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@@ -1,17 +1,19 @@
 
 
- 
 \documentclass[conference]{IEEEtran}
 
+
 \ifCLASSINFOpdf
-  
+
 \else
-  
+
 \fi
 
 \hyphenation{op-tical net-works semi-conduc-tor}
 
-\usepackage{float}
+
+\usepackage{etoolbox}
+\usepackage{float} 
 \usepackage{epsfig}
 \usepackage{calc}
  \usepackage{times,amssymb,amsmath,latexsym}
@@ -32,34 +34,33 @@
 \usepackage{epsfig}
 \usepackage{caption}
 \usepackage{multicol}
+\usepackage{times}
+\usepackage{graphicx,epstopdf}
+\epstopdfsetup{suffix=}
+\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{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}
-}
+\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  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
+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
@@ -68,46 +69,28 @@ 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}
 
-%\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
-communications and embedded micro-sensing MEMS technologies which have
-led to the  emergence of 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 it 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
-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.
-Obviously, the deactivation of nodes  is only relevant if the coverage
-of the monitored area  is not affected.  Consequently, future softwares
-may  need to  adapt  appropriately to  achieve  acceptable quality  of
-service  for  applications.  In  this  paper  we  concentrate on  the area
+\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
@@ -120,257 +103,95 @@ 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
+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
+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
+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.
-
-%\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}
-{\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).
-
-{\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.
-
-{\bf Activity scheduling}
-
-Activitiy 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.
-
-{\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
+\indent In this section, we only review some recent work with the coverage lifetime maximization  problem, where the  objective is to  optimally schedule sensors'  activities in
+order to  extend network lifetime  in WSNS. 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. 
-
-{\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.  \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  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}, probably near
-the optimal solution,    is also proposed.
-
-{\bf Our contribution}
-
-There are  three main questions which  should be addressed  to build a
+decides  its status  (active/sleep)  based on  the perimeter  coverage
+model, which  proposed in \cite{Huang:2003:CPW:941350.941367}. 
+Shibo et al.\cite{Shibo} studied the coverage problem, which is formulated as a minimum weight submodular set cover problem. To address this problem, 
+ a distributed truncated greedy algorithm (DTGA) is proposed. They exploited from the  
+temporal and spatialcorrelations among the data sensed by different sensor nodes and leverage
+prediction to extend the WSNs lifetime.
+Bang et al. \cite{Bang} proposed a coverage-aware clustering protocol(CACP), which used computation method for the optimal cluster size to minimize the average energy consumption rate per unit area. They defied in this protocol a cost metric that prefer the redundant sensors 
+with higher power as best candidates for cluster heads and select the active sensors that cover the area of interest more efficiently.
+Zhixin et al. \cite{Zhixin} propose a Distributed Energy-
+Efficient Clustering with Improved Coverage(DEECIC) algorithm
+which aims at clustering with the least number of cluster
+heads to cover the whole network and assigning a unique ID
+to each node based on local information. In addition, this
+protocol periodically updates cluster heads according to the
+joint information of nodes $â $residual energy and distribution.
+Although DEECIC does not require knowledge of a node's
+geographic location, it guarantees full coverage of the
+network. However, the protocol does not make any activity
+scheduling to set redundant sensors in passive mode in order
+to conserve energy. C. Liu and G. Cao \cite{Changlei} studied how to
+schedule sensor active time to maximize their coverage during a specified network lifetime. Their objective is to maximize the spatial-temporal coverage by scheduling sensors activity after they have been deployed. They proposed both centralized and distributed algorithms. The distributed parallel optimization protocol can ensure each sensor to converge to local optimality without conflict with each other. S. Misra et al. \cite{Misra} proposed a localized algorithm for coverage in sensor
+networks. The algorithm conserve the energy while ensuring the network coverage by activating the subset of sensors, with the minimum overlap area.The proposed method preserves
+the network connectivity by formation of the network backbone. L. Zhang et al. \cite{Zhang} presented a novel distributed clustering algorithm
+called Adaptive Energy Efficient Clustering (AEEC) to maximize network lifetime. In this study, they are introduced an optimization, which includes restricted global re-clustering,
+intra-cluster node sleeping scheduling and adaptive
+transmission range adjustment to conserve the energy, while connectivity and coverage is ensured. J. A. Torkestani \cite{Torkestani} proposed a learning automata-based energy-efficient coverage protocol
+ named as LAEEC to construct the degree-constrained connected dominating set (DCDS) in WSNs. He shows 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. 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
+%\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 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
+%\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.
+  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
+  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
+  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
+  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}
+%\end{itemize}
+
+
 
 \section{Activity scheduling}
 \label{pd}
@@ -418,7 +239,7 @@ each phase in more details.
 \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
@@ -430,14 +251,14 @@ active mode.
 %The working phase works in rounding fashion. Each round include 3 steps described as follow :
 
 \subsection{Leader election phase}
-This  step includes choosing  the Wireless  Sensor Node  Leader (WSNL)
+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{Decision phase}
@@ -462,7 +283,7 @@ 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
@@ -487,7 +308,7 @@ 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 the coverage area, 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 the primary points of
 this sensor are covered.
@@ -507,7 +328,7 @@ increased or decreased if necessary)  as references to ensure that the
 monitored  region  of interest  is  covered  by  the selected  set  of
 sensors, instead of using all the points in the area.
 
-\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\\  
@@ -547,13 +368,13 @@ $X_{13}=( p_x + R_s * (0), p_y + R_s * (\frac{-\sqrt{2}}{2})) $.
 
 %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  proposed an
-integer program which forces undercoverage and overcoverage of targets
+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 $J$.
@@ -623,7 +444,7 @@ X_{j} \in \{0,1\}, &\forall j \in J
   sensing in the round (1 if yes and 0 if not);
 \item $\Theta_{p}$  : {\it overcoverage}, the number  of sensors minus
   one that are covering the primary point $p$;
-\item $U_{p}$  : {\it undercoverage},  indicates whether or  not the principal point
+\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}
 
@@ -631,7 +452,7 @@ 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
+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
@@ -687,12 +508,12 @@ 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 last 60 seconds. Thus, an
+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 by using  some performance
 metrics such as: coverage ratio,  number of active nodes ratio, energy
@@ -732,7 +553,7 @@ subregion.
 \parskip 0pt 
 \begin{figure}[h!]
 \centering
-\includegraphics[scale=0.55]{TheCoverageRatio150.eps} %\\~ ~ ~(a)
+\includegraphics[scale=0.5]{TheCoverageRatio150g.eps} %\\~ ~ ~(a)
 \caption{The impact of the number of rounds on the coverage ratio for 150 deployed nodes}
 \label{fig3}
 \end{figure} 
@@ -742,7 +563,7 @@ subregion.
 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 
@@ -754,7 +575,7 @@ for 150 deployed nodes.
 
 \begin{figure}[h!]
 \centering
-\includegraphics[scale=0.55]{TheActiveSensorRatio150.eps} %\\~ ~ ~(a)
+\includegraphics[scale=0.5]{TheActiveSensorRatio150g.eps} %\\~ ~ ~(a)
 \caption{The impact of the number of rounds on the active sensors ratio for 150 deployed nodes }
 \label{fig4}
 \end{figure} 
@@ -772,7 +593,7 @@ lifetime of the network.
 \subsection{The 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}}
@@ -787,7 +608,7 @@ for all three approaches and for 150 deployed nodes.
 %\centering
 % \begin{multicols}{6}
 \centering
-\includegraphics[scale=0.55]{TheEnergySavingRatio150.eps} %\\~ ~ ~(a)
+\includegraphics[scale=0.5]{TheEnergySavingRatio150g.eps} %\\~ ~ ~(a)
 \caption{The impact of the number of rounds on the energy saving ratio for 150 deployed nodes}
 \label{fig5}
 \end{figure} 
@@ -802,13 +623,13 @@ 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 number of stopped simulation runs}
+\subsection{The percentage of stopped simulation runs}
 
-We  will now  study  the number  of  simulations which  stopped due  to
+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 average number of stopped simulation
+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
+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
@@ -818,8 +639,8 @@ optimization participates in extending the network lifetime.
 
 \begin{figure}[h!]
 \centering
-\includegraphics[scale=0.55]{TheNumberofStoppedSimulationRuns150.eps} 
-\caption{The number of stopped simulation runs compared to the number of rounds for 150 deployed nodes }
+\includegraphics[scale=0.5]{TheNumberofStoppedSimulationRuns150g.eps} 
+\caption{The percentage of stopped simulation runs compared to the number of rounds for 150 deployed nodes }
 \label{fig6}
 \end{figure} 
 
@@ -835,7 +656,7 @@ 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  the energy
 consumption point  of view.  A  centralized method, like  the strategy
@@ -850,7 +671,7 @@ communications have a small impact on the network lifetime.
 
 \begin{figure}[h!]
 \centering
-\includegraphics[scale=0.55]{TheEnergyConsumption.eps} 
+\includegraphics[scale=0.5]{TheEnergyConsumptiong.eps} 
 \caption{The energy consumption}
 \label{fig7}
 \end{figure} 
@@ -866,7 +687,7 @@ 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
+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
@@ -876,7 +697,7 @@ 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{THE EXECUTION TIME(S) VS THE NUMBER OF SENSORS}
 % title of Table
 \centering
 
@@ -925,7 +746,7 @@ with two  leaders and the simple  heuristic is illustrated.
 %\centering
 % \begin{multicols}{6}
 \centering
-\includegraphics[scale=0.5]{TheNetworkLifetime.eps} %\\~ ~ ~(a)
+\includegraphics[scale=0.5]{TheNetworkLifetimeg.eps} %\\~ ~ ~(a)
 \caption{The network lifetime }
 \label{fig8}
 \end{figure} 
@@ -944,7 +765,7 @@ 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 forks}
+\section{Conclusion and future works}
 \label{sec:conclusion}
 
 In this paper, we have  addressed the problem of the coverage and the lifetime
@@ -972,22 +793,24 @@ 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  a  single  round,  using
+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.  This single  round  will still  consists  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 round is far more
+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.
-
 % use section* for acknowledgement
 %\section*{Acknowledgment}
 
+
+
+
 \bibliographystyle{IEEEtran}
 \bibliography{bare_conf}
 
-% that's all folks
+
 \end{document}
 
 
