X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/Sensornets15.git/blobdiff_plain/91bc2e81f592252c7d007665a2d6a29b30c87861..8b80452d5111e437e7929c9beb82f9d4a7983557:/Example.tex?ds=sidebyside

diff --git a/Example.tex b/Example.tex
index dbc4580..02ee54e 100644
--- a/Example.tex
+++ b/Example.tex
@@ -42,22 +42,22 @@ Optimization, Scheduling.}
   as possible a network failure due to battery-depleted nodes.  In this paper we
   propose a protocol, called Distributed Lifetime Coverage Optimization protocol
   (DiLCO), which maintains the coverage  and improves the lifetime of a wireless
-  sensor  network. As  a  first step  we  partition the  area  of interest  into
-  subregions using a classical  divide-and-conquer method. Our DiLCO protocol is
-  then distributed  on the sensor nodes in  each subregion in a  second step. To
-  fulfill  our   objective,  the   proposed  protocol  combines   two  effective
-  techniques:   a  leader   election   in  each   subregion,   followed  by   an
-  optimization-based node activity scheduling  performed by each elected leader.
-  This two-step process takes place periodically, in order to choose a small set
-  of nodes remaining  active for sensing during a time slot.   Each set is built
-  to ensure  coverage at  a low  energy cost, allowing  to optimize  the network
-  lifetime. More  precisely, a period  consists of four  phases: (i)~Information
-  Exchange,  (ii)~Leader   Election,  (iii)~Decision,  and   (iv)~Sensing.   The
-  decision process, which results in  an activity scheduling vector,  is carried
-  out by a leader node through  the solving of an integer program. In comparison
-  with  some other  protocols, the  simulations  done using  the discrete  event
-  simulator OMNeT++ show that our approach  is able to increase the WSN lifetime
-  and provides improved coverage performance. }
+  sensor network. First, we partition the area of interest into subregions using
+  a classical divide-and-conquer method.  Our DiLCO protocol is then distributed
+  on  the sensor  nodes  in each  subregion in  a  second step.  To fulfill  our
+  objective, the  proposed protocol combines two effective  techniques: a leader
+  election in  each subregion, followed  by an optimization-based  node activity
+  scheduling  performed by  each elected  leader.  This  two-step  process takes
+  place periodically, in  order to choose a small set  of nodes remaining active
+  for sensing during a time slot.  Each set is built to ensure coverage at a low
+  energy  cost, allowing  to optimize  the network  lifetime. More  precisely, a
+  period  consists   of  four  phases:   (i)~Information  Exchange,  (ii)~Leader
+  Election,  (iii)~Decision,  and  (iv)~Sensing.   The decision  process,  which
+  results in  an activity  scheduling vector,  is carried out  by a  leader node
+  through  the solving  of an  integer program.  In comparison  with  some other
+  protocols,  the simulations done  using the  discrete event  simulator OMNeT++
+  show  that our  approach is  able to  increase the  WSN lifetime  and provides
+  improved coverage performance. }
 
 \onecolumn \maketitle \normalsize \vfill
 
@@ -73,12 +73,12 @@ during the  last few  years, is  the design of  energy efficient  approaches for
 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
 interest in the most efficient way~\cite{Nayak04}.  On the other hand we want to
-use as less 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.
+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.
 
 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
@@ -90,52 +90,53 @@ 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 DiLCO protocol considers periods, where a period
-starts with a discovery phase to  exchange information between sensors of a 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 the sensors
-for the  sensing phase of the current  period is obtained by  solving an integer
-program. The  resulting activation  vector is broadcasted  by a leader  to every
-node of its subregion.
+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
+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 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
 formulation    which    is    used     to    schedule    the    activation    of
 sensors. Section~\ref{sec:Simulation Results  and Analysis} shows the simulation
-results. The paper  ends with conclusions and some  suggestions for further work
+results. The paper  ends with a conclusion and some  suggestions for further work
 in Section~\ref{sec:Conclusion and Future Works}.
 
 \section{\uppercase{Literature Review}}
 \label{sec:Literature Review}
 
-\noindent In  this section, we  summarize some related works  regarding coverage
+\noindent In  this section, we  summarize some related works  regarding the coverage
 problem  and distinguish  our DiLCO  protocol from  the works  presented  in the
 literature.
 
 The most discussed coverage  problems in literature
-can  be classified into  three types  \cite{li2013survey}: area  coverage (where
-every point inside an area is  to be monitored), target coverage (where the main
-objective is to  cover only a finite number of  discrete points called targets),
-and  barrier coverage (to  prevent intruders  from entering  into the  region of
-interest). 
+can  be classified into  three types  \cite{li2013survey}: area  coverage \cite{Misra} where
+every point inside an area is  to be monitored, target coverage  \cite{yang2014novel} where the main
+objective is to  cover only a finite number of  discrete points called targets,
+and  barrier coverage \cite{Kumar:2005}\cite{kim2013maximum} to  prevent intruders  from entering  into the  region of interest. In \cite{Deng2012} authors transform the area coverage problem to the target coverage problem taking into account the intersection points among disks of sensors nodes or between disk of sensor nodes and boundaries. 
 {\it In DiLCO  protocol, the area coverage, i.e. the coverage  of every point in
   the sensing  region, is transformed  to the coverage  of a fraction  of points
   called primary points. }
 
+
 The major  approach to extend network  lifetime while preserving  coverage is to
 divide/organize the  sensors into a suitable  number of set  covers (disjoint or
-non-disjoint)  where each  set completely  covers a  region of  interest  and to
+non-disjoint),  where each  set completely  covers a  region of  interest,  and to
 activate these set  covers successively. The network activity  can be planned in
 advance and scheduled  for the entire network lifetime  or organized in periods,
-and the set of  active sensor nodes is decided at the  beginning of each period.
+and the set of  active sensor nodes is decided at the  beginning of each period \cite{ling2009energy}.
 Active node selection is determined based on the problem requirements (e.g. area
-monitoring,  connectivity,  power   efficiency).  Different  methods  have  been
-proposed in literature.
-{\it DiLCO protocol  works in periods, where each  period contains a preliminary
+monitoring,  connectivity,  power   efficiency). For instance, Jaggi et al. \cite{jaggi2006}
+address the problem of maximizing network lifetime by dividing sensors into the maximum number of disjoint subsets such that each subset can ensure both coverage and connectivity. A greedy algorithm is applied once to solve this problem and the computed sets are activated in succession to achieve the desired network lifetime. 
+Vu \cite{chin2007}, Padmatvathy et al. \cite{pc10}, propose algorithms working in a periodic fashion where a cover set is computed at the beginning of each period.
+{\it Motivated by these works, DiLCO protocol  works in periods, where each  period contains a preliminary
   phase  for information  exchange and  decisions, followed  by a  sensing phase
   where one cover set is in charge of the sensing task.}
 
-Various   approaches,   including   centralized,  distributed,   and   localized
+Various   approaches,   including   centralized,  or distributed
 algorithms, have been proposed to extend the network lifetime.
 %For instance, in order to hide the occurrence of faults, or the sudden unavailability of
 %sensor nodes, some distributed algorithms have been developed in~\cite{Gallais06,Tian02,Ye03,Zhang05,HeinzelmanCB02}. 
@@ -145,28 +146,35 @@ cooperatively by communicating with their neighbors which of them will remain in
 sleep    mode   for    a   certain    period   of    time.     The   centralized
 algorithms~\cite{cardei2005improving,zorbas2010solving,pujari2011high}     always
 provide nearly or close to optimal  solution since the algorithm has global view
-of the whole  network, but such a method has the  disadvantage of requiring high
+of the whole  network. But such a method has the  disadvantage of requiring high
 communication costs,  since the  node (located at  the base station)  making the
-decision needs information from all the sensor nodes in the area.
+decision needs information from all the sensor nodes in the area and the amount of information can be huge.
+{\it  In order to be suitable for large-scale network,  in the DiLCO  protocol,  the area  coverage  is divided  into several  smaller
+  subregions, and in  each  one, a  node called the leader is  in charge for
+  selecting the active sensors for the current period.}
 
-A large  variety of coverage scheduling  algorithms have been  proposed. Many of
+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
 by including in priority the sensor  nodes which cover critical targets, that is
-to  say targets  that  are covered  by  the smallest  number  of sensors.  Other
-approaches  are based  on  mathematical programming  formulations and  dedicated
+to  say targets  that  are covered  by  the smallest  number  of sensors \cite{berman04,zorbas2010solving}.  Other
+approaches  are based  on  mathematical programming  formulations~\cite{cardei2005energy,5714480,pujari2011high,Yang2014} and  dedicated
 techniques (solving with a branch-and-bound algorithms available in optimization
 solver).  The problem is formulated  as an optimization problem (maximization of
 the  lifetime  or  number  of  cover  sets) under  target  coverage  and  energy
 constraints.   Column  generation techniques,  well-known  and widely  practiced
-techniques for solving  linear programs with too many  variables, have been also
-used~\cite{castano2013column,rossi2012exact,deschinkel2012column}.
+techniques for solving  linear programs with too many  variables, have also been 
+used~\cite{castano2013column,rossi2012exact,deschinkel2012column}. {\it  In DiLCO  protocol,  each leader,  in  each subregion,  solves an  integer
+  program with a double objective  consisting in minimizing the overcoverage and
+  limiting  the  undercoverage.  This  program  is inspired  from  the  work  of
+  \cite{pedraza2006}  where the  objective is  to maximize  the number  of cover
+  sets.}
 
 % ***** Part which must be rewritten - Start
 
 % Start of Ali's papers catalog => there's no link between them or with our work
 % (use of subregions; optimization based method; etc.)
-
+\iffalse
 Diongue  and  Thiare~\cite{diongue2013alarm}  proposed  an  energy  aware  sleep
 scheduling  algorithm  for lifetime  maximization  in  wireless sensor  networks
 (ALARM).  The proposed approach permits to schedule redundant nodes according to
@@ -199,9 +207,7 @@ the sensor nodes in the network.
 
 % What is the link between the previous work and this paragraph about DiLCO ?
 
-{\it  In DiLCO  protocol,  the area  coverage  is divided  into several  smaller
-  subregions, and in  each of which, a  node called the leader is  on charge for
-  selecting the active sensors for the current period.}
+
 
 Yang et al.~\cite{yang2014energy} investigated  full area coverage problem under
 the probabilistic  sensing model in the  sensor networks. They  have studied the
@@ -214,13 +220,9 @@ extend the network lifetime.
 The work proposed by  \cite{qu2013distributed} considers the coverage problem in
 WSNs where  each sensor has variable  sensing radius. The final  objective is to
 maximize the network coverage lifetime in WSNs.
-
+\fi
 % Same remark, no link with the two previous citations...
-{\it  In DiLCO  protocol,  each leader,  in  each subregion,  solves an  integer
-  program with a double objective  consisting in minimizing the overcoverage and
-  limiting  the  undercoverage.  This  program  is inspired  from  the  work  of
-  \cite{pedraza2006}  where the  objective is  to maximize  the number  of cover
-  sets.}
+
  
 % ***** Part which must be rewritten - End
 
@@ -344,7 +346,7 @@ consumptions into account to evaluate the performance of our protocol.
 
 \noindent  We consider  a sensor  network composed  of static  nodes distributed
 independently and uniformly at random.  A high density deployment ensures a high
-coverage ratio of the interested area at the starting. The nodes are supposed to
+coverage ratio of the interested area at the start. The nodes are supposed to
 have homogeneous characteristics from a  communication and a processing point of
 view, whereas they  have heterogeneous energy provisions.  Each  node has access
 to its location thanks,  either to a hardware component (like a  GPS unit), or a
@@ -410,7 +412,7 @@ $X_{13}=( p_x + R_s * (0), p_y + R_s * (\frac{-\sqrt{2}}{2})) $.
 
 \fi
 
-\subsection{The main idea}
+\subsection{Main idea}
 \label{main_idea}
 
 \noindent We start  by applying a divide-and-conquer algorithm  to partition the
@@ -426,27 +428,27 @@ executed   simultaneously  in   each   subregion.
 
 As  shown  in Figure~\ref{fig2},  the  proposed  DiLCO  protocol is  a  periodic
 protocol where  each period is  decomposed into 4~phases:  Information Exchange,
-Leader Election ,  Decision, and Sensing. For each period  there will be exactly
+Leader Election,  Decision, and Sensing. For  each period there  will be exactly
 one  cover  set  in charge  of  the  sensing  task.   A periodic  scheduling  is
 interesting  because it  enhances the  robustness  of the  network against  node
 failures. First,  a node  that has not  enough energy  to complete a  period, or
 which fails before  the decision is taken, will be  excluded from the scheduling
 process. Second,  if a node  fails later, whereas  it was supposed to  sense the
-region  of interest,  it will  only  affect the  quality of  coverage until  the
-definition of a new cover set  in the next period.  Constraints, like the energy
+region of  interest, it will only affect  the quality of the  coverage until the
+definition of  a new  cover set  in the next  period.  Constraints,  like energy
 consumption, can be easily taken into consideration since the sensors can update
 and exchange their  information during the first phase.  Let  us notice that the
 phases  before  the sensing  one  (Information  Exchange,  Leader Election,  and
 Decision) are  energy consuming for all the  nodes, even nodes that  will not be
 retained by the leader to keep watch over the corresponding area.
 
-During the execution of the DiLCO protocol, two kinds of packets will be used:
+During the execution of the DiLCO protocol, two kinds of packet will be used:
 %\begin{enumerate}[(a)]
 \begin{itemize} 
 \item INFO  packet: sent  by each  sensor node to  all the  nodes inside  a same
   subregion for information exchange.
 \item ActiveSleep packet:  sent by the leader to all the  nodes in its subregion
-  to inform them to be stay Active or to go Sleep during the sensing phase.
+  to inform them to stay Active or to go Sleep during the sensing phase.
 \end{itemize}
 %\end{enumerate}
 and each sensor node will have five possible status in the network:
@@ -565,7 +567,7 @@ sensor in the subregion and then describe it in more detail.  \fi
 \end{algorithm}
 
 \iffalse
-The DiLCO protocol work in rounds and executed at each sensor node in the network , each sensor node can still sense data while being in
+The DiLCO protocol work in rounds and executed at each sensor node in the network, each sensor node can still sense data while being in
 LISTENING mode. Thus, by entering the LISTENING mode at the beginning of each round,
 sensor nodes still executing sensing task while participating in the leader election and decision phases. More specifically, The DiLCO protocol algorithm works as follow: 
 Initially, the sensor node check it's remaining energy in order to participate in the current round. Each sensor node determines it's position and it's subregion based Embedded GPS  or Location Discovery Algorithm. After that, All the sensors collect position coordinates, current remaining energy, sensor node id, and the number of its one-hop live neighbors during the information exchange. It stores this information into a list L.
@@ -581,7 +583,7 @@ objective is  to find a  maximum number of  disjoint cover sets.   To accomplish
 this goal,  the authors proposed  an integer program which  forces undercoverage
 and overcoverage of targets to become minimal at the same time.  They use binary
 variables $x_{jl}$ to  indicate if sensor $j$ belongs to cover  set $l$.  In our
-model, we  consider binary  variable $X_{j}$ which  determine the  activation of
+model, we consider that the binary variable $X_{j}$ determines the activation of
 sensor $j$  in the sensing  phase. We also  consider primary points  as targets.
 The set of primary points is denoted by $P$ and the set of sensors by $J$.
 
@@ -638,7 +640,7 @@ U_{p} = \left \{
 %\label{c1} 
 %\sum_{t \in T} X_{j,t} \leq \frac{RE_j}{e_t} &\forall j \in J \\
 %\label{c2}
-\Theta_{p}\in \mathbb{N} , &\forall p \in P\\
+\Theta_{p}\in \mathbb{N}, &\forall p \in P\\
 U_{p} \in \{0,1\}, &\forall p \in P \\
 X_{j} \in \{0,1\}, &\forall j \in J
 \end{array}
@@ -724,7 +726,7 @@ node typically  consists of  four units: a  MicroController Unit, an  Atmels AVR
 ATmega103L in  case of Medusa II,  to perform the  computations; a communication
 (radio) unit able to send and  receive messages; a sensing unit to collect data;
 a power supply  which provides the energy consumed by  node. Except the battery,
-all the other unit  can be be switched off to save  energy according to the node
+all the other unit  can be switched off to save  energy according to the node
 status.   Table~\ref{table4} summarizes  the energy  consumed (in  milliWatt per
 second) by a node for each of its possible status.
 
@@ -770,15 +772,15 @@ receive such  packets, we  use the equation  giving the  energy spent to  send a
 1-bit-content   message  defined   in~\cite{raghunathan2002energy}   (we  assume
 symmetric  communication costs), and  we set  their respective  size to  112 and
 24~bits. The energy required to send  or receive a 1-bit-content message is thus
-is equal to 0.2575 mW.
+ equal to 0.2575 mW.
 
 Each node has an initial energy level, in Joules, which is randomly drawn in the
-interval  $[500-700]$.  If  it's  energy  provision reaches  a  value below  the
+interval  $[500-700]$.  If  its  energy  provision reaches  a  value below  the
 threshold  $E_{th}=36$~Joules, the  minimum energy  needed  for a  node to  stay
-active during one period, it will no more participate in the coverage task. This
+active during one period, it will no longer take part in the coverage task. This
 value  corresponds  to the  energy  needed by  the  sensing  phase, obtained  by
 multiplying the energy consumed in active  state (9.72 mW) by the time in seconds
-for one period (3600 seconds), and  adding the energy for the pre-sensing phases.
+for one period (3,600 seconds), and  adding the energy for the pre-sensing phases.
 According to  the interval of initial energy,  a sensor may be  active during at
 most 20 rounds.
 
@@ -807,7 +809,7 @@ the efficiency of our approach:
 \mbox{CR}(\%) = \frac{\mbox{$n$}}{\mbox{$N$}} \times 100.
 \end{equation*}
 where  $n$ is  the number  of covered  grid points  by active  sensors  of every
-subregions during  the current  sensing phase  and $N$ is  total number  of grid
+subregions during  the current  sensing phase  and $N$ is the total number  of grid
 points in  the sensing field. In  our simulations, we have  a layout of  $N = 51
 \times 26 = 1326$ grid points.
 %The accuracy of this method depends on the distance between grids. In our
@@ -829,7 +831,7 @@ Where: $A_r^t$ is the number of active sensors in the subregion $r$ during round
 \fi
 
 \item {{\bf  Energy Consumption}:}  energy consumption (EC)  can be seen  as the
-  total   energy   consumed   by   the   sensors   during   $Lifetime_{95}$   or
+  total amount of  energy   consumed   by   the   sensors   during   $Lifetime_{95}$   or
   $Lifetime_{50}$, divided  by the number of periods.  Formally, the computation
   of EC can be expressed as follows:
   \begin{equation*}
@@ -838,9 +840,9 @@ Where: $A_r^t$ is the number of active sensors in the subregion $r$ during round
       + E^{a}_m+E^{s}_m \right)}{M},
   \end{equation*}
 
-where $M$  corresponds to the number  of periods.  The total  energy consumed by
+where $M$  corresponds to the number  of periods.  The total amount of energy consumed by
 the  sensors (EC)  comes  through  taking into  consideration  four main  energy
-factors. The  first one , denoted $E^{\scriptsize  \mbox{com}}_m$, represent the
+factors. The  first one, denoted $E^{\scriptsize  \mbox{com}}_m$, represents the
 energy consumption  spent by  all the nodes  for wireless  communications during
 period $m$.   $E^{\scriptsize \mbox{list}}_m$,  the next factor,  corresponds to
 the  energy consumed by  the sensors  in LISTENING  status before  receiving the
@@ -875,7 +877,7 @@ In this subsection, we first focus  on the performance of our DiLCO protocol for
 different numbers  of subregions.  We consider partitions  of the WSN  area into
 $2$, $4$, $8$, $16$, and $32$ subregions. Thus the DiLCO protocol is declined in
 five versions:  DiLCO-2, DiLCO-4,  DiLCO-8, DiLCO-16, and  DiLCO-32. Simulations
-without  partitioning  the  area  of  interest,  case  which  corresponds  to  a
+without  partitioning  the  area  of  interest,  cases  which  correspond  to  a
 centralized  approach, are  not presented  because they  require  high execution
 times to solve the integer program and therefore consume too much energy.
 
@@ -888,7 +890,7 @@ chosen to remain active during the sensing phase.
 \subsubsection{Coverage ratio} 
 
 Figure~\ref{fig3} shows  the average coverage  ratio for 150 deployed  nodes. It
-can  be seen  that both  DESK and  GAF provide  a little  better  coverage ratio
+can  be seen  that both  DESK and  GAF provide  a   coverage ratio which is slightly better
 compared to DiLCO  in the first thirty periods. This can  be easily explained by
 the number of  active nodes: the optimization process  of our protocol activates
 less nodes  than DESK  or GAF, resulting  in a  slight decrease of  the coverage
@@ -904,7 +906,7 @@ efficient than DESK  and GAF, since they can provide the  same level of coverage
 (except in the first periods where  DESK and GAF slightly outperform them) for a
 greater number  of periods. In fact, when  our protocol is applied  with a large
 number of subregions (from 8 to 32~regions), it activates a restricted number of
-nodes, and thus allow to extend the network lifetime.
+nodes, and thus enables the extension of the network lifetime.
 
 \parskip 0pt    
 \begin{figure}[t!]
@@ -977,8 +979,8 @@ 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 excessive  subdivision of the  area of interest
-prevents   to  ensure   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.
 
@@ -1002,9 +1004,9 @@ 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
-ensure the  wider monitoring.  For a  same 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
-the larger level  of coverage ($95\%$) in case of  our protocol, the subdivision
+the larger level  of coverage ($95\%$) in the case of  our protocol, the subdivision
 in $16$~subregions seems to be the most appropriate.
 
 % with  our DiLCO-16/50, DiLCO-32/50, DiLCO-16/95 and DiLCO-32/95 protocols
@@ -1017,7 +1019,7 @@ in $16$~subregions seems to be the most appropriate.
 \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 longest
+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,
 communication and computing capacities,  require protocols that optimize the use
 of  the  available resources  to  fulfill the  sensing  task.   To address  this
@@ -1025,16 +1027,15 @@ 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
 Optimization is applied in each  subregion to optimize the coverage and lifetime
-performances.   In a subregion,  our protocol  consists to  elect a  leader node
+performances.   In a subregion,  our protocol  consists in  electing a  leader node
 which will then perform a sensor activity scheduling. The challenges include how
 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
 many performance metrics  like coverage ratio or network  lifetime. We have also
-study the  impact of the  number of subregions  chosen to subdivide the  area of
+studied the  impact of the  number of subregions  chosen to subdivide the  area of
 interest,  considering  different  network  sizes.  The  experiments  show  that
-increasing the  number of subregions improves  the lifetime. The  more there are
-subregions,  the  more  the  network  is  robust  against  random  disconnection
+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
@@ -1073,9 +1074,10 @@ difficult, but will reduce the communication overhead. \fi
 
 \section*{\uppercase{Acknowledgements}}
 
-\noindent  As  a Ph.D.  student,  Ali Kadhum  IDREES  would  like to  gratefully
+\noindent  As a  Ph.D.   student, Ali  Kadhum  IDREES would  like to  gratefully
 acknowledge  the University  of Babylon  - IRAQ  for the  financial  support and
-Campus France for the received support.
+Campus France for  the received support. This paper is  also partially funded by
+the Labex ACTION program (contract ANR-11-LABX-01-01).
 
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