Processing of the paper completed (except section 2)

diff --git a/Example.aux b/Example.aux
index 41dd5f6bb940a41ecff40c3c711b334def264bc4..88d471ba2bebfb9fc33a8b2af1d1e7edda4eea6a 100644 (file)
--- a/Example.aux
+++ b/Example.aux
@@ -48,7 +48,6 @@
 \bibcite{idrees2014coverage}{Idrees et\nobreakspace  {}al., 2014}
 \bibcite{li2013survey}{Li and Vasilakos, 2013}
 \bibcite{ling2009energy}{Ling and Znati, 2009}
 \bibcite{idrees2014coverage}{Idrees et\nobreakspace  {}al., 2014}
 \bibcite{li2013survey}{Li and Vasilakos, 2013}
 \bibcite{ling2009energy}{Ling and Znati, 2009}

-\bibcite{Sudip03}{Misra et\nobreakspace  {}al., 2009}

 \bibcite{Nayak04}{Nayak and Stojmenovic, 2010}
 \bibcite{pedraza2006}{Pedraza et\nobreakspace  {}al., 2006}
 \bibcite{qu2013distributed}{Qu and Georgakopoulos, 2013}
 \bibcite{Nayak04}{Nayak and Stojmenovic, 2010}
 \bibcite{pedraza2006}{Pedraza et\nobreakspace  {}al., 2006}
 \bibcite{qu2013distributed}{Qu and Georgakopoulos, 2013}

diff --git a/Example.bib b/Example.bib
index 4a54d83133a492b8fd16165a670d3e0e9948f501..f5ce0f749ac25833c94eaa6c2291ca36f85355ce 100644 (file)
--- a/Example.bib
+++ b/Example.bib
@@ -22,10 +22,9 @@
 @inproceedings{vashistha2007energy,
   title={Energy efficient area monitoring using information coverage in wireless sensor networks},
   author={Vashistha, Sumit and Azad, Amar Prakash and Chockalingam, Ananthanarayanan},
 @inproceedings{vashistha2007energy,
   title={Energy efficient area monitoring using information coverage in wireless sensor networks},
   author={Vashistha, Sumit and Azad, Amar Prakash and Chockalingam, Ananthanarayanan},

-  booktitle={World of Wireless, Mobile and Multimedia Networks, 2007. WoWMoM 2007. IEEE International Symposium on a},
+  booktitle={World of Wireless, Mobile and Multimedia Networks, 2007. WoWMoM 2007. IEEE International Symposium},

   pages={1--10},
   pages={1--10},

-  year={2007},
-  organization={IEEE}
+  year={2007}

 }
 
 
 }
 
 

diff --git a/Example.tex b/Example.tex
index 8ed81a642e304cb0eef1c8bad61eb1ce8328095b..08ab194a3105ffded45a1cadf830bca3d73fece1 100644 (file)
--- a/Example.tex
+++ b/Example.tex
@@ -200,7 +200,7 @@ The main contributions of our DiLCO Protocol can be summarized as follows:
 
 \fi
 
 
 \fi
 

-\section{ The DiLCO Protocol Description}
+\section{\uppercase{Description of the DiLCO protocol}}

 \label{sec:The DiLCO Protocol Description}
 
 \noindent In this section, we  introduce the DiLCO protocol which is distributed
 \label{sec:The DiLCO Protocol Description}
 
 \noindent In this section, we  introduce the DiLCO protocol which is distributed


@@ -224,7 +224,7 @@ simple  energy model that  takes communication,  sensing and  computation energy
 consumptions into account to evaluate the performance of our protocol. 
 \fi
 
 consumptions into account to evaluate the performance of our protocol. 
 \fi
 

-\subsection{ Assumptions and models}
+\subsection{Assumptions and models}

 
 \noindent  We consider  a sensor  network composed  of static  nodes distributed
 independently and uniformly at random.  A high density deployment ensures a high
 
 \noindent  We consider  a sensor  network composed  of static  nodes distributed
 independently and uniformly at random.  A high density deployment ensures a high


@@ -324,7 +324,7 @@ 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.
 
 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 excution of the DiLCO protocol, two kinds of packets will be used:
+During the execution of the DiLCO protocol, two kinds of packets will be used:

 %\begin{enumerate}[(a)]
 \begin{itemize} 
 \item INFO  packet: sent  by each  sensor node to  all the  nodes inside  a same
 %\begin{enumerate}[(a)]
 \begin{itemize} 
 \item INFO  packet: sent  by each  sensor node to  all the  nodes inside  a same


@@ -365,7 +365,7 @@ Active-Sleep packet to know its state for the coming sensing phase.
 \subsubsection{Information Exchange Phase}
 
 Each sensor node $j$ sends its position, remaining energy $RE_j$, and
 \subsubsection{Information Exchange Phase}
 
 Each sensor node $j$ sends its position, remaining energy $RE_j$, and

-the number of neighbours  $NBR_j$ to all wireless sensor nodes in
+the number of neighbors  $NBR_j$ 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
 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


@@ -380,7 +380,7 @@ 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
 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 neighbours,  larger remaining  energy, and  then in  case of
+number  of neighbors,  larger remaining  energy, and  then in  case of

 equality, larger index. 
 
 \subsubsection{Decision phase}
 equality, larger index. 
 
 \subsubsection{Decision phase}


@@ -457,7 +457,7 @@ The sensor node enter in listening mode waiting to receive ActiveSleep packet fr
 \fi
 
 
 \fi
 
 

-\section{Coverage problem formulation}
+\section{\uppercase{Coverage problem formulation}}

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


@@ -700,29 +700,15 @@ Where: $A_r^t$ is the number of active sensors in the subregion $r$ during round
 
 \fi
 
 
 \fi
 

-\item {{\bf Network Lifetime}:} we define the network lifetime as the time until
-  the  coverage  ratio  drops  below  a  predefined  threshold.   We  denote  by
-  $Lifetime_{95}$ (respectively $Lifetime_{50}$) the amount of time during which
-  the  network can  satisfy an  area coverage  greater than  $95\%$ (respectively
-  $50\%$). We assume that the sensor  network can fulfill its task until all its
-  nodes have  been drained of their  energy or it  becomes disconnected. Network
-  connectivity  is crucial because  an active  sensor node  without connectivity
-  towards a base  station cannot transmit any information  regarding an observed
-  event in the area that it monitors.
- 
-\item {{\bf  Energy Consumption}:}  Energy Consumption (EC)  can be seen  as the
+\item {{\bf  Energy Consumption}:}  energy consumption (EC)  can be seen  as the

   total   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:
   total   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*}
-\scriptsize
-\mbox{EC} = \frac{\sum\limits_{m=1}^{M} \left( E^{\mbox{com}}_m+E^{\mbox{list}}_m+E^{\mbox{comp}}_m  + E^{a}_m+E^{s}_m \right)}{M},
-\end{equation*}
-
-%\begin{equation*}
-%\scriptsize
-%\mbox{EC} =  \frac{\mbox{$\sum\limits_{d=1}^D E^c_d$}}{\mbox{$D$}} + \frac{\mbox{$\sum\limits_{d=1}^D %E^l_d$}}{\mbox{$D$}} + \frac{\mbox{$\sum\limits_{d=1}^D E^a_d$}}{\mbox{$D$}} + %\frac{\mbox{$\sum\limits_{d=1}^D E^s_d$}}{\mbox{$D$}}.
-%\end{equation*}
+  \begin{equation*}
+    \scriptsize
+    \mbox{EC} = \frac{\sum\limits_{m=1}^{M} \left( E^{\mbox{com}}_m+E^{\mbox{list}}_m+E^{\mbox{comp}}_m  
+      + E^{a}_m+E^{s}_m \right)}{M},
+  \end{equation*}

 
 where $M$  corresponds to the number  of periods.  The total  energy consumed by
 the  sensors (EC)  comes  through  taking into  consideration  four main  energy
 
 where $M$  corresponds to the number  of periods.  The total  energy consumed by
 the  sensors (EC)  comes  through  taking into  consideration  four main  energy


@@ -735,6 +721,16 @@ refers to the energy needed by all the leader nodes to solve the integer program
 during a period.  Finally, $E^a_{m}$ and $E^s_{m}$ indicate  the energy consumed
 by the whole network in the sensing phase (active and sleeping nodes).
 
 during a period.  Finally, $E^a_{m}$ and $E^s_{m}$ indicate  the energy consumed
 by the whole network in the sensing phase (active and sleeping nodes).
 

+\item {{\bf Network Lifetime}:} we define the network lifetime as the time until
+  the  coverage  ratio  drops  below  a  predefined  threshold.   We  denote  by
+  $Lifetime_{95}$ (respectively $Lifetime_{50}$) the amount of time during which
+  the  network can  satisfy an  area coverage  greater than  $95\%$ (respectively
+  $50\%$). We assume that the sensor  network can fulfill its task until all its
+  nodes have  been drained of their  energy or it  becomes disconnected. Network
+  connectivity  is crucial because  an active  sensor node  without connectivity
+  towards a base  station cannot transmit any information  regarding an observed
+  event in the area that it monitors.
+

 \iffalse 
 \item {{\bf Execution Time}:} a  sensor  node has  limited  energy  resources  and computing  power,
 therefore it is important that the proposed algorithm has the shortest
 \iffalse 
 \item {{\bf Execution Time}:} a  sensor  node has  limited  energy  resources  and computing  power,
 therefore it is important that the proposed algorithm has the shortest


@@ -752,7 +748,7 @@ disconnected (some nodes are dead and are not able to send information to the ba
 
 
 %\subsection{Performance Analysis for different subregions}
 
 
 %\subsection{Performance Analysis for different subregions}

-\subsection{Performance Analysis}
+\subsection{Performance analysis}

 \label{sub1}
 
 In this subsection, we first focus  on the performance of our DiLCO protocol for
 \label{sub1}
 
 In this subsection, we first focus  on the performance of our DiLCO protocol for


@@ -769,7 +765,7 @@ second one, called GAF  ~\cite{xu2001geography}, consists in dividing the region
 into fixed  squares.  During the decision  phase, in each square,  one sensor is
 chosen to remain active during the sensing phase.
 
 into fixed  squares.  During the decision  phase, in each square,  one sensor is
 chosen to remain active during the sensing phase.
 

-\subsubsection{Coverage Ratio} 
+\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
 
 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


@@ -794,7 +790,7 @@ nodes, and thus allow to extend the network lifetime.
 \begin{figure}[t!]
 \centering
  \includegraphics[scale=0.45] {R/CR.pdf} 
 \begin{figure}[t!]
 \centering
  \includegraphics[scale=0.45] {R/CR.pdf} 

-\caption{The Coverage Ratio}
+\caption{Coverage ratio}

 \label{fig3}
 \end{figure} 
 
 \label{fig3}
 \end{figure} 
 


@@ -803,68 +799,93 @@ nodes, and thus allow to extend the network lifetime.
 %slightly more efficient than other protocols, because they subdivides
 %the area of interest into 8, 16 and 32~subregions if one of the subregions becomes disconnected, the coverage may be still ensured in the remaining subregions.%
 
 %slightly more efficient than other protocols, because they subdivides
 %the area of interest into 8, 16 and 32~subregions if one of the subregions becomes disconnected, the coverage may be still ensured in the remaining subregions.%
 

-\subsubsection{Energy Consumption}
-
-% MICHEL - TO BE CONTINUED
-
-Based on  previous results in  figure~\ref{fig3}, we keep DiLCO-16  and DiLCO-32
-and we  compare their performances in  terms of energy consumption  with the two
-other  approaches. We  measure the  energy consumed  by the  sensors  during the
-communication,  listening, computation,  active, and  sleep modes  for different
-network  densities.  Figure~\ref{fig95} illustrates  the energy  consumption for
-different network sizes.
-% for $Lifetime95$ and $Lifetime50$. 
-We  denote by  $DiLCO-/50$ (respectively  $DiLCO-/95$) as  the amount  of energy
-consumed  during which the  network can  satisfy an  area coverage  greater than
-$50\%$ (repectively  $95\%$) and  we refer  to the same  definition for  the two
-other approaches.
+\subsubsection{Energy consumption}
+
+Based on  the results shown in  Figure~\ref{fig3}, we focus on  the DiLCO-16 and
+DiLCO-32 versions of our protocol,  and we compare their energy consumption with
+the DESK and GAF approaches. For each sensor node we measure the energy consumed
+according to its successive status,  for different network densities.  We denote
+by $\mbox{\it  Protocol}/50$ (respectively $\mbox{\it  Protocol}/95$) the amount
+of energy consumed  while the area coverage is  greater than $50\%$ (repectively
+$95\%$),  where  {\it  Protocol}  is  one  of the  four  protocols  we  compare.
+Figure~\ref{fig95} presents  the energy consumptions observed  for network sizes
+going from 50  to 250~nodes. Let us  notice that the same network  sizes will be
+used for the different performance metrics.
+

 \begin{figure}[h!]
 \centering
 \includegraphics[scale=0.45]{R/EC.pdf} 
 \begin{figure}[h!]
 \centering
 \includegraphics[scale=0.45]{R/EC.pdf} 

-\caption{The Energy Consumption}
+\caption{Energy consumption}

 \label{fig95}
 \end{figure} 
 
 \label{fig95}
 \end{figure} 
 

-The  results show  that  DiLCO-16/50, DiLCO-32/50,  DiLCO-16/95 and  DiLCO-32/95
-protocols  are  the  most  competitive  from the  energy  consumption  point  of
-view. The  other approaches have a  high energy consumption due  to activating a
-larger number of redundant nodes.
+The  results  depict the  good  performance of  the  different  versions of  our
+protocol.   Indeed,  the protocols  DiLCO-16/50,  DiLCO-32/50, DiLCO-16/95,  and
+DiLCO-32/95  consume less  energy than  their DESK  and GAF  counterparts  for a
+similar level of area coverage.   This observation reflects the larger number of
+nodes set active by DESK and GAF.

 
 
 %In fact,  a distributed  method on the subregions greatly reduces the number of communications and the time of listening so thanks to the partitioning of the initial network into several independent subnetworks. 
 %As shown in Figures~\ref{fig95} and ~\ref{fig50} , DiLCO-2 consumes more energy than the other versions of DiLCO, especially for large sizes of network. This is easy to understand since the bigger the number of sensors involved in the integer program, the larger the time computation to solve the optimization problem as well as the higher energy consumed during the communication.  
 
 
 
 %In fact,  a distributed  method on the subregions greatly reduces the number of communications and the time of listening so thanks to the partitioning of the initial network into several independent subnetworks. 
 %As shown in Figures~\ref{fig95} and ~\ref{fig50} , DiLCO-2 consumes more energy than the other versions of DiLCO, especially for large sizes of network. This is easy to understand since the bigger the number of sensors involved in the integer program, the larger the time computation to solve the optimization problem as well as the higher energy consumed during the communication.  
 

-\subsubsection{Execution Time}
-We observe the impact of the network size and of the number of subregions on the computation time. We report the average execution times in seconds needed to solve the optimization problem for the different approaches and various numbers of sensors. 
-The original execution time is computed on a laptop DELL with intel Core i3 2370 M (2.4 GHz) processor (2 cores) and the MIPS (Million Instructions Per Second) rate equal to 35330. To be consistent with the use of a sensor node with Atmels AVR ATmega103L microcontroller (6 MHz) and a MIPS rate equal to 6 to run the optimization resolution, this time is multiplied by 2944.2 $\left( \frac{35330}{2} \times \frac{1}{6}\right)$ and reported on Figure~\ref{fig8}.
+\subsubsection{Execution time}
+
+Another interesting point to investigate  is the evolution of the execution time
+with the size of the WSN and  the number of subregions. Therefore, we report for
+every version of  our protocol the average execution times  in seconds needed to
+solve the optimization problem for  different WSN sizes. The execution times are
+obtained on a laptop DELL  which has an Intel Core~i3~2370~M~(2.4~GHz) dual core
+processor and a MIPS rating equal to 35330. The corresponding execution times on
+a MEDUSA II sensor node are then  extrapolated according to the MIPS rate of the
+Atmels  AVR  ATmega103L  microcontroller  (6~MHz),  which  is  equal  to  6,  by
+multiplying    the    laptop     times    by    $\left(\frac{35330}{2}    \times
+\frac{1}{6}\right)$.  The  expected times  on  a  sensor  node are  reported  on
+Figure~\ref{fig8}.

 
 \begin{figure}[h!]
 \centering
 \includegraphics[scale=0.45]{R/T.pdf}  
 
 \begin{figure}[h!]
 \centering
 \includegraphics[scale=0.45]{R/T.pdf}  

-\caption{Execution Time (in seconds)}
+\caption{Execution time in seconds}

 \label{fig8}
 \end{figure} 
 
 \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 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. Excessive subdivision of the area of interest prevents to ensure good coverage especially on the borders of the subregions.
+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
+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 excessive  subdivision of the  area of interest
+prevents   to  ensure   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.

 
 %The DiLCO-32 has more suitable times in the same time it turn on redundent nodes more.  We think that in distributed fashion the solving of the  optimization problem in a subregion can be tackled by sensor nodes. Overall, to be able to deal  with very large networks,  a distributed method is clearly required.
 
 
 %The DiLCO-32 has more suitable times in the same time it turn on redundent nodes more.  We think that in distributed fashion the solving of the  optimization problem in a subregion can be tackled by sensor nodes. Overall, to be able to deal  with very large networks,  a distributed method is clearly required.
 

+\subsubsection{Network lifetime}

 
 

-\subsubsection{The Network Lifetime}
-In figure~\ref{figLT95}, network lifetime is illustrated for different network sizes. The term $/50$ (respectively  $/95$) next to the name of the method refers to the amount of time during which the network can satisfy an area coverage greater than $50\%$ ($Lifetime50$)(repectively $95\%$ ($Lifetime95$)) 
+In the next figure, the network lifetime is illustrated. Obviously, the lifetime
+increases with  the network  size, whatever the  considered protocol,  since the
+correlated node  density also  increases.  A high  network density means  a high
+node redundancy  which allows  to turn-off  many nodes and  thus to  prolong the
+network lifetime.

 
 \begin{figure}[h!]
 \centering
 \includegraphics[scale=0.45]{R/LT.pdf}  
 
 \begin{figure}[h!]
 \centering
 \includegraphics[scale=0.45]{R/LT.pdf}  

-\caption{The Network Lifetime}
+\caption{Network lifetime}

 \label{figLT95}
 \end{figure} 
 
 \label{figLT95}
 \end{figure} 
 

-
-As highlighted by figure~\ref{figLT95}, the network lifetime obviously
-increases when the size of the network increases. For the same level of coverage, DiLCO outperforms DESK and GAF for the lifetime of the network. If we focus on level of coverage greater than $95\%$, The subdivision in $16$ subregions seems to be the most appropriate. 
-
+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
+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
+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
 % that leads to the larger lifetime improvement in comparison with other approaches. By choosing the best 
 
 % with  our DiLCO-16/50, DiLCO-32/50, DiLCO-16/95 and DiLCO-32/95 protocols
 % that leads to the larger lifetime improvement in comparison with other approaches. By choosing the best 


@@ -872,29 +893,33 @@ increases when the size of the network increases. For the same level of coverage
 % letting the other ones sleep in order to be used later in next rounds. Comparison shows that our DiLCO-16/50, DiLCO-32/50, DiLCO-16/95 and DiLCO-32/95 protocols, which are used distributed optimization over the subregions, are the best one because it is robust to network disconnection during the network lifetime as well as it consume less energy in comparison with other approaches. It also means that distributing the protocol 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.
 
 % letting the other ones sleep in order to be used later in next rounds. Comparison shows that our DiLCO-16/50, DiLCO-32/50, DiLCO-16/95 and DiLCO-32/95 protocols, which are used distributed optimization over the subregions, are the best one because it is robust to network disconnection during the network lifetime as well as it consume less energy in comparison with other approaches. It also means that distributing the protocol 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{\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 longest
+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
+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
+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
+interest,  considering  different  network  sizes.  The  experiments  show  that
+increasing the  number of subregions allows  to improves the  lifetime. The more
+there  are   subregions,  the  more   the  network  is  robust   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{Conclusion and Future Works}}
-\label{sec:Conclusion and Future Works}
-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 divide-and-conquer method, and then a DiLCO protocol for optimizing the 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 set of active nodes to ensure a high level of coverage.
-We have compared this method with two other approaches using many metrics as coverage ratio, execution time, lifetime.
-Some experiments have been performed to study the choice of the number of
-subregions  which subdivide  the  sensing field,  considering different  network
-sizes. They show that as the number of subregions increases, so does the network
-lifetime. Moreover,  it makes  the DiLCO protocol  more robust  against random
-network  disconnection due  to node  failures.  However,  too  much subdivisions
-reduces the advantage  of the optimization. In fact, there  is a balance between
-the  benefit  from the  optimization  and the  execution  time  needed to  solve
-it. Therefore, the subdivision in $16$ subregions seems to be the most appropriate. 

 \iffalse
 \noindent 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
 \iffalse
 \noindent 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


@@ -925,18 +950,17 @@ optimization  methods. \iffalse The round  will still consist of 4 phases, but t
 The computation of all cover sets in one time is far more
 difficult, but will reduce the communication overhead. \fi
 \fi
 The computation of all cover sets in one time is far more
 difficult, but will reduce the communication overhead. \fi
 \fi

-\section*{\uppercase{Acknowledgements}}
-\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.
-
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+\section*{\uppercase{Acknowledgements}}

 
 

+\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.

 
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