Almost final modifications

[Sensornets15.git] / Example.tex

diff --git a/Example.tex b/Example.tex
index 38cc14f5cca00795a4c2108785bb15b62fa44b31..b2b473fa653c7fe59132b1f9da281b64f687570b 100644 (file)
--- a/Example.tex
+++ b/Example.tex
@@ -26,7 +26,8 @@
 
 %\title{Authors' Instructions  \subtitle{Preparation of Camera-Ready Contributions to SCITEPRESS Proceedings} }
 
 
 %\title{Authors' Instructions  \subtitle{Preparation of Camera-Ready Contributions to SCITEPRESS Proceedings} }
 

-\title{Distributed Lifetime Coverage Optimization Protocol in Wireless Sensor Networks}
+\title{Distributed Lifetime Coverage Optimization Protocol \\
+  in Wireless Sensor Networks}

 
 \author{Ali Kadhum Idrees$^{a,b}$, Karine Deschinkel$^{a}$,\\ Michel Salomon$^{a}$, and Rapha\"el Couturier$^{a}$\\
 $^{a}$FEMTO-ST Institute, UMR 6174 CNRS, \\ University  Bourgogne  Franche-Comt\'e, Belfort, France\\
 
 \author{Ali Kadhum Idrees$^{a,b}$, Karine Deschinkel$^{a}$,\\ Michel Salomon$^{a}$, and Rapha\"el Couturier$^{a}$\\
 $^{a}$FEMTO-ST Institute, UMR 6174 CNRS, \\ University  Bourgogne  Franche-Comt\'e, Belfort, France\\


@@ -78,37 +79,47 @@ email: ali.idness@edu.univ-fcomte.fr,\\ $\lbrace$karine.deschinkel, michel.salom
 \label{sec:introduction}
 
 \noindent 
 \label{sec:introduction}
 
 \noindent 

-Energy efficiency is  a crucial issue in wireless  sensor networks since sensory
+Energy efficiency is  a crucial issue in wireless sensor  networks since sensory

 consumption, in  order to  maximize the network  lifetime, represents  the major
 difficulty when designing WSNs. As a consequence, one of the scientific research
 challenges in  WSNs, which has  been addressed by  a large amount  of literature
 during the  last few  years, is  the design of  energy efficient  approaches for
 consumption, in  order to  maximize the network  lifetime, represents  the major
 difficulty when designing WSNs. As a consequence, one of the scientific research
 challenges in  WSNs, which has  been addressed by  a large amount  of literature
 during the  last few  years, is  the design of  energy efficient  approaches for

-coverage and connectivity~\cite{conti2014mobile}.   Coverage reflects how well a
+coverage and connectivity~\cite{conti2014mobile}.  Coverage  reflects how well a

 sensor  field is  monitored. On  the one  hand we  want to  monitor the  area of
 sensor  field is  monitored. On  the one  hand we  want to  monitor the  area of

-interest in the most efficient way~\cite{Nayak04}.  On the other hand we want to
-use  as little energy  as possible.   Sensor nodes  are battery-powered  with no
-means  of recharging  or replacing,  usually  due to  environmental (hostile  or
-unpractical environments)  or cost reasons.   Therefore, it is desired  that the
-WSNs are deployed  with high densities so as to  exploit the overlapping sensing
-regions of some sensor  nodes to save energy by turning off  some of them during
-the sensing phase to prolong the network lifetime. \textcolor{blue}{A WSN can use various types of sensors such as \cite{ref17,ref19}: thermal, seismic, magnetic, visual, infrared, acoustic, and radar. These sensors are capable of observing  different physical conditions such as: temperature, humidity, pressure, speed, direction, movement, light, soil makeup, noise levels, presence or absence of certain kinds of objects, and mechanical stress levels on attached objects. Consequently, there is a wide range of WSN applications such as~\cite{ref22}: health-care, environment, agriculture, public safety, military, transportation systems, and industry applications.}
-
-In this  paper we design  a protocol that  focuses on the area  coverage problem
+interest in the most  efficient way~\cite{Nayak04}, \textcolor{blue}{which means
+  that we want to maintain the best coverage as long as possible}.  On the other
+hand  we  want  to  use  as   little  energy  as  possible.   Sensor  nodes  are
+battery-powered  with  no means  of  recharging  or  replacing, usually  due  to
+environmental (hostile or unpractical environments) or cost reasons.  Therefore,
+it is desired  that the WSNs are  deployed with high densities so  as to exploit
+the overlapping sensing  regions of some sensor nodes to  save energy by turning
+off  some   of  them   during  the   sensing  phase   to  prolong   the  network
+lifetime.  \textcolor{blue}{A WSN  can  use  various types  of  sensors such  as
+  \cite{ref17,ref19}:  thermal, seismic,  magnetic, visual,  infrared, acoustic,
+  and  radar.  These  sensors  are   capable  of  observing  different  physical
+  conditions  such  as:  temperature,   humidity,  pressure,  speed,  direction,
+  movement, light,  soil makeup,  noise levels, presence  or absence  of certain
+  kinds  of  objects,   and  mechanical  stress  levels   on  attached  objects.
+  Consequently, there is a wide  range of WSN applications such as~\cite{ref22}:
+  health-care, environment, agriculture, public safety, military, transportation
+  systems, and industry applications.}
+
+In this  paper we design  a protocol that focuses  on the area  coverage problem

 with  the objective  of maximizing  the network  lifetime. Our  proposition, the
 with  the objective  of maximizing  the network  lifetime. Our  proposition, the

-Distributed  Lifetime  Coverage  Optimization  (DiLCO) protocol,  maintains  the
+Distributed  Lifetime  Coverage  Optimization (DiLCO)  protocol,  maintains  the

 coverage  and improves  the lifetime  in  WSNs. The  area of  interest is  first
 coverage  and improves  the lifetime  in  WSNs. The  area of  interest is  first

-divided  into subregions using  a divide-and-conquer  algorithm and  an activity
+divided into  subregions using  a divide-and-conquer  algorithm and  an activity

 scheduling  for sensor  nodes is  then  planned by  the elected  leader in  each
 subregion. In fact, the nodes in a subregion can be seen as a cluster where each
 scheduling  for sensor  nodes is  then  planned by  the elected  leader in  each
 subregion. In fact, the nodes in a subregion can be seen as a cluster where each

-node sends sensing data to the  cluster head or the sink node.  Furthermore, the
+node sends sensing data to the cluster  head or the sink node.  Furthermore, the

 activities in a subregion/cluster can continue even if another cluster stops due
 to too many node failures.  Our DiLCO protocol considers periods, where a period
 activities in a subregion/cluster can continue even if another cluster stops due
 to too many node failures.  Our DiLCO protocol considers periods, where a period

-starts with  a discovery  phase to exchange  information between sensors  of the
-same  subregion, in order  to choose  in a  suitable manner  a sensor  node (the
+starts with  a discovery phase  to exchange  information between sensors  of the
+same subregion,  in order  to choose  in a  suitable manner  a sensor  node (the

 leader) to carry out the coverage  strategy. In each subregion the activation of
 leader) to carry out the coverage  strategy. In each subregion the activation of

-the sensors for  the sensing phase of the current period  is obtained by solving
-an integer program.  The resulting activation vector is  broadcast by a leader
-to every node of its subregion. 
+the sensors for the  sensing phase of the current period  is obtained by solving
+an integer program.  The resulting activation vector is broadcast by a leader to
+every node of its subregion.

 
 % MODIF - BEGIN
 Our previous  paper ~\cite{idrees2014coverage} relies almost  exclusively on the
 
 % MODIF - BEGIN
 Our previous  paper ~\cite{idrees2014coverage} relies almost  exclusively on the


@@ -116,16 +127,21 @@ framework of the  DiLCO approach and the coverage problem  formulation.  In this
 paper  we   made  more  realistic   simulations  by  taking  into   account  the
 characteristics of  a Medusa II sensor  ~\cite{raghunathan2002energy} to measure
 the energy consumption and the computation  time.  We have implemented two other
 paper  we   made  more  realistic   simulations  by  taking  into   account  the
 characteristics of  a Medusa II sensor  ~\cite{raghunathan2002energy} to measure
 the energy consumption and the computation  time.  We have implemented two other

-existing \textcolor{blue}{and distributed approaches}(DESK ~\cite{ChinhVu}, and GAF  ~\cite{xu2001geography}) in order to  compare their performances
-with our approach.  We also focus on performance analysis based on the number of
-subregions. 
+existing \textcolor{blue}{and distributed approaches} (DESK ~\cite{ChinhVu}, and
+GAF ~\cite{xu2001geography})  in order  to compare  their performances  with our
+approach. \textcolor{blue}{We focus  on DESK and GAF protocols  for two reasons.
+  First our protocol is inspired by both  of them: DiLCO uses a regular division
+  of the  area of interest  as in GAF  and a temporal  division in rounds  as in
+  DESK.  Second, DESK  and GAF are well-known protocols, easy  to implement, and
+  often  used  as references  for  comparison}.  We  also focus  on  performance
+analysis based on the number of subregions.

 % MODIF - END
 
 The remainder  of the  paper continues with  Section~\ref{sec:Literature Review}
 where a  review of some related  works is presented. The  next section describes
 % MODIF - END
 
 The remainder  of the  paper continues with  Section~\ref{sec:Literature Review}
 where a  review of some related  works is presented. The  next section describes

-the  DiLCO  protocol,  followed   in  Section~\ref{cp}  by  the  coverage  model
+the  DiLCO  protocol,  followed  in   Section~\ref{cp}  by  the  coverage  model

 formulation    which    is    used     to    schedule    the    activation    of
 formulation    which    is    used     to    schedule    the    activation    of

-sensors. Section~\ref{sec:Simulation Results  and Analysis} shows the simulation
+sensors. Section~\ref{sec:Simulation Results and  Analysis} shows the simulation

 results. The paper ends with a  conclusion and some suggestions for further work
 in Section~\ref{sec:Conclusion and Future Works}.
 
 results. The paper ends with a  conclusion and some suggestions for further work
 in Section~\ref{sec:Conclusion and Future Works}.
 


@@ -184,6 +200,25 @@ of  information can  be huge.   {\it  In order  to be  suitable for  large-scale
   smaller subregions, and in each one, a node called the leader is in charge for
   selecting the active sensors for the current period.}
 
   smaller subregions, and in each one, a node called the leader is in charge for
   selecting the active sensors for the current period.}
 

+% MODIF - BEGIN
+\textcolor{blue}{ Our approach to select the leader node in a subregion is quite
+  different   from    cluster   head    selection   methods   used    in   LEACH
+  \cite{DBLP:conf/hicss/HeinzelmanCB00}         or          its         variants
+  \cite{ijcses11}. Contrary  to LEACH, the division  of the area of  interest is
+  supposed to be performed before the  leader election. Moreover, we assume that
+  the sensors are deployed almost uniformly  and with high density over the area
+  of interest, such  that the division is  fixed and regular.  As  in LEACH, our
+  protocol works in round fashion.  In each round, during the pre-sensing phase,
+  nodes make autonomous  decisions. In LEACH, each sensor elects  itself to be a
+  cluster head,  and each non-cluster  head will  determine its cluster  for the
+  round. In  our protocol, nodes in  the same subregion select  their leader. In
+  both protocols,  the amount  of remaining  energy in each  node is  taken into
+  account  to promote  the nodes  that have  the most  energy to  become leader.
+  Contrary to  the LEACH protocol  where all sensors  will be active  during the
+  sensing-phase, our protocol  allows to deactivate a subset  of sensors through
+  an optimization process which reduces significantly the energy consumption.}
+% MODIF - END
+

 A large  variety of coverage scheduling  algorithms has been  developed. Many of
 the existing  algorithms, dealing with the  maximization of the  number of cover
 sets, are heuristics.  These heuristics  involve the construction of a cover set
 A large  variety of coverage scheduling  algorithms has been  developed. Many of
 the existing  algorithms, dealing with the  maximization of the  number of cover
 sets, are heuristics.  These heuristics  involve the construction of a cover set


@@ -238,13 +273,13 @@ corresponding to  a sensor node is covered  by its neighboring nodes  if all its
 primary points are covered. Obviously,  the approximation of coverage is more or
 less accurate according to the number of primary points.
 
 primary points are covered. Obviously,  the approximation of coverage is more or
 less accurate according to the number of primary points.
 

-

 \subsection{Main idea}
 \label{main_idea}
 \noindent We start  by applying a divide-and-conquer algorithm  to partition the
 area of interest  into smaller areas called subregions and  then our protocol is
 \subsection{Main idea}
 \label{main_idea}
 \noindent We start  by applying a divide-and-conquer algorithm  to partition the
 area of interest  into smaller areas called subregions and  then our protocol is

-executed   simultaneously  in   each   subregion. \textcolor{blue}{Sensor nodes  are assumed to
-be deployed  almost uniformly over the  region and the subdivision of the area of interest is regular.}
+executed  simultaneously in  each subregion.  \textcolor{blue}{Sensor nodes  are
+  assumed to be deployed almost uniformly over the region and the subdivision of
+  the area of interest is regular.}

 
 \begin{figure}[ht!]
 \centering
 
 \begin{figure}[ht!]
 \centering


@@ -290,23 +325,37 @@ and each sensor node will have five possible status in the network:
 \end{itemize}
 %\end{enumerate}
 
 \end{itemize}
 %\end{enumerate}
 

-An outline of the  protocol implementation is given by Algorithm~\ref{alg:DiLCO}
+An outline of the protocol  implementation is given by Algorithm~\ref{alg:DiLCO}

 which describes  the execution of  a period  by a node  (denoted by $s_j$  for a
 which describes  the execution of  a period  by a node  (denoted by $s_j$  for a

-sensor  node indexed by  $j$). At  the beginning  a node  checks whether  it has
-enough energy \textcolor{blue}{(its energy should be greater than a fixed treshold $E_{th}$)} to stay active during the next sensing phase. If yes, it exchanges
-information  with  all the  other  nodes belonging  to  the  same subregion:  it
-collects from each node its position coordinates, remaining energy ($RE_j$), ID,
-and  the number  of  one-hop neighbors  still  alive. \textcolor{blue}{INFO packet contains two parts: header and data payload. The sensor ID is included in the header, where the header size is 8 bits. The data part includes position coordinates (64 bits), remaining energy (32 bits), and the number of one-hop live neighbors (8 bits). Therefore the size of the INFO packet is 112 bits.} Once  the  first phase  is
-completed, the nodes  of a subregion choose a leader to  take the decision based
-on  the  following  criteria   with  decreasing  importance:  larger  number  of
-neighbors, larger remaining energy, and  then in case of equality, larger index.
-After that,  if the sensor node is  leader, it will execute  the integer program
-algorithm (see Section~\ref{cp})  which provides a set of  sensors planned to be
-active in the next sensing phase. As leader, it will send an Active-Sleep packet
-to each sensor  in the same subregion to  indicate it if it has to  be active or
-not.  Alternately, if  the  sensor  is not  the  leader, it  will  wait for  the
-Active-Sleep packet to know its state for the coming sensing phase.
-
+sensor node  indexed by  $j$). At  the beginning  a node  checks whether  it has
+enough  energy  \textcolor{blue}{(its energy  should  be  greater than  a  fixed
+  treshold $E_{th}$)} to  stay active during the next sensing  phase. If yes, it
+exchanges information with all the other  nodes belonging to the same subregion:
+it collects from each node  its position coordinates, remaining energy ($RE_j$),
+ID,  and the  number of  one-hop neighbors  still alive.   \textcolor{blue}{INFO
+  packet contains two parts: header and  data payload. The sensor ID is included
+  in  the header,  where the  header  size is  8  bits. The  data part  includes
+  position coordinates (64 bits), remaining energy  (32 bits), and the number of
+  one-hop live neighbors (8 bits). Therefore the  size of the INFO packet is 112
+  bits.} Once the  first phase is completed,  the nodes of a  subregion choose a
+leader to  take the  decision based  on the  following criteria  with decreasing
+importance: larger  number of  neighbors, larger remaining  energy, and  then in
+case of equality,  larger index.  After that,  if the sensor node  is leader, it
+will  solve an  integer program  (see Section~\ref{cp}).   \textcolor{blue}{This
+  integer program  contains boolean variables  $X_j$ where ($X_j=1$)  means that
+  sensor $j$ will be active in the  next sensing phase. Only sensors with enough
+  remaining energy are  involved in the integer  program ($J$ is the  set of all
+  sensors  involved).  As  the  leader consumes  energy  (computation energy  is
+  denoted by $E^{comp}$) to solve the  optimization problem, it will be included
+  in the integer program only if it has enough energy to achieve the computation
+  and to  stay alive during the  next sensing phase, that  is to say if  $RE_j >
+  E^{comp}+E_{th}$. Once  the optimization problem  is solved, each  leader will
+  send an ActiveSleep packet to each sensor in the same subregion to indicate it
+  if it has to be active or not.  Otherwise, if the sensor is not the leader, it
+  will wait for the ActiveSleep packet to  know its state for the coming sensing
+  phase.}
+%which provides a set of  sensors planned to be
+%active in the next sensing phase.

 
 \begin{algorithm}[h!]                
 
 
 \begin{algorithm}[h!]                
 


@@ -354,7 +403,7 @@ We formulate the coverage optimization problem with an integer program.
 The objective function consists in minimizing the undercoverage and the overcoverage of the area as suggested in \cite{pedraza2006}. 
 The area coverage problem is expressed as the coverage of a fraction of points called primary points. 
 Details on the choice and the number of primary points can be found in \cite{idrees2014coverage}. The set of primary points is denoted by $P$
 The objective function consists in minimizing the undercoverage and the overcoverage of the area as suggested in \cite{pedraza2006}. 
 The area coverage problem is expressed as the coverage of a fraction of points called primary points. 
 Details on the choice and the number of primary points can be found in \cite{idrees2014coverage}. The set of primary points is denoted by $P$

-and the set of sensors by $J$. As we consider a boolean disk coverage model, we use the boolean indicator $\alpha_{jp}$ which is equal to 1 if the primary point $p$ is in the sensing range of the sensor $j$. The binary variable $X_j$ represents the activation or not of the sensor $j$. So we can express the number of  active sensors  that cover  the primary  point $p$ by $\sum_{j \in J} \alpha_{jp} * X_{j}$. We deduce the overcoverage denoted by $\Theta_p$ of the primary point $p$ :
+and the set of alive sensors by $J$. As we consider a boolean disk coverage model, we use the boolean indicator $\alpha_{jp}$ which is equal to 1 if the primary point $p$ is in the sensing range of the sensor $j$. The binary variable $X_j$ represents the activation or not of the sensor $j$. So we can express the number of  active sensors  that cover  the primary  point $p$ by $\sum_{j \in J} \alpha_{jp} * X_{j}$. We deduce the overcoverage denoted by $\Theta_p$ of the primary point $p$ :

 \begin{equation}
  \Theta_{p} = \left \{ 
 \begin{array}{l l}
 \begin{equation}
  \Theta_{p} = \left \{ 
 \begin{array}{l l}


@@ -398,17 +447,16 @@ X_{j} \in \{0,1\}, &\forall j \in J
 \end{array}
 \right.
 \end{equation}
 \end{array}
 \right.
 \end{equation}

-The objective function is a weighted sum of overcoverage and undercoverage. The goal is to limit the overcoverage in order to activate a minimal number of sensors while simultaneously preventing undercoverage. Both  weights $w_\theta$  and $w_U$ must  be carefully  chosen in
-order to  guarantee that the  maximum number of  points are covered  during each
-period.
+The objective function is a weighted sum of overcoverage and undercoverage. The goal is to limit the overcoverage in order to activate a minimal number of sensors while simultaneously preventing undercoverage.  \textcolor{blue}{ By
+    choosing  $w_{U}$ much  larger than $w_{\theta}$,  the coverage  of a
+    maximum of  primary points  is ensured.  Then for the  same number  of covered
+    primary points,  the solution  with a  minimal number  of active  sensors is
+    preferred. }
+%Both  weights $w_\theta$  and $w_U$ must  be carefully  chosen in
+%order to  guarantee that the  maximum number of  points are covered  during each
+%period.

 % MODIF - END
 
 % MODIF - END
 

-
-
-
-
-
-

 \iffalse 
 
 \indent Our model is based on the model proposed by \cite{pedraza2006} where the
 \iffalse 
 
 \indent Our model is based on the model proposed by \cite{pedraza2006} where the


@@ -714,7 +762,7 @@ nodes, and thus enables the extension of the network lifetime.
 \parskip 0pt    
 \begin{figure}[t!]
 \centering
 \parskip 0pt    
 \begin{figure}[t!]
 \centering

- \includegraphics[scale=0.45] {CR.pdf} 
+ \includegraphics[scale=0.475] {CR.pdf} 

 \caption{Coverage ratio}
 \label{fig3}
 \end{figure} 
 \caption{Coverage ratio}
 \label{fig3}
 \end{figure} 


@@ -735,7 +783,7 @@ used for the different performance metrics.
 
 \begin{figure}[h!]
 \centering
 
 \begin{figure}[h!]
 \centering

-\includegraphics[scale=0.45]{EC.pdf} 
+\includegraphics[scale=0.475]{EC.pdf} 

 \caption{Energy consumption per period}
 \label{fig95}
 \end{figure} 
 \caption{Energy consumption per period}
 \label{fig95}
 \end{figure} 


@@ -771,20 +819,20 @@ Figure~\ref{fig8}.
 
 \begin{figure}[h!]
 \centering
 
 \begin{figure}[h!]
 \centering

-\includegraphics[scale=0.45]{T.pdf}  
+\includegraphics[scale=0.475]{T.pdf}  

 \caption{Execution time in seconds}
 \label{fig8}
 \end{figure} 
 
 Figure~\ref{fig8} shows that DiLCO-32 has very low execution times in comparison
 \caption{Execution time in seconds}
 \label{fig8}
 \end{figure} 
 
 Figure~\ref{fig8} shows that DiLCO-32 has very low execution times in comparison

-with  other DiLCO  versions, because  the activity  scheduling is  tackled  by a
+with  other DiLCO  versions, because  the activity  scheduling is  tackled by  a

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

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

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


@@ -798,7 +846,7 @@ network lifetime.
 
 \begin{figure}[h!]
 \centering
 
 \begin{figure}[h!]
 \centering

-\includegraphics[scale=0.45]{LT.pdf}  
+\includegraphics[scale=0.475]{LT.pdf}  

 \caption{Network lifetime}
 \label{figLT95}
 \end{figure} 
 \caption{Network lifetime}
 \label{figLT95}
 \end{figure} 


@@ -806,37 +854,38 @@ network lifetime.
 As  highlighted by  Figure~\ref{figLT95},  when the  coverage  level is  relaxed
 ($50\%$) the network lifetime also  improves. This observation reflects the fact
 that  the higher  the coverage  performance, the  more nodes  must be  active to
 As  highlighted by  Figure~\ref{figLT95},  when the  coverage  level is  relaxed
 ($50\%$) the network lifetime also  improves. This observation reflects the fact
 that  the higher  the coverage  performance, the  more nodes  must be  active to

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

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

-the larger level  of coverage ($95\%$) in the case of  our protocol, the subdivision
-in $16$~subregions seems to be the most appropriate.
+the  larger  level  of coverage  ($95\%$)  in  the  case  of our  protocol,  the
+subdivision in $16$~subregions seems to be the most appropriate.

 
 
 \section{\uppercase{Conclusion and future work}}
 \label{sec:Conclusion and Future Works} 
 
 
 
 \section{\uppercase{Conclusion and future work}}
 \label{sec:Conclusion and Future Works} 
 

-A crucial problem in WSN is  to schedule the sensing activities of the different
-nodes  in order to  ensure both  coverage of  the area  of interest  and longer
+A crucial problem in WSN is to  schedule the sensing activities of the different
+nodes  in order  to ensure  both coverage  of the  area of  interest and  longer

 network lifetime. The inherent limitations of sensor nodes, in energy provision,
 network lifetime. The inherent limitations of sensor nodes, in energy provision,

-communication and computing capacities,  require protocols that optimize the use
-of  the  available resources  to  fulfill the  sensing  task.   To address  this
-problem, this paper proposes a  two-step approach. Firstly, the field of sensing
+communication and computing capacities, require  protocols that optimize the use
+of  the available  resources  to  fulfill the  sensing  task.   To address  this
+problem, this paper proposes a two-step  approach. Firstly, the field of sensing

 is  divided into  smaller  subregions using  the  concept of  divide-and-conquer
 method. Secondly,  a distributed  protocol called Distributed  Lifetime Coverage
 is  divided into  smaller  subregions using  the  concept of  divide-and-conquer
 method. Secondly,  a distributed  protocol called Distributed  Lifetime Coverage

-Optimization is applied in each  subregion to optimize the coverage and lifetime
-performances.   In a subregion,  our protocol  consists in  electing a  leader node
+Optimization is applied in each subregion  to optimize the coverage and lifetime
+performances.  In a  subregion, our protocol consists in electing  a leader node

 which will then perform a sensor activity scheduling. The challenges include how
 which will then perform a sensor activity scheduling. The challenges include how

-to  select   the  most  efficient  leader   in  each  subregion   and  the  best
+to  select   the  most  efficient  leader   in  each  subregion  and   the  best

 representative set of active nodes to ensure a high level of coverage. To assess
 the performance of our approach, we  compared it with two other approaches using
 representative set of active nodes to ensure a high level of coverage. To assess
 the performance of our approach, we  compared it with two other approaches using

-many performance metrics  like coverage ratio or network  lifetime. We have also
-studied the  impact of the  number of subregions  chosen to subdivide the  area of
+many performance metrics  like coverage ratio or network lifetime.  We have also
+studied the impact of  the number of subregions chosen to  subdivide the area of

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

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

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