correct anglais

diff --git a/Example.tex b/Example.tex
index b2b473fa653c7fe59132b1f9da281b64f687570b..042bfca908ad73e6386c28eda8aaf589caa11498 100644 (file)
--- a/Example.tex
+++ b/Example.tex
@@ -56,19 +56,8 @@ email: ali.idness@edu.univ-fcomte.fr,\\ $\lbrace$karine.deschinkel, michel.salom
   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
   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.
-% MODIF - BEGIN
-  Simulations are conducted using the discret event simulator
-  OMNET++.  We  refer to the characterictics  of a Medusa II  sensor for
-  the energy consumption  and the computation time.   In comparison with
-  two other existing  methods, our approach is able to  increase the WSN
-  lifetime and provides improved coverage performance. }
-% MODIF - END
+  energy cost,  allowing to optimize  the network lifetime. Simulations are conducted using the discrete event simulator OMNET++. We refer to the characterictics  of a Medusa II  sensor for the energy consumption  and the computation time.   In comparison with two other existing  methods, our approach is able to  increase the WSN lifetime and provides improved coverage performances. }
+

 
 %\onecolumn
 
 
 %\onecolumn
 


@@ -86,15 +75,15 @@ 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
 sensor  field is  monitored. On  the one  hand we  want to  monitor the  area of
 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}, \textcolor{blue}{which means
-  that we want to maintain the best coverage as long as possible}.  On the other
+interest in the most  efficient way~\cite{Nayak04}, 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
 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
+lifetime.  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,
   \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,


@@ -102,7 +91,7 @@ lifetime.  \textcolor{blue}{A WSN  can  use  various types  of  sensors such  as
   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
   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.}
+  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


@@ -127,13 +116,13 @@ 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
+existing and distributed approaches (DESK ~\cite{ChinhVu}, and

 GAF ~\cite{xu2001geography})  in order  to compare  their performances  with our
 GAF ~\cite{xu2001geography})  in order  to compare  their performances  with our

-approach. \textcolor{blue}{We focus  on DESK and GAF protocols  for two reasons.
+approach. We focused  on DESK and GAF protocols  for two reasons.

   First our protocol is inspired by both  of them: DiLCO uses a regular division
   of the  area of interest  as in GAF  and a temporal  division in rounds  as in
   DESK.  Second, DESK  and GAF are well-known protocols, easy  to implement, and
   First our protocol is inspired by both  of them: DiLCO uses a regular division
   of the  area of interest  as in GAF  and a temporal  division in rounds  as in
   DESK.  Second, DESK  and GAF are well-known protocols, easy  to implement, and

-  often  used  as references  for  comparison}.  We  also focus  on  performance
+  often  used  as references  for  comparison.  We  also focus  on  performance

 analysis based on the number of subregions.
 % MODIF - END
 
 analysis based on the number of subregions.
 % MODIF - END
 


@@ -174,7 +163,7 @@ and the set  of active sensor nodes  is decided at the beginning  of each period
 requirements  (e.g.  area   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
 requirements  (e.g.  area   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
+so 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
 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


@@ -201,13 +190,13 @@ of  information can  be huge.   {\it  In order  to be  suitable for  large-scale
   selecting the active sensors for the current period.}
 
 % MODIF - BEGIN
   selecting the active sensors for the current period.}
 
 % MODIF - BEGIN

-\textcolor{blue}{ Our approach to select the leader node in a subregion is quite
+ Our approach to select the leader node in a subregion is quite

   different   from    cluster   head    selection   methods   used    in   LEACH
   \cite{DBLP:conf/hicss/HeinzelmanCB00}         or          its         variants
   \cite{ijcses11}. Contrary  to LEACH, the division  of the area of  interest is
   supposed to be performed before the  leader election. Moreover, we assume that
   the sensors are deployed almost uniformly  and with high density over the area
   different   from    cluster   head    selection   methods   used    in   LEACH
   \cite{DBLP:conf/hicss/HeinzelmanCB00}         or          its         variants
   \cite{ijcses11}. Contrary  to LEACH, the division  of the area of  interest is
   supposed to be performed before the  leader election. Moreover, we assume that
   the sensors are deployed almost uniformly  and with high density over the area

-  of interest, such  that the division is  fixed and regular.  As  in LEACH, our
+  of interest, so  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
   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


@@ -216,7 +205,7 @@ of  information can  be huge.   {\it  In order  to be  suitable for  large-scale
   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
   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.}
+  an optimization process which significantly reduces  the energy consumption.

 % MODIF - END
 
 A large  variety of coverage scheduling  algorithms has been  developed. Many of
 % MODIF - END
 
 A large  variety of coverage scheduling  algorithms has been  developed. Many of


@@ -277,9 +266,9 @@ less accurate according to the number of primary points.
 \label{main_idea}
 \noindent We start  by applying a divide-and-conquer algorithm  to partition the
 area of interest  into smaller areas called subregions and  then our protocol is
 \label{main_idea}
 \noindent We start  by applying a divide-and-conquer algorithm  to partition the
 area of interest  into smaller areas called subregions and  then our protocol is

-executed  simultaneously in  each subregion.  \textcolor{blue}{Sensor nodes  are
+executed  simultaneously in  each subregion. Sensor nodes  are

   assumed to be deployed almost uniformly over the region and the subdivision of
   assumed to be deployed almost uniformly over the region and the subdivision of

-  the area of interest is regular.}
+  the area of interest is regular.

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


@@ -328,20 +317,20 @@ and each sensor node will have five possible status in the network:
 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
 sensor node  indexed by  $j$). At  the beginning  a node  checks whether  it has
 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
 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
+enough  energy (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 ($RE_j$),
 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
+ID,  and the  number of  one-hop neighbors  still alive.  INFO
+  packet contains two parts: header and payload data. 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
   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
+  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
 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
+will  solve an  integer program  (see Section~\ref{cp}).  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
   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


@@ -353,7 +342,7 @@ will  solve an  integer program  (see Section~\ref{cp}).   \textcolor{blue}{This
   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
   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.}
+  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.
 


@@ -447,11 +436,11 @@ X_{j} \in \{0,1\}, &\forall j \in J
 \end{array}
 \right.
 \end{equation}
 \end{array}
 \right.
 \end{equation}

-The objective function is a weighted sum of overcoverage and undercoverage. The goal is to limit the overcoverage in order to activate a minimal number of sensors while simultaneously preventing undercoverage.  \textcolor{blue}{ By
+The objective function is a weighted sum of overcoverage and undercoverage. The goal is to limit the overcoverage in order to activate a minimal number of sensors while simultaneously preventing undercoverage.  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
     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. }
+    preferred. 

 %Both  weights $w_\theta$  and $w_U$ must  be carefully  chosen in
 %order to  guarantee that the  maximum number of  points are covered  during each
 %period.
 %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.

diff --git a/reponse.tex b/reponse.tex
index 9b38abbff3cf186db856fe180549bae912ff7177..2c33ca64219a2e678a2dc4a1026e8aae91ff635f 100644 (file)
--- a/reponse.tex
+++ b/reponse.tex
@@ -38,7 +38,7 @@
 
 \vspace{-0.5cm}\hspace{-2cm}FEMTO-ST Institute, UMR 6714 CNRS
 
 
 \vspace{-0.5cm}\hspace{-2cm}FEMTO-ST Institute, UMR 6714 CNRS
 

-\hspace{-2cm}University Bourgogne Franche-Comt\'e
+\hspace{-2cm}University of Bourgogne Franche-Comte

 
 \hspace{-2cm}IUT Belfort-Montb\'eliard, BP 527, 90016 Belfort Cedex, France.
 
 
 \hspace{-2cm}IUT Belfort-Montb\'eliard, BP 527, 90016 Belfort Cedex, France.
 


@@ -81,62 +81,106 @@ The paper present a new system to optimize sensord detections. The work present
 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:}
 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.   \\\\
-    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.\\\\
+%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 so 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, so 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 significantly reduces 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.}}
 
 \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?}\\
 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.}}
 
 \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 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.}}\\
+\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 strengthened 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.}}\\

 
 \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 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.}\\
 
 \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 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.}}\\
+\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 works.}}\\

 
 \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? }\\
 
 \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).}}\\
+\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  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  constant weighting $w_{U}$ greater than $\left|P\right|$ (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.}\\
 
 \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.}}\\
+\textcolor{blue}{\textbf{\textsc{Answer:} The parameters of the other
+    two protocols were optimized using  the same energy consumption
+    model as of one of the protocols only with slight modifications to
+    ensure a 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.}\\
 
 \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.}}
+\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. The DiLCO protocol is based on the 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.}}

 
 \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 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'')}\\
 
 \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 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.}}\\
+\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''. The 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  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 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.}\\
 
 \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 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.}}\\
+\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 30 m. 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 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.}\\
 
 \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.''}}\\
+\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. Then, if a node fails later, while 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 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 ?}\\
 
 \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.}}\\
+\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 (3,600 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 1,000~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 at 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 6. About the information collected (line 36-38), what are they used for  ?}\\
 
 \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.}}\\
+\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 are 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 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 ?}\\
 
 \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 $E_{th}>E^{comp}$.}}\\
+\textcolor{blue}{\textbf{\textsc{Answer:} You are right. We have
+    answered this question in  previous comments. The 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 1,000~seconds. Therefore the energy required to compute $E^{comp}$, 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 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)}\\
 
 \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}...}\\
+\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.}}\\
+

 
 \noindent {\bf 9. How $w_\theta$ and $w_U$ are chosen ? (end of section 4). How dependent if the  method toward these parameters ?}\\
 
 \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.}}\\
+\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 thus to activate a minimum number of sensors. We discuss this point in our answer for question~4 of reviewer~3.}}\\

 
 \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 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.}}\\


@@ -148,10 +192,16 @@ The paper addresses the problem of lifetime coverage in wireless sensor networks
 \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:} 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.}}\\
+\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 explained  previously 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 ?}\\
 
 \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.}}\\
+\textcolor{blue}{\textbf{\textsc{Answer:} In fact, simulations are
+    performed on a DELL laptop. 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 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 $P$.}}\\


@@ -160,7 +210,8 @@ The paper addresses the problem of lifetime coverage in wireless sensor networks
 \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:} 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++.}}\\
+\textcolor{blue}{\textbf{\textsc{Answer :}  Yes you are right, we will
+    investigate it more precisely in the future. At the moment, 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 simulations 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.