New modifications

diff --git a/Example.tex b/Example.tex
index 3b522661430b3a17e87f6845d1e45241ea42fa74..06be2737b984dd37e7e399b71be63edb87edfb7f 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\\


@@ -78,20 +79,30 @@ 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.}
+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
 
 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


@@ -116,9 +127,10 @@ 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.   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}
 % MODIF - END
 
 The remainder  of the  paper continues with  Section~\ref{sec:Literature Review}


@@ -290,26 +302,38 @@ 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 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, 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 Active-Sleep 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
-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.
 
 %which provides a set of  sensors planned to be
 %active in the next sensing phase.
 

-
-

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

diff --git a/reponse.tex b/reponse.tex
index 014db29ce4bdf5d40dc06ccede57eb73389e7a15..8a70d92772b408bd89761fe000d641f9b811544d 100644 (file)
--- a/reponse.tex
+++ b/reponse.tex
@@ -69,191 +69,98 @@ As below, we  would like to clarify  some of the points raised  by the reviewers
 and we hope the reviewers and the  editors will be satisfied by our responses to
 the comments and the revision for the original manuscript.
 
 and we hope the reviewers and the  editors will be satisfied by our responses to
 the comments and the revision for the original manuscript.
 

-

 \section*{Response to Reviewer $\#$1 Comments}
 
 \section*{Response to Reviewer $\#$1 Comments}
 

-The paper present a new system  to optimize sensord detections. The work present
-the algorithm in a cleare and well  descrived way. The main problem is connected
-with the luck of  examples and also on the practical  applications. I suggest in
-future to make a more formal description of the process.\\
-
-
-\textcolor{blue}{\textbf{\textsc{Answer:} Right.   We have included  a paragraph
-    on  the  examples  and  practical  applications of  WSNs  in  section~1.  }}
-\textcolor{red}{Je pense que  la question porte sur un  exemple d'application de
-  notre protocole?}
+The paper present a new system to optimize sensord detections. The work present the algorithm in a cleare and well descrived way. The main problem is connected with the luck of examples and also on the practical applications. I suggest in future to make a more formal description of the process.\\
+\textcolor{blue}{\textbf{\textsc{Answer:} Right. We have included  a paragraph on examples and  practical applications of  WSNs in section~1.}}
+\textcolor{red}{Je pense que la question porte sur un exemple d'application de notre protocole?}

 \textcolor{magenta}{Je pense que oui.}
 
 \textcolor{magenta}{Je pense que oui.}
 

-

 \section*{Response to Reviewer $\#$3 Comments}
 
 \section*{Response to Reviewer $\#$3 Comments}
 

-This work proposed a distributed lifetime coverage optimization (DiLCO) protocol
-to apply to predefined subregions, which are generated from the area of interest
-using  a classical  divide-and-conquer  method,  to improve  the  lifetime of  a
-wireless  sensor network.  Their proposed  protocol is  devised with  a two-step
-process, including a leader election technique  in each subregion and a sensor's
-activity scheduling  by each elected  leader. In general, it  is a good  idea to
-pre-divide  the network  domain  into  several sub-areas,  and  assign a  single
-cluster head in each sub-area for achieving more balanced energy dissipation for
-the  wireless sensor  network.  As  we known,  Heinzelman  et  al. (2000)  first
-proposed  a  clustering  protocol  called LEACH  for  periodical  data-gathering
-applications. Also many  variants of LEACH protocol or a  variety of distributed
-protocols had  proposed enhanced energy efficient  adaptive clustering protocols
-by  pre-dividing the  network domain  into  several sub-areas,  and assigning  a
-single  cluster  head   in  each  sub-area  to  achieve   more  balanced  energy
-dissipation.  Hence,  I  suggest  that  the  authors  could  clearly  state  the
-differences  and  benefits between  their  leader  selection technique  and  the
-methods   of   cluster   head   election   in   LEACH   or   other   distributed
-protocols. Moreover,  they used the two  protocols, DESK and GAF,  for assessing
-the performance of  their protocols is not convincible. The  authors may include
-more well-known or recently developed protocols for comparison.
-
-
-\textcolor{blue}{\textbf{\textsc{Answer :}
+This work proposed a distributed lifetime coverage optimization (DiLCO) protocol to apply to predefined subregions, which are generated from the area of interest using a classical divide-and-conquer method, to improve the lifetime of a wireless sensor network. Their proposed protocol is devised with a two-step process, including a leader election technique in each subregion and a sensor's activity scheduling by each elected leader. In general, it is a good idea to pre-divide the network domain into several sub-areas, and assign a single cluster head in each sub-area for achieving more balanced energy dissipation for the wireless sensor network. As we known, Heinzelman et al. (2000) first proposed a clustering protocol called LEACH for periodical data-gathering applications. Also many variants of LEACH protocol or a variety of distributed protocols had proposed enhanced energy efficient adaptive clustering protocols by pre-dividing the network domain into several sub-areas, and assigning a single cluster head in each sub-area to achieve more balanced energy dissipation. Hence, I suggest that the authors could clearly state the differences and benefits between their leader selection technique and the methods of cluster head election in LEACH or other distributed protocols. Moreover, they used the two protocols, DESK and GAF, for assessing the performance of their protocols is not convincing. The authors may include more well-known or recently developed protocols for comparison.
+
+\textcolor{blue}{\textbf{\textsc{Answer:}

 %The difference between our leader selection technique and the methods of cluster head election in LEACH or other distributed protocols in that our approach  assumes  that the sensors are deployed almost uniformly and with high density over the region. So we only need  to fix a regular division of the  region into subregions to make the problem tractable.  The subdivision is made using divide-and-conquer concept such that the number of hops between any pairs  of sensors inside a subregion is  less than or equal to~3. The sensors inside each subregion cooperate to elect one leader. Leader applies sensor activity scheduling based optimization to provide the schedule to the sensor nodes in the subregion. The advantage of our approach is to minimize the energy consumption required for communication. The sensors only require to communicate with the other sensors inside the subregion to elect the leader instead of communicating with other nodes in the WSN. \\Whereas in LEACH and other cluster head election methods, the cluster heads are elected in distributed way where sensors  elect  themselves  to  be local cluster-heads  at any  given time  with  a  certain  probability. These cluster-head  nodes  broadcast  their  status  to  the  other  sensors  in the network.  Each sensor node determines to which cluster it wants to belong by choosing the cluster-head that requires the minimum communication energy. Once all the nodes are organized into clusters, each cluster-head creates a schedule for the nodes in its cluster.   \\\\
 %The difference between our leader selection technique and the methods of cluster head election in LEACH or other distributed protocols in that our approach  assumes  that the sensors are deployed almost uniformly and with high density over the region. So we only need  to fix a regular division of the  region into subregions to make the problem tractable.  The subdivision is made using divide-and-conquer concept such that the number of hops between any pairs  of sensors inside a subregion is  less than or equal to~3. The sensors inside each subregion cooperate to elect one leader. Leader applies sensor activity scheduling based optimization to provide the schedule to the sensor nodes in the subregion. The advantage of our approach is to minimize the energy consumption required for communication. The sensors only require to communicate with the other sensors inside the subregion to elect the leader instead of communicating with other nodes in the WSN. \\Whereas in LEACH and other cluster head election methods, the cluster heads are elected in distributed way where sensors  elect  themselves  to  be local cluster-heads  at any  given time  with  a  certain  probability. These cluster-head  nodes  broadcast  their  status  to  the  other  sensors  in the network.  Each sensor node determines to which cluster it wants to belong by choosing the cluster-head that requires the minimum communication energy. Once all the nodes are organized into clusters, each cluster-head creates a schedule for the nodes in its cluster.   \\\\

-In our  approach, the  leader selection  technique is  quite different  from the
-LEACH  protocol or  from  its  variants. Contrary  to  the  LEACH protocol,  the
-division of  the area  of interest  into subregions is  assumed to  be performed
-before the head  election. Moreover, we assume that 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. \\\\ As explained by  the reviewer, there is a large variety
-of energy-efficient  protocols for WSN. We  focus on GAF and  DESK protocols for
-two main reasons. First, our protocol is  inspired by both of them. DiLCO uses a
-regular division  of the  area as  in GAF  protocol and  a temporal  division in
-rounds  as in  DESK.  Second,  GAF and  DESK are  well-known protocols,  easy to
-implement, and  often used as  references for comparison.  \textcolor{red}{je ne
-  sais pas si on ne devrait pas inclure une ref \`a LEACH dans la biblio, mais je
-  ne sais pas trop comment l'introduire dans le papier...}
-\textcolor{magenta}{Le premier paragraphe de ta r\'eponse me semble pas mal, juste pour situer
-notre protocole par rapport à LEACH. On pourrait le mettre dans la section~2 ?}\\\\ }}
+    In our  approach, the leader selection technique is quite different from the LEACH protocol or from its variants. Contrary to the LEACH protocol, the division of the area of interest into subregions is assumed to be performed before the head election. Moreover, we assume that 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.\\\\
+As explained by the reviewer, there is a large variety of energy-efficient protocols for WSN. We focus on GAF and DESK protocols for two main reasons. First, our protocol is inspired by both of them. DiLCO uses a regular division of the area as in GAF protocol and a temporal division in rounds as in DESK. Second,  GAF and DESK are well-known protocols, easy to implement, and often used as references for comparison. \textcolor{red}{je ne sais pas si on ne devrait pas inclure une ref \`a LEACH dans la biblio, mais je ne sais pas trop comment l'introduire dans le papier...}
+\textcolor{magenta}{Le premier paragraphe de ta r\'eponse me semble pas mal, juste pour situer notre protocole par rapport à LEACH. On pourrait le mettre dans la section~2 ?}\\\\ }}

 %In fact, GAF algorithm is chosen for comparison as a competitor because it is famous and easy to implement, as well as many authors referred to it in many publications. DESK algorithm is also selected as competitor in the comparison because it works into rounds fashion (network lifetime divided into rounds) similar to our approaches, as well as DESK is a full distributed coverage approach. }}
 
 %In fact, GAF algorithm is chosen for comparison as a competitor because it is famous and easy to implement, as well as many authors referred to it in many publications. DESK algorithm is also selected as competitor in the comparison because it works into rounds fashion (network lifetime divided into rounds) similar to our approaches, as well as DESK is a full distributed coverage approach. }}
 

-% Michel => TO BE CONTINUED
-

 \noindent The following improvements may be suggested to make it even better:\\
 \noindent The following improvements may be suggested to make it even better:\\

-\noindent {\bf 1. What is the "new idea" or contribution of this work?}    \\
-\textcolor{blue}{\textbf{\textsc{Answer :}       
-The contribution of this work is to design a protocol that focuses on the area coverage problem with the objective of maximizing the network lifetime. Our proposition, the Distributed Lifetime Coverage Optimization
-(DiLCO) protocol, maintains the coverage and improves the lifetime in WSNs. Our protocol combines two energy efficient mechanisms: leader election and sensor activity scheduling based optimization to optimize the coverage and the network lifetime inside each subregion. we strengthen our simulations by taking into account the characteristics of a Medusa II sensor (Raghunathan et al., 2002) to measure the energy consumption and the computation time. We have implemented two other existing distributed approaches: DESK (Vu et al., 2006) and GAF (Xu et al., 2001)) in order to compare their performances with our approach.
-}}\\
-
-\noindent {\bf 2. There are many parameters (listed in Page 5) that must be predefined before the proposed method begins. The reviewer suggests that the all special characters and symbols should be described or defined in the text. }    \\
-\textcolor{blue}{\textbf{\textsc{Answer :} All special characters and symbols have been carefully checked : they were always described and defined in the text, except for $E_{th}$ in algorithm 1. So we added a description in section 3.2 before its use in the algorithm.}}\\
-
-\noindent {\bf 3. From their simulations using the five versions: DiLCO-2, DiLCO-4, DiLCO-8, DiLCO-16, and DiLCO-32. The authors concluded that the more subregions enable the extension of the network lifetime. From their experimental simulations, the subdivision in 16 subregions seems to be the most relevant. However, I was wondering if this was possible to derive an expression for the real optimal number of subregions. In general, the optimal number of subregions depends on the size of sensor field and the location of base station.}  \\
-\textcolor{blue}{\textbf{\textsc{Answer :}  In fact, the optimal number of subregions depends on the area of interest size, sensing range of sensor, and the location of base station. The optimal number of subregions will be investigated in future. }}\\
-
-\noindent {\bf 4. The authors should try to indicate which parameters are critical to performance, is there a significant parameter difference, $w_U$ and $w_\Theta$ in Eq. (4) for example, when the protocol is applied of different WSNs? }    \\
-\textcolor{blue}{\textbf{\textsc{Answer :}  As mentioned in the paper, the integer
-    program is based  on the model proposed  by F. Pedraza, A.  L. Medaglia, and
-    A. Garcia  (``Efficient coverage algorithms for  wireless sensor networks'')
-    with some modifications.   The originality of  the model is
-    to solve  both objectives  in a parallel  fashion : maximizing the coverage and minimizing the overcoverage. Nevertheless  the weights
-    $w_\theta$ and  $w_U$ must be  properly chosen so  as to guarantee  that the
-    maximum number of points which are  covered during each round is maximum. 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. It has been proved in the paper mentioned above that this guarantee is satisfied for a weighting constant $w_{U}$ greater than $P$ (when $w_{\theta}$ is fixed to 1). }}\\
-
-\noindent {\bf 5. It is unclear whether the parameters of the other two protocols were optimized at all. If they were not, as I suspect, there is no way of knowing whether, indeed, the proposed protocol outperforms the other two on the simulations of WSNs reported in the paper. All experiments would have to be made replicable and the comparisons with other protocols should be fair and crystal clear.}    \\
-\textcolor{blue}{\textbf{\textsc{Answer :}   The parameters of the other two protocols were optimized at all as well as we used the same energy consumption model of  one of them with slight modification for ensuring fair comparison.   }}\\
-
-\noindent {\bf 6. I think the authors have a not too bad work here in hands, but the resulting paper is lacking some of convincible originality.}    \\
-\textcolor{blue}{\textbf{\textsc{Answer :}  To the best of our knowledge, no hybrid coverage optimization protocol (as our DiLCO protocol) that is globally distributed on the subregions and locally centralized using optimization has ever been proposed in the literature. DiLCO protocol is based on combination of two energy efficient mechanisms: leader election and sensor activity scheduling based optimization so as to optimize the coverage and the network lifetime in each subregion.  }}\\
+\noindent {\bf 1. What is the ``new idea" or contribution of this work?}\\
+\textcolor{blue}{\textbf{\textsc{Answer:} The contribution of this work is to design a protocol that focuses on the area coverage problem with the objective of maximizing the network lifetime. Our proposition, the Distributed Lifetime Coverage Optimization (DiLCO) protocol, maintains the coverage and improves the lifetime in WSNs. Our protocol combines two energy efficient mechanisms: leader election and sensor activity scheduling based optimization to optimize the coverage and the network lifetime inside each subregion. We strengthen our simulations and made them more realistic by taking into account the characteristics of a Medusa II sensor (Raghunathan et al., 2002) to measure the energy consumption and the computation time. We have implemented two other existing distributed approaches: DESK (Vu et al., 2006) and GAF (Xu et al., 2001), in order to compare their performances with our approach. These two approaches are well-known and often considered as references in comparison studies.}}\\

 
 

-\section*{Response to Reviewer $\#$5 Comments}
-The paper addresses the problem of lifetime coverage in wireless sensor networks. The main issue here is the energy to maintain full coverage of the network while achieving sensing, communication,  and computation tasks. The author suggest a new protocol, named DiLCO, aiming at solving the aforementioned objective using a discrete optimization approach. The focus of the paper is clear and the basic idea looks attractive. However, from my opinion, number of clarifications are needed in order for me to be able to validate the whole contribution of the authors. Some of them include:
+\noindent {\bf 2. There are many parameters (listed in Page~5) that must be predefined before the proposed method begins. The reviewer suggests that the all special characters and symbols should be described or defined in the text.}\\
+\textcolor{blue}{\textbf{\textsc{Answer:} All special characters and symbols have been carefully checked: they were always described and defined in the text, except for $E_{th}$ in Algorithm~1. So we added a description in subsection~3.2 before its use in the algorithm.}}\\

 
 

-\noindent {\bf  1. The concept of efficiency is not clearly stated, is it the amount of energy used by the protocol or the time it takes to completion ? (line 52 of the introduction "most efficient")}    \\
-\textcolor{blue}{\textbf{\textsc{Answer :} The concept of efficiency refers to the ability of maintaining the best coverage as long as possible. As  previously explained,  the  model with the  appropriate weights ensures  that a  maximum number of  points are
-    covered by the set of still  alive sensors. The efficiency is measured through
-    the performance metrics "coverage ratio" and "network lifetime". Coverage ratio remains around 100\% as
-    long as  possible (as long  as there are enough  alive sensors to  cover all
-    primary   points)   and   then   decreases. Network Lifetime is defined as the time until the coverage ratio drops below a predefined threshold.  }}\\
+\noindent {\bf 3. From their simulations using the five versions: DiLCO-2, DiLCO-4, DiLCO-8, DiLCO-16, and DiLCO-32. The authors concluded that the more subregions enable the extension of the network lifetime. From their experimental simulations, the subdivision in 16 subregions seems to be the most relevant. However, I was wondering if this was possible to derive an expression for the real optimal number of subregions. In general, the optimal number of subregions depends on the size of sensor field and the location of base station.}\\
+\textcolor{blue}{\textbf{\textsc{Answer:} In fact, as noticed by the reviewer, the optimal number of subregions depends on the area of interest size, sensing  range of sensor, and the location of base station. The optimal number of subregions will be investigated in future.}}\\

 
 

-\noindent {\bf  2. The topology of the graph is not considered in the paper. Isn't it important ?  In which class of graphs the author think they will perform better ? are there some disadvantageous topologies ?}    \\
-\textcolor{blue}{\textbf{\textsc{Answer :} The study of the topology of the graph is out of the scope of our paper. We do not focus on specific patterns of sensors' deployment. We consider a highly dense network of sensors uniformly deployed in the area of interest. }}\\
-%Uniform graph partition is used by subdividing the sensing field into smaller subgraphs (subregion) using divide-and-conquer concept. The subgraph consists of sensor nodes which are previously deployed over the sensing field uniformly with high density to ensure that any primary point on the sensing field is covered by at least one sensor node. The graph partition problem has gained importance due to its application for clustering. The topology of the graph has important impact on the protocol performance. Random graph has negative  effect on our DiLCO protocol because we suppose that the sensing field is subdivided uniformly.  }}
+\noindent {\bf 4. The authors should try to indicate which parameters are critical to performance, is there a significant parameter difference, $w_U$ and $w_\Theta$ in Eq. (4) for example, when the protocol is applied of different WSNs? }\\
+\textcolor{blue}{\textbf{\textsc{Answer:} As mentioned in the paper, the integer program is based on the model proposed by F. Pedraza, A. L. Medaglia, and A. Garcia (``Efficient coverage algorithms for wireless sensor networks'') with some modifications. The originality of the model is to solve both objectives in a parallel fashion: maximizing the coverage and minimizing the overcoverage. Nevertheless the weights $w_\theta$ and $w_U$ must be properly chosen so as to guarantee that the maximum number of points which are covered during each round is maximum. 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. It has been proved in the paper mentioned above that this guarantee is satisfied for a weighting constant $w_{U}$ greater than $\left|P\right|$ (when $w_{\theta}$ is fixed to 1).}}\\

 
 

-\noindent {\bf  3. In line 42 of section  3, why  do we need $R_c \geq 2R_s$ ? Isn't it sufficient to have $Rc  >  Rs$ ? What is the implication of a stronger hypothesis ? How realistic is it ? Again, this raised the question of the topology.}\\
-\textcolor{blue}{\textbf{\textsc{Answer :}   We assume that the communication range $R_c$ satisfies the condition $Rc \geq 2R_s$. In fact, Zhang and Hou ("Maintaining Sensing Coverage and. Connectivity in Large Sensor Networks",2005) proved that if the transmission range fulfills the previous hypothesis, the complete coverage of a convex area implies connectivity among active nodes. In this paper, communication ranges and sensing ranges of real sensors are given. Communication range is comprised between 30 and 300 meters. And the sensing range does not exceed 30m. \textcolor{red}{In the case of MEDUSA II sensor node,...........}}}\\
+\noindent {\bf 5. It is unclear whether the parameters of the other two protocols were optimized at all. If they were not, as I suspect, there is no way of knowing whether, indeed, the proposed protocol outperforms the other two on the simulations of WSNs reported in the paper. All experiments would have to be made replicable and the comparisons with other protocols should be fair and crystal clear.}\\
+\textcolor{blue}{\textbf{\textsc{Answer:} The parameters of the other two protocols were optimized at all as well as we used the same energy consumption model of one of them with slight modification for ensuring fair comparison.}}\\

 
 

-\noindent {\bf  4. In line 63 of subsection 3.2, it is not clear why the periodic scheduling is in favor of a more robust network. Please, explain.}    \\
-\textcolor{blue}{\textbf{\textsc{Answer :}  We explain it in the subsection 3.2. : " 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 the  coverage until the
-definition of  a new  cover set  in the next  period. "    }}\\
+\noindent {\bf 6. I think the authors have a not too bad work here in hands, but the resulting  paper is lacking some of convincible originality.}\\
+\textcolor{blue}{\textbf{\textsc{Answer:} To the best of our knowledge, no hybrid coverage optimization protocol (as our DiLCO protocol) that is globally distributed on the subregions and locally centralized using optimization has ever been proposed in the literature. DiLCO protocol is based on combination of two energy efficient mechanisms: leader election and sensor activity scheduling based optimization so as to optimize the coverage and the network lifetime in each subregion.}}

 
 

-\noindent {\bf  5. The next sentence mention "enough energy to complete a period". This is another point where the author could be more rigorous. Indeed, how accurate is the evaluation of the required energy for a period ?}    \\
-\textcolor{blue}{\textbf{\textsc{Answer :}  The evaluation of the required energy to complete a period takes into account the energy consumed for information exchange with neigbors inside a subregion and the energy needed to stay active during the sensing period. Here, the sensing period duration is equal to one hour but may adapted dynamically according to the QoS requirements. The threshold value $E_{th}$ has been fixed to 36 Joules. This value has been computed by multiplying the energy consumed in the active state (9.72 mW) by the time in second for one period (3600 seconds), and adding the energy for the pre-sensing phases. We explain that in subsection 5.1. In our simulation, the time computation required by a leader to solve the integer program does not exceed 1000 seconds regardless the size of the network and the number of subregions (see figure 4), except the case with two subregions (DilCO-2) where the times computation become much too long as the network size increases. So the energy required for computation $E^{comp}$, estimated to 26.83 mW per second, will never exceed 26.83 Joules. All sensors whose remaining energy is greater than $E_{th}=36$ Joules are potential leaders. Once a leader is selected, it will be itself included in the coverage problem formulation only if its remaining energy before computation is greater than $E_{th}+E^{comp}$. We added a sentence in section 3.2. before the description of the algorithm to clarify this point. Recall that $E^{comp}>E_{th}$ makes no sense. In such a case, the energy required for the decision phase would be greater than the energy required for the sensing phase.}}\\
+\section*{Response to Reviewer $\#$5 Comments}
+The paper addresses the problem of lifetime coverage in wireless sensor networks. The main issue here is the energy to maintain full coverage of the network while achieving sensing, communication, and computation tasks. The author suggest a new protocol, named DiLCO, aiming at solving the aforementioned objective using a discrete optimization approach. The focus of the paper is clear and the basic idea looks attractive. However, from my opinion, number of clarifications are needed in order for me to be able to validate the whole contribution of the authors. Some of them include:

 
 

-\noindent {\bf  6. About the information collected (line 36-38) , what are they used for ?}    \\
-\textcolor{blue}{\textbf{\textsc{Answer :}   The information collected is used for leader election and decision phases. Details on the INFO packet have been added at the end of section~3.2. After
-    the information exchange among the sensor  nodes in the subregion, each node
-    will have all the  information needed to decide if it will  be the leader or
-    not. The decision is based on selecting  the sensor node that has the larger
-    number of one-hop neighbors. If this value is the same for many sensors, the
-    node that has the largest remaining energy will be selected as a leader.  If
-    there exists  sensors with the same  number of neighbors and  the same value
-    for the remaining energy, the sensor node that has the largest index will be
-    finally selected as a leader. }}\\
+\noindent {\bf 1. The concept of efficiency is not clearly stated, is it the amount of energy used by the protocol or the time it takes to completion ? (line  52 of the introduction ``most efficient'')}\\
+\textcolor{blue}{\textbf{\textsc{Answer:} The concept of efficiency refers to the ability of maintaining the best coverage as long as possible. As previously explained, the model with the appropriate weights ensures that a maximum number of points are covered by the set of still alive sensors. The efficiency is measured through the performance metrics ``coverage ratio'' and ``network  lifetime''. Coverage ratio remains around 100\% as long as possible (as long as there  are enough alive sensors to cover all primary points) and then decreases. Network Lifetime is defined as the time until the coverage ratio drops below a predefined threshold.}}\\

 
 

-\noindent {\bf  7. The way the leader is elected could emphasize first on the remaining energy.  Is it sure that the remaining energy will be sufficient to solve the integer program algorithm ?}    \\
-\textcolor{blue}{\textbf{\textsc{Answer :}   You are right. We have answered this question in previous comments. Remaining energy for DiLCO-4, DiLCO-8, DiLCO-16, and DiLCO-32 protocol versions will be sufficient to solve the integer program algorithm (see Figure 4: Execution time in seconds) in so far as the time computation does not exceed 1000 seconds. Therefore the energy required for computation $E^{comp}$, estimated to 26.83 mW per second, will never exceed 26.83 Joules. However only sensors able to be alive during one sensing period will be included in the coverage problem formulation. To sum up, a sensor may be elected as a leader only if its remaining energy is greater than $E^{comp}$, a leader may participate in the sensing phase only if its remaining energy is greater than $E_{th}+E^{comp}$. Recall that $E_{th}>E^{comp}$.}}\\
+\noindent {\bf  2. The topology of the graph is not considered in the paper. Isn't it important ? In which class of graphs the author think they will perform  better ? are there some disadvantageous topologies  ?}\\
+\textcolor{blue}{\textbf{\textsc{Answer:} The study of the topology of the graph is out of the scope of our paper. We do not focus on specific patterns of sensors' deployment. We consider a highly dense network of sensors uniformly deployed in the area of interest. }}\\
+%Uniform graph partition is used by subdividing the sensing field into smaller subgraphs (subregion) using divide-and-conquer concept. The subgraph consists of sensor nodes which are previously deployed over the sensing field uniformly with high density to ensure that any primary point on the sensing field is covered by at least one sensor node. The graph partition problem has gained importance due to its application for clustering. The topology of the graph has important impact on the protocol performance. Random graph has negative effect on our DiLCO protocol because we suppose that the sensing field is subdivided uniformly.  }}

 
 

-\noindent {\bf  8. Regarding the MIP formulation at the end of section 4, the first constraint does not appear as a constraint for me as it is an invariant (as shown on top)}    \\
-\textcolor{blue}{\textbf{\textsc{Answer :} This constraint is essential to make the integer program consistent. Whithout this constraint, one optimal solution may be $\theta_p=0 \quad \forall p \in P$, and $U_p=0 \quad \forall p \in P$, whatever the values of $X_j$. And no real optimization is performed. }}\\
+\noindent {\bf 3. In line 42 of section 3, why do we need $R_c \geq 2R_s$ ? Isn't it sufficient to have $Rc > Rs$ ? What is the implication of a stronger hypothesis ? How realistic is it ? Again, this raised the question of the topology.}\\
+\textcolor{blue}{\textbf{\textsc{Answer:} We assume that the communication range $R_c$ satisfies the condition $Rc \geq  2R_s$. In fact, Zhang and Hou (``Maintaining Sensing Coverage and Connectivity in Large Sensor Networks'', 2005) proved that if the transmission range fulfills the previous hypothesis, the complete coverage of a convex area implies connectivity among active nodes. In this paper, communication ranges and sensing ranges of real sensors are given. Usually, the communication range goes from several tens of meters up to several hundreds (typically between 30 and 300 meters) and the sensing range does not exceed 30m. In the case of MEDUSA II sensor node, communications are performed by a TR1000 RFM Radio transceiver, which has transmission power of 0.75~mW at maximum and an approximate transmission range of 20~m.}}\\

 
 

-\noindent {\bf  9. How $ w_\theta $ and $ w_U $ are chosen ? (end of section 4). How dependent if the method toward these parameters ?}    \\
-\textcolor{blue}{\textbf{\textsc{Answer :}   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. In fact, $ w_U $ should  be large enough compared to $w_{\Theta}$ to prevent overcoverage and so to activate a minimum  number of sensors. We discuss this point in our answer for question 4 of reviewer 3.}}\\
+\noindent {\bf 4. In line 63 of subsection~3.2, it is not clear why the periodic scheduling is in favor of a more robust network. Please, explain.}\\
+\textcolor{blue}{\textbf{\textsc{Answer :} We explain it in subsection~3.2.: ``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 the coverage until the definition of a new cover set in the next period.''}}\\

 
 

-\noindent {\bf  10. In table 2, the "listening" and the "computation" status are both (ON, ON, ON), is that correct ?}    \\
-\textcolor{blue}{\textbf{\textsc{Answer :}  Yes, in both cases, sensors continue their processing, communication, and sensing tasks.     }}\\
+\noindent {\bf 5. The next sentence mention ``enough energy to complete a period''. This is another point where the author could be more rigorous. Indeed, how accurate is the evaluation of the required energy for a period ?}\\
+\textcolor{blue}{\textbf{\textsc{Answer:} The evaluation of the required energy to complete a period  takes into account the energy consumed for information exchange with neigbors inside a subregion and the energy needed to stay active during the sensing period. In our case, the sensing period duration is equal to one hour but might be adapted dynamically according to the QoS requirements. Thus, the threshold value  $E_{th}$, which has been fixed to 36~Joules, has been computed by multiplying the energy consumed in the active state (9.72  mW) by the time in second for one period (3600 seconds), and adding the energy for the pre-sensing phases. We explain that in subsection~5.1. In our simulation, the computation time required by a leader node to solve the integer program does not exceed 1000~seconds regardless the size of the network and the number of subregions (see Figure~4), except the case with two subregions (DiLCO-2) where the computation time becomes much too long as the network size increases. So the energy required for computation, $E^{comp}$, estimated to 26.83~mW per second, will never exceed 26.83~Joules. All sensors whose remaining energy is greater than $E_{th}=36$ Joules are potential leaders. Once a leader is selected, it will be itself included in the coverage problem formulation only if its remaining energy before computation is greater than $E_{th}+E^{comp}$. We added a sentence in subsection~3.2 before the description of the algorithm, to clarify this point. Recall that $E^{comp}>E_{th}$ makes no sense: in such  a case, the energy required for the decision phase would be greater than the energy required for the sensing phase.}}\\

 
 

-\noindent {\bf  11. In line 60-61, you choose active energy as reference, is that sufficient for the computation ?}    \\
-\textcolor{blue}{\textbf{\textsc{Answer :} We discuss this point in our answers for question 5 and 7.}}\\
+\noindent {\bf 6. About the information collected (line 36-38), what are they used for  ?}\\
+\textcolor{blue}{\textbf{\textsc{Answer:} These information are used for leader election and decision phases. Details on the INFO packet have been added at the end of subsection~3.2. After the information exchange among the sensor nodes in the subregion, each node will  have all the information needed to decide if it will be the leader or not. The decision is based on selecting the sensor node that has the larger number of one-hop neighbors. If this value is the same for many sensors, the node that has the largest remaining energy will be selected as a leader. If there exists sensors with the same number of neighbors and the same value for the remaining energy, the sensor node that has the largest index will be finally selected as a leader.}}\\

 
 

-\noindent {\bf  12. The equation of EC has the communication energy duplicated}    \\
-\textcolor{blue}{\textbf{\textsc{Answer :}   In fact, there is no duplication.  The  first   one,  denoted   $E^{\scriptsize  \mbox{com}}_m$, represents  the  energy  consumption  spent   by  all  the  nodes  for  wireless
-communications  during period  $m$. The second, $E^{\scriptsize \mbox{comp}}_m$  refers to the  energy needed by all  the leader nodes  to solve the  integer program  during a  period. }}\\
+\noindent {\bf 7. The way the leader is elected could emphasize first on the remaining energy. Is it sure that the remaining energy will be sufficient to solve the integer program algorithm ?}\\
+\textcolor{blue}{\textbf{\textsc{Answer:} You are right. We have answered this question in  previous comments. Remaining energy for DiLCO-4, DiLCO-8, DiLCO-16, and  DiLCO-32 protocol versions will be sufficient to solve the integer program algorithm (see Figure 4: execution time in seconds) in so far as the computation does not exceed 1000~seconds. Therefore the energy required for computation $E^{comp}$, estimated  to 26.83 mW per second, will never exceed 26.83 Joules. However only sensors able to be alive during one sensing period will be included in the coverage problem formulation. To sum up, a sensor may be elected as a leader only if its remaining energy is greater than $E^{comp}$, a leader may participate in the sensing phase only if its remaining energy is greater than $E_{th}+E^{comp}$. Recall that $E_{th}>E^{comp}$.}}\\

 
 

-\noindent {\bf  13. Figure 2 should be discussed including the initial energy and the topology of the graph}    \\
-\textcolor{blue}{\textbf{\textsc{Answer :}   Each node has an initial energy level, in Joules, which is randomly drawn in $[500-700]$. 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 longer take part in the coverage task. As previously explained in answer 2, we consider a highly dense network of sensors uniformly deployed in the area of interest.}}\\
+\noindent {\bf 8. Regarding the MIP formulation at the end of section 4, the first constraint does not appear as a constraint for me as it is an invariant (as shown on top)}\\
+\textcolor{blue}{\textbf{\textsc{Answer:} This constraint is  essential to  make the  integer program  consistent. Whithout this constraint, one optimal solution might be $\theta_p=0 \quad \forall p \in P$, and $U_p=0 \quad \forall p \in P$, whatever the values of $X_j$. And no real optimization is then performed.}}
+\textcolor{red}{Je pense  que sa remarque concerne la premiere contrainte sous {\it subject to}...}\\

 
 

-\noindent {\bf  14. You mention a DELL laptop. How this could be assimilated to a sensor ?}    \\
-\textcolor{blue}{\textbf{\textsc{Answer :}   In fact, simulations are performed on a laptop DELL. But to be consistent with the use of real sensors in practice, we multiply the execution times obtained with the DELL laptop by a constant. This is explained in subsection 5.2.3.}}\\
+\noindent {\bf 9. How $w_\theta$ and $w_U$ are chosen ? (end of section 4). How dependent if the  method toward these parameters ?}\\
+\textcolor{blue}{\textbf{\textsc{Answer:} 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. In fact, $w_U$ should be large enough compared to $w_{\Theta}$ to prevent overcoverage and so to activate a minimum number of sensors. We discuss this point in our answer for question~4 of reviewer~3.}}\\

 
 

-\noindent {\bf  15. In figure 4, what makes the execution times different ?}    \\
-\textcolor{blue}{\textbf{\textsc{Answer :} The execution times are different according to the size of the integer problem to solve. The size of the problem depends  on the number of variables and
-  constraints. The number of variables is  linked to the number of alive sensors
-  $J$, and the number  of primary points
-  $P$.  Thus  the integer  program contains $J$  variables of  type $X_j$,
-  $P$ overcoverage variables and $P$  undercoverage variables. The number of
-  constraints  is equal  to $P$.}}\\
+\noindent {\bf 10. In table 2, the ``listening" and the ``computation" status are both (ON, ON, ON), is that correct ?}\\
+\textcolor{blue}{\textbf{\textsc{Answer:} Yes, in both cases, sensors continue their processing, communication, and sensing tasks.}}\\

 
 

-\noindent {\bf  16. Why is it important to mention a divide-and-conquer approach (conclusion)}    \\
-\textcolor{blue}{\textbf{\textsc{Answer :}   it is important to mention a divide-and-conquer approach because of the subdivision of the sensing field is based on this concept.   }}\\
+\noindent {\bf 11. In line 60-61, you choose active energy as reference, is that sufficient for the  computation ?}\\
+\textcolor{blue}{\textbf{\textsc{Answer:} We discuss this point in our answers for questions~5 and 7.}}\\

 
 

-\noindent {\bf  17. The connectivity among subregion should be studied too.}    \\
-\textcolor{blue}{\textbf{\textsc{Answer :}  Yes you are right, we will investigated it more precisely in future. Up to now, we make the assumption that the communication range $R_c$ satisfies the condition $Rc \geq 2R_s$. In fact, Zhang and Hou ("Maintaining Sensing Coverage and. Connectivity in Large Sensor Networks",2005) proved that if the transmission range fulfills the previous hypothesis, the complete coverage of a convex area implies connectivity among active nodes. Therefore, as long as the coverage ratio is greater than $95\%$, we can assume that the connectivity is maintained. And we check it this hypothesis by simulation with OMNET++.}}\\\\
+\noindent {\bf 12. The equation of EC has the communication energy duplicated}\\
+\textcolor{blue}{\textbf{\textsc{Answer:} In fact, there is no duplication. The first one, denoted $E^{\scriptsize  \mbox{com}}_m$, represents the energy consumption spent by all the nodes for wireless communications during period $m$. The second, $E^{\scriptsize \mbox{comp}}_m$, refers to the energy needed by all the leader nodes to solve the integer program during a period.}}\\

 
 

+\noindent {\bf 13. Figure 2 should be discussed including the initial energy and the topology of the graph}\\
+\textcolor{blue}{\textbf{\textsc{Answer:} Each node has an initial energy level, in Joules, which is randomly drawn in $[500-700]$. 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 longer take part in the coverage task. As previously explained in answer 2, we consider a highly dense network of sensors uniformly deployed in the area of interest.}}\\

 
 

+\noindent {\bf 14. You mention a DELL laptop. How this could be assimilated to a sensor ?}\\
+\textcolor{blue}{\textbf{\textsc{Answer:} In fact, simulations are performed on a laptop DELL. But to be consistent with the use of real sensors in practice, we multiply the execution times obtained with the DELL laptop by a constant. This is explained in subsection~5.2.3.}}\\

 
 

+\noindent {\bf 15. In Figure 4, what makes the execution times different ?}\\
+\textcolor{blue}{\textbf{\textsc{Answer:} The execution times are different according to the size of the integer problem to solve. The size of the problem depends on the number of variables and constraints. The number of variables is linked to the number of alive sensors $J$, and the number of primary points $P$. Thus the integer program contains $J$ variables of type $X_j$, $P$ overcoverage variables, and $P$ undercoverage variables. The number of constraints is equal to $P$.}}\\

 
 

+\noindent {\bf 16. Why is it important to mention a divide-and-conquer approach (conclusion)}\\
+\textcolor{blue}{\textbf{\textsc{Answer:} It is important to mention a divide-and-conquer approach because the subdivision of the sensing field is based on this concept.}}\\

 
 

+\noindent {\bf 17. The connectivity among subregion should be studied too.}\\
+\textcolor{blue}{\textbf{\textsc{Answer :}  Yes you are right, we will investigated it more precisely in future. Up to now, we make the assumption that the communication range $R_c$ satisfies the condition $Rc \geq 2R_s$. In fact, Zhang and Hou (``Maintaining Sensing Coverage and Connectivity in Large Sensor Networks", 2005) proved that if the transmission range fulfills the previous hypothesis, the complete coverage of a convex area implies connectivity among active nodes. Therefore, as long as the coverage ratio is greater than $95\%$, we can assume that the connectivity is maintained. We have checked this hypothesis by simulation with OMNET++.}}\\

 
 We are very grateful to the  reviewers who, by their recommendations, allowed us
 to improve the quality of our article.
 
 We are very grateful to the  reviewers who, by their recommendations, allowed us
 to improve the quality of our article.


@@ -262,6 +169,4 @@ Best regards\\
 The authors
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 The authors
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