X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/UIC2013.git/blobdiff_plain/39b48f032a13fc6524febe806cb05a43d808f416..HEAD:/bare_conf.tex?ds=sidebyside

diff --git a/bare_conf.tex b/bare_conf.tex
index 252ea78..bbe85c3 100644
--- a/bare_conf.tex
+++ b/bare_conf.tex
@@ -11,7 +11,6 @@
 
 \hyphenation{op-tical net-works semi-conduc-tor}
 
-
 \usepackage{etoolbox}
 \usepackage{float} 
 \usepackage{epsfig}
@@ -40,7 +39,6 @@
 \DeclareGraphicsExtensions{.ps}
 \DeclareGraphicsRule{.ps}{pdf}{.pdf}{`ps2pdf -dEPSCrop -dNOSAFER #1 \noexpand\OutputFile}
 
-
 \begin{document}
 %
 % paper title
@@ -69,7 +67,7 @@ subregions using  a divide-and-conquer method and  then the scheduling
 of sensor node  activity is planned for each  subregion.  The proposed
 scheduling  considers rounds  during which  a small  number  of nodes,
 remaining active  for sensing, is  selected to ensure  coverage.  Each
-round consists  of four phases:  (i)~Information Exchange, (ii)~Leader
+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.
 Simulation  results show that  the proposed  approach can  prolong the
@@ -86,47 +84,69 @@ Optimization, Scheduling.
 
 \section{Introduction}
 
-\noindent  The fast developments  in the  low-cost sensor  devices and
-wireless  communications  have allowed  the  emergence  the WSNs.  WSN
-includes  a large  number of  small ,  limited-power sensors  that can
-sense, process and transmit data  over a wireless communication . They
-communicate with each other by using multi-hop wireless communications
-, cooperate together to monitor the area of interest, and the measured
-data can be reported to a monitoring center called, sink, for analysis
-it~\cite{Ammari01, Sudip03}.  There are several  applications used the
-WSN  including health,  home,  environmental, military,and  industrial
-applications~\cite{Akyildiz02}.   The coverage problem  is one  of the
-fundamental  challenges   in  WSNs~\cite{Nayak04}  that   consists  in
-monitoring  efficiently and  continuously  the area  of interest.  The
-limited energy  of sensors represents  the main challenge in  the WSNs
-design~\cite{Ammari01},  where  it  is  difficult  to  replace  and/or
-recharge their batteries because the the area of interest nature (such
-as hostile environments) and the cost.  So, it is necessary that a WSN
-deployed  with high  density because  spatial redundancy  can  then be
-exploited to increase  the lifetime of the network  . However, turn on
-all the sensor  nodes, which monitor the same region  at the same time
-leads to decrease the lifetime  of the network. To extend the lifetime
-of the network, the main idea  is to take advantage of the overlapping
-sensing regions  of some  sensor nodes to  save energy by  turning off
-some  of them  during the  sensing phase~\cite{Misra05}.  WSNs require
-energy-efficient  solutions to  improve the  network lifetime  that is
-constrained   by    the   limited   power   of    each   sensor   node
-~\cite{Akyildiz02}.   In  this  paper,  we  concentrate  on  the  area
-coverage  problem,  with  the  objective  of  maximizing  the  network
-lifetime  by using  an adaptive  scheduling. The  area of  interest is
-divided into subregions and an activity scheduling for sensor nodes is
-planned for each subregion.  In fact,  the nodes in a subregion can be
-seen as  a cluster where each  node sends sensing data  to the cluster
-head   or  the   sink  node.    Furthermore,  the   activities   in  a
-subregion/cluster can  continue even if  another cluster stops  due to
-too many node failures.  Our scheduling scheme considers rounds, where
-a round starts with a  discovery phase to exchange information between
-sensors of  the subregion, in order  to choose in a  suitable manner a
-sensor node to  carry out a coverage strategy.  This coverage strategy
-involves  the  solving  of  an  integer program,  which  provides  the
-activation of the sensors for the sensing phase of the current round.
-
-The remainder of the paper is organized as follows.  The next section
+%\indent  The fast  developments  in the  low-cost  sensor devices  and
+%wireless  communications have  allowed  the emergence  the WSNs.   WSN
+%includes  a large  number  of small,  limited-power  sensors that  can
+%sense, process  and transmit data over a  wireless communication. They
+%communicate   with   each    other   by   using   multi-hop   wireless
+%communications, cooperate  together to  monitor the area  of interest,
+%and the  measured data can be  reported to a  monitoring center called
+%sink  for analysis it~\cite{Sudip03}.  There are  several applications
+%used  the WSN  including  health, home,  environmental, military,  and
+%industrial applications~\cite{Akyildiz02}. The coverage problem is one
+%of the fundamental challenges  in WSNs~\cite{Nayak04} that consists in
+%monitoring    efficiently    and     continuously    the    area    of
+%interest. Thelimited  energy of sensors represents  the main challenge
+%in the  WSNs design~\cite{Sudip03}, where  it is difficult  to replace
+%and/or  recharge their  batteries  because the  the  area of  interest
+%nature  (such  as  hostile  environments)  and the  cost.  So,  it  is
+%necessary  that  a WSN  deployed  with  high  density because  spatial
+%redundancy  can then  be exploited  to  increase the  lifetime of  the
+%network. However, turn on all the sensor nodes, which monitor the same
+%region at the same time leads to decrease the lifetime of the network.
+
+Recent   years  have  witnessed   significant  advances   in  wireless
+communications and embedded micro-sensing MEMS technologies which have
+led to the emergence of Wireless  Sensor Networks (WSNs) as one of the
+most promising  technologies \cite{Akyildiz02}. In  fact, they present
+huge   potential  in   several  domains   ranging  from   health  care
+applications to military applications. A sensor network is composed of
+a  large  number of  tiny  sensing devices  deployed  in  a region  of
+interest.  Each  device  has  processing  and  wireless  communication
+capabilities, which enable it to sense its environment, to compute, to
+store information  and to  deliver report messages  to a  base station
+\cite{Sudip03}.  One of  the main design issues in  WSNs is to prolong
+the network  lifetime, while  achieving acceptable quality  of service
+for  applications. Indeed,  sensors  nodes have  limited resources  in
+terms of memory, energy and computational power.
+
+Since sensor nodes have limited battery life and 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 advantage
+of the overlapping sensing regions of some sensor nodes to save energy
+by turning  off some of them during  the sensing phase~\cite{Misra05}.
+Obviously, the deactivation of nodes  is only relevant if the coverage
+of the monitored  area is not affected. In  this paper, we concentrate
+on  the area coverage  problem \cite{Nayak04},  with the  objective of
+maximizing the network lifetime  by using an adaptive scheduling.  The
+area of interest is divided into subregions and an activity scheduling
+for sensor nodes is planned for each subregion.  In fact, the nodes in
+a subregion  can be seen  as a cluster  where each node  sends sensing
+data  to  the  cluster  head  or  the  sink  node.   Furthermore,  the
+activities in a subregion/cluster can continue even if another cluster
+stops due to too many  node failures.  Our scheduling scheme considers
+rounds,  where a  round  starts  with a  discovery  phase to  exchange
+information between sensors of the  subregion, in order to choose in a
+suitable manner a sensor node  to carry out a coverage strategy.  This
+coverage strategy  involves the solving  of an integer  program, which
+provides the  activation of the sensors  for the sensing  phase of the
+current round.
+
+The remainder of the paper is organized as follows. The next section
 % Section~\ref{rw}
 reviews the related work in the field.  Section~\ref{pd} is devoted to
 the    scheduling     strategy    for    energy-efficient    coverage.
@@ -144,77 +164,41 @@ the coverage lifetime maximization  problem, where the objective is to
 optimally  schedule  sensors'  activities  in  order  to  extend  WSNs
 lifetime.
 
-In \cite{chin2007}  is 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
+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 advantage  from both
-temporal  and spatial  correlations between  data sensed  by different
-sensors,  and   leverage  prediction,  to  improve   the  lifetime.  A
-Coverage-Aware  Clustering Protocol (CACP),  which uses  a computation
-method  to  find  the  cluster  size  minimizing  the  average  energy
-consumption rate  per unit area, has  been proposed by Bang  et al. in
-\cite{Bang}. Their protocol is based on a cost metric that selects the
-redundant  sensors with higher  power as  best candidates  for cluster
-heads and the active sensors that  cover the area of interest the more
-efficiently.
-
-% TO BE CONTINUED
-
-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.
+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:
+to build a scheduling strategy.\\
 %\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.
+{\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 
 {\bf What are the rules to decide which node has to be turned on
@@ -225,25 +209,13 @@ to build a scheduling strategy:
   objectives.
 
 %\item 
-{\bf Which  node should make such a  decision?}  As mentioned in
-  \cite{pc10}, both centralized  and distributed algorithms have their
-  own  advantages and  disadvantages. Centralized  coverage algorithms
-  have the advantage  of requiring very low processing  power from the
-  sensor  nodes, which  have usually  limited  processing capabilities.
-  Distributed  algorithms  are  very  adaptable  to  the  dynamic  and
-  scalable nature of sensors network.  Authors in \cite{pc10} conclude
-  that there is a threshold in  terms of network size to switch from a
-  localized  to  a  centralized  algorithm.  Indeed, the  exchange  of
-  messages  in large  networks may  consume a  considerable  amount of
-  energy in a centralized approach  compared to a distributed one. Our
-  work does not  consider only one leader to  compute and to broadcast
-  the scheduling decision  to all the sensors.  When  the network size
-  increases,  the network  is  divided into  many  subregions and  the
-  decision is made by a leader in each subregion.
+{\bf Which  node should make such  a decision?}  A  leader node should
+make such  a decision. Our work  does not consider only  one leader to
+compute and to  broadcast the scheduling decision to  all the sensors.
+When  the network  size increases,  the network  is divided  into many
+subregions and the decision is made by a leader in each subregion.
 %\end{itemize}
 
-
-
 \section{Activity scheduling}
 \label{pd}
 
@@ -260,8 +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
@@ -338,12 +308,9 @@ starting a new round.
 widely used sensor coverage model in the literature. Each sensor has a
 constant sensing range $R_s$. All  space points within a disk centered
 at  the sensor with  the radius  of the  sensing range  is said  to be
-covered by this sensor. We also assume that the communication range is
-at   least  twice    the size of the   sensing  range.   In  fact,   Zhang  and
-Zhou~\cite{Zhang05} proved that if  the transmission range fulfills the
-previous  hypothesis, a  complete coverage  of a  convex  area implies
-connectivity among the working nodes in the active mode.
-%To calculate the coverage ratio for the area of interest, we can propose the following coverage model which is called Wireless Sensor Node Area Coverage Model to ensure that all the area within each node sensing range are covered. We can calculate the positions of the points in the circle disc of the sensing range of wireless sensor node based on the Unit Circle in figure~\ref{fig:cluster1}:
+covered by this sensor. We also assume that the communication range $R_c \geq 2R_s$ ~\cite{Zhang05}. 
+
+
 
 %\begin{figure}[h!]
 %\centering
@@ -408,17 +375,14 @@ $X_{13}=( p_x + R_s * (0), p_y + R_s * (\frac{-\sqrt{2}}{2})) $.
 %\includegraphics[scale=0.10]{fig26.pdf}\\~ ~ ~(e)
 %\includegraphics[scale=0.10]{fig27.pdf}\\~ ~ ~(f)
 %\end{multicols} 
-\caption{Wireless sensor node represented by 13 primary points}
+\caption{Sensor node represented by 13 primary points}
 \label{fig2}
 \end{figure}
 
 \section{Coverage problem formulation}
 \label{cp}
-%We can formulate our optimization problem as energy cost minimization by minimize the number of active sensor nodes and maximizing the coverage rate at the same time in each $A^k$ . This optimization problem can be formulated as follow: Since that we use a homogeneous wireless sensor network, we will assume that the cost of keeping a node awake is the same for all wireless sensor nodes in the network. We can define the decision parameter  $X_j$ as in \eqref{eq11}:\\
 
 
-%To satisfy the coverage requirement, the set of the principal points that will represent all the sensor nodes in the monitored region as $PSET= \lbrace P_1,\ldots ,P_p, \ldots , P_{N_P^k} \rbrace $, where $N_P^k = N_{sp} * N^k $ and according to the proposed model in figure ~\ref{fig:cluster2}. These points can be used by the wireless sensor node leader which will be chosen in each region in A to build a new parameter $\alpha_{jp}$  that represents the coverage possibility for each principal point $P_p$ of each wireless sensor node $s_j$ in $A^k$ as in \eqref{eq12}:\\
-
 \indent   Our   model   is   based   on  the   model   proposed   by
 \cite{pedraza2006} where the objective is  to find a maximum number of
 disjoint  cover sets.   To accomplish  this goal,  authors  proposed an
@@ -510,31 +474,6 @@ weights  $w_\theta$  and  $w_U$  must  be properly  chosen  so  as  to
 guarantee that  the maximum number  of points are covered  during each
 round.
  
-%In equation \eqref{eq15}, there are two main objectives: the first one using  the Overcoverage parameter to minimize the number of active sensor nodes in the produced final solution vector $X$ which leads to improve the life time of wireless sensor network. The second goal by using the  Undercoverage parameter  to maximize the coverage in the region by means of covering each primary point in $SSET^k$.The two objectives are achieved at the same time. The constraint which represented in equation \eqref{eq16} refer to the coverage function for each primary point $P_p$ in $SSET^k$ , where each $P_p$ should be covered by
-%at least one sensor node in $A^k$. The objective function in \eqref{eq15} involving two main objectives to be optimized simultaneously, where optimal decisions need to be taken in the presence of trade-offs between the two conflicting main objectives in \eqref{eq15} and this refer to that our coverage optimization problem is a multi-objective optimization problem and we can use the BPSO to solve it. The concept of Overcoverage and Undercoverage inspired from ~\cite{Fernan12} but we use it with our model as stated in subsection \ref{Sensing Coverage Model} with some modification to be applied later by BPSO.
-%\subsection{Notations and assumptions}
-
-%\begin{itemize}
-%\item $m$ : the number of targets
-%\item $n$ : the number of sensors
-%\item $K$ : maximal number of cover sets
-%\item $i$ : index of target ($i=1..m$)
-%\item $j$ : index of sensor ($j=1..n$)
-%\item $k$ : index of cover set ($k=1..K$)
-%\item $T_0$ : initial set of targets
-%\item $S_0$ : initial set of sensors
-%\item $T $ : set of targets which are not covered by at least one cover set
-%\item $S$ : set of available sensors
-%\item $S_0(i)$ : set of sensors which cover the target $i$
-%\item $T_0(j)$ : set of targets covered by sensor $j$
-%\item $C_k$ : cover set of index $k$
-%\item $T(C_k)$ : set of targets covered by the cover set $k$
-%\item $NS(i)$ : set of  available sensors which cover the target $i$
-%\item $NC(i)$ : set of cover sets which do not cover the target $i$
-%\item $|.|$ : cardinality of the set
-
-%\end{itemize}
-
 \section{Simulation results}
 \label{exp}
 
@@ -604,7 +543,7 @@ subregion.
 \parskip 0pt 
 \begin{figure}[h!]
 \centering
-\includegraphics[scale=0.5]{TheCoverageRatio150g.eps} %\\~ ~ ~(a)
+\includegraphics[scale=0.37]{CR1.eps} %\\~ ~ ~(a)
 \caption{The impact of the number of rounds on the coverage ratio for 150 deployed nodes}
 \label{fig3}
 \end{figure} 
@@ -626,7 +565,7 @@ for 150 deployed nodes.
 
 \begin{figure}[h!]
 \centering
-\includegraphics[scale=0.5]{TheActiveSensorRatio150g.eps} %\\~ ~ ~(a)
+\includegraphics[scale=0.37]{ASR1.eps} %\\~ ~ ~(a)
 \caption{The impact of the number of rounds on the active sensors ratio for 150 deployed nodes }
 \label{fig4}
 \end{figure} 
@@ -641,7 +580,7 @@ that even if a network is disconnected in one subregion, the other one
 usually  continues  the optimization  process,  and  this extends  the
 lifetime of the network.
 
-\subsection{The impact of the number of rounds on the energy saving ratio} 
+\subsection{Impact of the number of rounds on the energy saving ratio} 
 
 In this experiment, we consider a performance metric linked to energy.
 This metric, called Energy Saving Ratio (ESR), is defined by:
@@ -659,7 +598,7 @@ for all three approaches and for 150 deployed nodes.
 %\centering
 % \begin{multicols}{6}
 \centering
-\includegraphics[scale=0.5]{TheEnergySavingRatio150g.eps} %\\~ ~ ~(a)
+\includegraphics[scale=0.37]{ESR1.eps} %\\~ ~ ~(a)
 \caption{The impact of the number of rounds on the energy saving ratio for 150 deployed nodes}
 \label{fig5}
 \end{figure} 
@@ -690,7 +629,7 @@ optimization participates in extending the network lifetime.
 
 \begin{figure}[h!]
 \centering
-\includegraphics[scale=0.5]{TheNumberofStoppedSimulationRuns150g.eps} 
+\includegraphics[scale=0.36]{SR1.eps} 
 \caption{The percentage of stopped simulation runs compared to the number of rounds for 150 deployed nodes }
 \label{fig6}
 \end{figure} 
@@ -722,7 +661,7 @@ communications have a small impact on the network lifetime.
 
 \begin{figure}[h!]
 \centering
-\includegraphics[scale=0.5]{TheEnergyConsumptiong.eps} 
+\includegraphics[scale=0.37]{EC1.eps} 
 \caption{The energy consumption}
 \label{fig7}
 \end{figure} 
@@ -748,7 +687,7 @@ nodes.   Overall,  to  be  able to  deal  with  very  large  networks,  a
 distributed method is clearly required.
 
 \begin{table}[ht]
-\caption{THE EXECUTION TIME(S) VS THE NUMBER OF SENSORS}
+\caption{EXECUTION TIME(S) VS. NUMBER OF SENSORS}
 % title of Table
 \centering
 
@@ -786,82 +725,65 @@ Sensors number & Strategy~2 & Strategy~1  & Simple heuristic \\ [0.5ex]
 
 Finally, we  have defined the network  lifetime as the  time until all
 nodes  have  been drained  of  their  energy  or each  sensor  network
-monitoring  an area has become  disconnected.  In  figure~\ref{fig8}, the
+monitoring an area has become disconnected.  In figure~\ref{fig8}, the
 network  lifetime for different  network sizes  and for  both strategy
-with two  leaders and the simple  heuristic is illustrated. 
-  We do  not consider  anymore the  centralized strategy  with one
-  leader, because, as shown above, this strategy results  in execution
-  times that quickly become unsuitable for a sensor network.
+with two leaders  and the simple heuristic is  illustrated.  We do not
+consider anymore the centralized strategy with one leader, because, as
+shown  above, this strategy  results in  execution times  that quickly
+become unsuitable for a sensor network.
 
 \begin{figure}[h!]
 %\centering
 % \begin{multicols}{6}
 \centering
-\includegraphics[scale=0.5]{TheNetworkLifetimeg.eps} %\\~ ~ ~(a)
+\includegraphics[scale=0.37]{LT1.eps} %\\~ ~ ~(a)
 \caption{The network lifetime }
 \label{fig8}
 \end{figure} 
 
 As  highlighted by figure~\ref{fig8},  the network  lifetime obviously
-increases when  the size  of the network  increases, with  our approach
-that leads to  the larger lifetime improvement.  By  choosing the  best 
-suited nodes, for each round,  to cover the  region of interest  and by
+increases when  the size of  the network increases, with  our approach
+that leads to  the larger lifetime improvement.  By  choosing the best
+suited nodes, for  each round, to cover the region  of interest and by
 letting the other ones sleep in order to be used later in next rounds,
-our strategy efficiently prolonges the network lifetime. Comparison shows that
-the larger  the sensor number  is, the more our  strategies outperform
-the simple heuristic.  Strategy~2, which uses two leaders, is the best
-one because it is robust to network disconnection in one subregion. It
-also  means   that  distributing  the  algorithm  in   each  node  and
-subdividing the sensing field  into many subregions, which are managed
-independently and simultaneously, is the most relevant way to maximize
-the lifetime of a network.
-
-\section{Conclusion and future works}
+our  strategy efficiently prolonges  the network  lifetime. Comparison
+shows that  the larger the sensor  number is, the  more our strategies
+outperform the simple heuristic.   Strategy~2, which uses two leaders,
+is the best  one because it is robust to  network disconnection in one
+subregion. It also means that  distributing the algorithm in each node
+and  subdividing the  sensing field  into many  subregions,  which are
+managed independently and simultaneously,  is the most relevant way to
+maximize the lifetime of a network.
+
+\section{Conclusion and future work}
 \label{sec:conclusion}
 
-In this paper, we have  addressed the problem of the coverage and the lifetime
-optimization  in wireless  sensor networks.   This is  a key  issue as
-sensor nodes  have limited  resources in terms  of memory,  energy and
-computational power. To  cope with this problem, the  field of sensing
-is   divided   into   smaller   subregions  using   the   concept   of
+In this paper,  we have addressed the problem of  the coverage and the
+lifetime optimization in WSNs. To cope with this problem, the field of
+sensing  is  divided into  smaller  subregions  using  the concept  of
 divide-and-conquer method,  and then a  multi-rounds coverage protocol
 will optimize  coverage and  lifetime performances in  each subregion.
 The  proposed  protocol  combines  two efficient  techniques:  network
 leader election  and sensor activity scheduling,  where the challenges
 include how to select the  most efficient leader in each subregion and
-the best  representative active nodes that will  optimize the network lifetime
-while  taking   the  responsibility  of   covering  the  corresponding
-subregion.   The network lifetime  in each  subregion is  divided into
-rounds, each round consists  of four phases: (i) Information Exchange,
-(ii) Leader Election, (iii) an optimization-based Decision in order to
-select  the  nodes remaining  active  for  the  last phase,  and  (iv)
-Sensing.  The  simulations show the relevance  of the proposed
-protocol in  terms of lifetime, coverage ratio,  active sensors ratio,
-energy saving,  energy consumption, execution time, and  the number of
-stopped simulation  runs due  to network disconnection.   Indeed, when
-dealing with  large and dense wireless sensor  networks, a distributed
-approach like the one we propose  allows to reduce the difficulty of a
-single global optimization problem  by partitioning it in many smaller
-problems, one per subregion, that can be solved more easily.
-
-In  future work, we plan  to study  and propose  a coverage  protocol, which
-computes  all  active  sensor  schedules  in  one time,  using
-optimization  methods  such  as  swarms optimization  or  evolutionary
-algorithms.  The round  will still  consist of 4  phases, but  the
-  decision phase will compute the schedules for several sensing phases,
-  which aggregated together, define a kind of meta-sensing phase.
-The computation of all cover sets in one time is far more
-difficult, but will reduce the communication overhead.
+the best  representative active  nodes. Results from  simulations show
+the relevance of the proposed  protocol in terms of lifetime, coverage
+ratio,  active  sensors  ratio,  energy  saving,  energy  consumption,
+execution  time, and  the number  of  stopped simulation  runs due  to
+network  disconnection.  Indeed,  when  dealing with  large and  dense
+wireless  sensor networks,  a  distributed approach  like  the one  we
+propose  allows   to  reduce  the   difficulty  of  a   single  global
+optimization problem by partitioning  it in many smaller problems, one
+per subregion,  that can  be solved more  easily.  In future  work, we
+plan to  study a  coverage protocol which  computes all  active sensor
+schedules in only one step for many rounds,  using optimization  methods
+such as  swarms optimization or evolutionary algorithms.
 % use section* for acknowledgement
 %\section*{Acknowledgment}
 
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