %\\~ ~ ~(a)
-\caption{The impact of the Number of Rounds on Active Sensors Ratio for 150 deployed nodes }
+\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} 
 
 The  results presented  in figure~\ref{fig4}  show the  superiority of
-both proposed  strategies, the Strategy  with Two Leaders and  the one
-with a  single Leader,  in comparison with  the Simple  Heuristic. The
-Strategy with One Leader uses less active nodes than the Strategy with
-Two Leaders until the last  rounds, because it uses central control on
-the whole sensing field.  The  advantage of the Strategy~2 approach is
+both proposed  strategies, the strategy  with two leaders and  the one
+with a  single leader,  in comparison with  the simple  heuristic. The
+strategy with one leader uses less active nodes than the strategy with
+two leaders until the last  rounds, because it uses central control on
+the whole sensing field.  The  advantage of the strategy~2 approach is
 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 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, is defined by:
+This metric, called Energy Saving Ratio (ESR), is defined by:
 \begin{equation*}
 \scriptsize
 \mbox{ESR}(\%) = \frac{\mbox{Number of alive sensors during this round}}
 {\mbox{Total number of sensors in the network for the region}} \times 100.
 \end{equation*}
-The  longer the ratio  is high,  the more  redundant sensor  nodes are
-switched off, and consequently  the longer the  network may  be alive.
+The  longer the ratio  is,  the more  redundant sensor  nodes are
+switched off, and consequently  the longer the  network may  live.
 Figure~\ref{fig5} shows the average  Energy Saving Ratio versus rounds
 for all three approaches and for 150 deployed nodes.
 
@@ -780,104 +598,96 @@ for all three approaches and for 150 deployed nodes.
 %\centering
 % \begin{multicols}{6}
 \centering
-\includegraphics[scale=0.55]{TheEnergySavingRatio150.eps} %\\~ ~ ~(a)
-\caption{The impact of the Number of Rounds on Energy Saving Ratio for 150 deployed nodes}
+\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} 
 
 The simulation  results show that our strategies  allow to efficiently
 save energy by  turning off some sensors during  the sensing phase. As
-expected, the Strategy with One Leader is usually slightly better than
-the second  strategy, because the  global optimization permit  to turn
+expected, the strategy with one leader is usually slightly better than
+the second  strategy, because the  global optimization permits  to turn
 off more  sensors. Indeed,  when there are  two subregions  more nodes
 remain awake  near the border shared  by them. Note that  again as the
-number of  rounds increases  the two leader  strategy becomes  the most
-performing, since its takes longer  to have the two subregion networks
+number of  rounds increases  the two leaders'  strategy becomes  the most
+performing one, since it takes longer  to have the two subregion networks
 simultaneously disconnected.
 
-\subsection{The Network Lifetime}
+\subsection{The percentage of stopped simulation runs}
 
-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
-becomes disconnected.  In figure~\ref{fig6}, the  network lifetime for
-different network sizes and for the three approaches is illustrated.
+We  will now  study  the percentage  of  simulations, which  stopped due  to
+network  disconnections per round  for each  of the  three approaches.
+Figure~\ref{fig6} illustrates the percentage of stopped simulation
+runs per  round for 150 deployed  nodes.  It can be  observed that the
+simple heuristic is  the approach, which  stops first because  the nodes
+are   randomly chosen.   Among  the  two   proposed  strategies,  the
+centralized  one  first  exhibits  network  disconnections.   Thus,  as
+explained previously, in case  of the strategy with several subregions
+the  optimization effectively  continues as  long  as a  network in  a
+subregion   is  still   connected.   This   longer   partial  coverage
+optimization participates in extending the network lifetime.
 
 \begin{figure}[h!]
-%\centering
-% \begin{multicols}{6}
 \centering
-\includegraphics[scale=0.5]{TheNetworkLifetime.eps} %\\~ ~ ~(a)
-\caption{The Network Lifetime }
+\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} 
 
-As  highlighted by figure~\ref{fig6},  the network  lifetime obviously
-increases when the  size of the network increase,  with our approaches
-that lead  to the larger  lifetime improvement.  By choosing  for each
-round the  well suited nodes  to cover the  region of interest  and by
-letting  the other ones sleep in order to be used  later in next  rounds, both
-proposed strategies efficiently prolong the 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.
-
-\subsection{The Energy Consumption}
+\subsection{The energy consumption}
 
 In this experiment, we study the effect of the multi-hop communication
-protocol  on the  performance of  the  Strategy with  Two Leaders  and
+protocol  on the  performance of  the  strategy with  two leaders  and
 compare  it  with  the  other  two  approaches.   The  average  energy
 consumption  resulting  from  wireless  communications  is  calculated
-considering the  energy spent by  all the nodes when  transmitting and
+by taking into account the  energy spent by  all the nodes when  transmitting and
 receiving  packets during  the network  lifetime. This  average value,
 which  is obtained  for 10~simulation  runs,  is then  divided by  the
 average number of rounds to define a metric allowing a fair comparison
 between networks having different densities.
 
-Figure~\ref{fig7} illustrates the Energy Consumption for the different
+Figure~\ref{fig7} illustrates the energy consumption for the different
 network  sizes and  the three  approaches. The  results show  that the
-Strategy  with  Two  Leaders  is  the  most  competitive  from  energy
-consumption point  of view.  A  centralized method, like  the Strategy
-with  One  Leader, has  a  high energy  consumption  due  to the  many
+strategy  with  two  leaders  is  the  most  competitive  from  the energy
+consumption point  of view.  A  centralized method, like  the strategy
+with  one  leader, has  a  high energy  consumption  due  to  many
 communications.   In fact,  a distributed  method greatly  reduces the
 number  of communications thanks  to the  partitioning of  the initial
 network in several independent subnetworks. Let us notice that even if
 a  centralized  method  consumes  far  more  energy  than  the  simple
 heuristic, since the energy cost of communications during a round is a
 small  part   of  the   energy  spent  in   the  sensing   phase,  the
-communications have a small impact on the lifetime.
+communications have a small impact on the network lifetime.
 
 \begin{figure}[h!]
 \centering
-\includegraphics[scale=0.55]{TheEnergyConsumption.eps} 
-\caption{The Energy Consumption  }
+\includegraphics[scale=0.37]{EC1.eps} 
+\caption{The energy consumption}
 \label{fig7}
 \end{figure} 
 
-\subsection{The impact of Number of Sensors on Execution Time}
+\subsection{The impact of the number of sensors on 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.
-Table~\ref{table1} gives  the average execution  times on a  laptop of
-the decision phase during one round.  They are given for the different
-approaches  and   various  numbers  of  sensors.   The   lack  of  any
-optimization explains why the  heuristic has very low execution times.
-Conversely, the  Strategy with One  Leader which requires to  solve an
-optimization  problem considering all  the nodes  presents redhibitory
-execution  times. Moreover,  increasing of  50~nodes the  network size
-multiplies the  time by almost a  factor of 10. The  Strategy with Two
-Leaders has more suitable times.  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 deal with very large networks a
+used   for  the  sensing   phase,  not   for  the   pre-sensing  ones.   
+Table~\ref{table1} gives the average  execution times  in seconds
+on a laptop of the decision phase (solving of the optimization problem)
+during one  round.  They  are given for  the different  approaches and
+various numbers of sensors.  The lack of any optimization explains why
+the heuristic has very  low execution times.  Conversely, the strategy
+with  one  leader, which  requires  to  solve  an optimization  problem
+considering  all  the  nodes  presents  redhibitory  execution  times.
+Moreover, increasing the network size by 50~nodes   multiplies the time
+by  almost a  factor of  10. The  strategy with  two leaders  has more
+suitable times.  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.
 
 \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
 
@@ -886,8 +696,8 @@ distributed method is clearly required.
 % centered columns (4 columns)
       \hline
 %inserts double horizontal lines
-Sensors Number & Strategy & Strategy  & Simple Heuristic \\ [0.5ex]
- & (with Two Leaders) & (with One Leader) & \\ [0.5ex]
+Sensors number & Strategy~2 & Strategy~1  & Simple heuristic \\ [0.5ex]
+ & (with two leaders) & (with one leader) & \\ [0.5ex]
 %Case & Strategy (with Two Leaders) & Strategy (with One Leader) & Simple Heuristic \\ [0.5ex]
 % inserts table
 %heading
@@ -911,67 +721,69 @@ Sensors Number & Strategy & Strategy  & Simple Heuristic \\ [0.5ex]
 % is used to refer this table in the text
 \end{table}
 
-\subsection{The Number of Stopped Simulation Runs}
+\subsection{The network lifetime}
 
-Finally, we will  study the number of simulation  which stopped due to
-network  disconnection, per round  for each  of the  three approaches.
-Figure~\ref{fig8}  illustrates the number  of stopped  simulation runs
-per  round  for 150  deployed  nodes.  It  can  be  observed that  the
-heuristic is  the approach which  stops the earlier because  the nodes
-are  chosen   randomly.   Among  the  two   proposed  strategies,  the
-centralized  one  first   exhibits  network  disconnection.  Thus,  as
-explained previously, in case  of the strategy with several subregions
-the  optimization effectively  continues as  long  as a  network in  a
-subregion   is  still   connected.   This   longer   partial  coverage
-optimization participates in extending the lifetime.
+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
+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.
 
 \begin{figure}[h!]
+%\centering
+% \begin{multicols}{6}
 \centering
-\includegraphics[scale=0.55]{TheNumberofStoppedSimulationRuns150.eps} 
-\caption{The Number of Stopped Simulation Runs against Rounds for 150 deployed nodes }
+\includegraphics[scale=0.37]{LT1.eps} %\\~ ~ ~(a)
+\caption{The network lifetime }
 \label{fig8}
 \end{figure} 
 
-\section{\uppercase{Conclusions and Future Works}}
+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
+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 work}
 \label{sec:conclusion}
 
-In this paper, we have  addressed the problem of coverage and 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
+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 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 results 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,  we  plan to  study  and  propose  a coverage  protocol  which
-computes  all  active  sensor  schedules  in  a  single  round,  using
-optimization  methods  such  as  swarms optimization  or  evolutionary
-algorithms. The computation of all cover sets in one round 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 only one step for many rounds,  using optimization  methods
+such as  swarms optimization or evolutionary algorithms.
 % use section* for acknowledgement
 %\section*{Acknowledgment}
 
 \bibliographystyle{IEEEtran}
 \bibliography{bare_conf}
 
-% that's all folks
 \end{document}
 
 
