ok

diff --git a/Example.aux b/Example.aux
index 5cc252bb56b4475c08a1300d3b147fea60f22cec..c3c1539aea38940230634e58b8e475ace12efce8 100644 (file)
--- a/Example.aux
+++ b/Example.aux
@@ -89,34 +89,37 @@
 \newlabel{sec:Conclusion and Future Works}{{6}{10}}
 \bibstyle{plain}
 \bibdata{Example}
 \newlabel{sec:Conclusion and Future Works}{{6}{10}}
 \bibstyle{plain}
 \bibdata{Example}

-\bibcite{berman04}{Berman and Calinescu, 2004}
-\bibcite{cardei2005improving}{Cardei and Du, 2005}
-\bibcite{cardei2005energy}{Cardei et\nobreakspace  {}al., 2005}
-\bibcite{castano2013column}{Casta{\~n}o et\nobreakspace  {}al., 2013}
-\bibcite{conti2014mobile}{Conti and Giordano, 2014}
-\bibcite{Deng2012}{Deng et\nobreakspace  {}al., 2012}
-\bibcite{deschinkel2012column}{Deschinkel, 2012}
-\bibcite{idrees2014coverage}{Idrees et\nobreakspace  {}al., 2014}
-\bibcite{jaggi2006}{Jaggi and Abouzeid, 2006}
-\bibcite{kim2013maximum}{Kim and Cobb, 2013}
-\bibcite{Kumar:2005}{Kumar et\nobreakspace  {}al., 2005}
-\bibcite{li2013survey}{Li and Vasilakos, 2013}
-\bibcite{ling2009energy}{Ling and Znati, 2009}
-\bibcite{pujari2011high}{Manju and Pujari, 2011}
-\bibcite{Misra}{Misra et\nobreakspace  {}al., 2011}
-\bibcite{Nayak04}{Nayak and Stojmenovic, 2010}
-\bibcite{pc10}{Padmavathy and Chitra, 2010}
-\bibcite{pedraza2006}{Pedraza et\nobreakspace  {}al., 2006}
-\bibcite{qu2013distributed}{Qu and Georgakopoulos, 2013}
-\bibcite{raghunathan2002energy}{Raghunathan et\nobreakspace  {}al., 2002}
-\bibcite{rossi2012exact}{Rossi et\nobreakspace  {}al., 2012}
-\bibcite{varga}{Varga, 2003}
-\bibcite{ChinhVu}{Vu et\nobreakspace  {}al., 2006}
-\bibcite{chin2007}{Vu, 2009}
-\bibcite{5714480}{Xing et\nobreakspace  {}al., 2010}
-\bibcite{xu2001geography}{Xu et\nobreakspace  {}al., 2001}
-\bibcite{yang2014novel}{Yang and Chin, 2014a}
-\bibcite{yangnovel}{Yang and Chin, 2014b}
-\bibcite{Yang2014}{Yang and Liu, 2014}
-\bibcite{Zhang05}{Zhang and Hou, 2005}
-\bibcite{zorbas2010solving}{Zorbas et\nobreakspace  {}al., 2010}
+\bibcite{ref17}{1}
+\bibcite{ref19}{2}
+\bibcite{berman04}{3}
+\bibcite{cardei2005improving}{4}
+\bibcite{cardei2005energy}{5}
+\bibcite{castano2013column}{6}
+\bibcite{conti2014mobile}{7}
+\bibcite{Deng2012}{8}
+\bibcite{deschinkel2012column}{9}
+\bibcite{idrees2014coverage}{10}
+\bibcite{jaggi2006}{11}
+\bibcite{kim2013maximum}{12}
+\bibcite{Kumar:2005}{13}
+\bibcite{li2013survey}{14}
+\bibcite{ling2009energy}{15}
+\bibcite{pujari2011high}{16}
+\bibcite{Misra}{17}
+\bibcite{Nayak04}{18}
+\bibcite{pc10}{19}
+\bibcite{pedraza2006}{20}
+\bibcite{qu2013distributed}{21}
+\bibcite{raghunathan2002energy}{22}
+\bibcite{ref22}{23}
+\bibcite{rossi2012exact}{24}
+\bibcite{varga}{25}
+\bibcite{chin2007}{26}
+\bibcite{ChinhVu}{27}
+\bibcite{5714480}{28}
+\bibcite{xu2001geography}{29}
+\bibcite{yang2014novel}{30}
+\bibcite{yangnovel}{31}
+\bibcite{Yang2014}{32}
+\bibcite{Zhang05}{33}
+\bibcite{zorbas2010solving}{34}

diff --git a/Example.tex b/Example.tex
index 38cc14f5cca00795a4c2108785bb15b62fa44b31..3b522661430b3a17e87f6845d1e45241ea42fa74 100644 (file)
--- a/Example.tex
+++ b/Example.tex
@@ -300,12 +300,14 @@ and  the number  of  one-hop neighbors  still  alive. \textcolor{blue}{INFO pack
 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.
 completed, the nodes  of a subregion choose a leader to  take the decision based
 on  the  following  criteria   with  decreasing  importance:  larger  number  of
 neighbors, larger remaining energy, and  then in case of equality, larger index.

-After that,  if the sensor node is  leader, it will execute  the integer program
-algorithm (see Section~\ref{cp})  which provides a set of  sensors planned to be
-active in the next sensing phase. As leader, it will send an Active-Sleep packet
+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
 to each sensor  in the same subregion to  indicate it if it has to  be active or

-not.  Alternately, if  the  sensor  is not  the  leader, it  will  wait for  the
-Active-Sleep packet to know its state for the coming sensing phase.
+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.}
+%which provides a set of  sensors planned to be
+%active in the next sensing phase.
+

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


@@ -354,7 +356,7 @@ We formulate the coverage optimization problem with an integer program.
 The objective function consists in minimizing the undercoverage and the overcoverage of the area as suggested in \cite{pedraza2006}. 
 The area coverage problem is expressed as the coverage of a fraction of points called primary points. 
 Details on the choice and the number of primary points can be found in \cite{idrees2014coverage}. The set of primary points is denoted by $P$
 The objective function consists in minimizing the undercoverage and the overcoverage of the area as suggested in \cite{pedraza2006}. 
 The area coverage problem is expressed as the coverage of a fraction of points called primary points. 
 Details on the choice and the number of primary points can be found in \cite{idrees2014coverage}. The set of primary points is denoted by $P$

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

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


@@ -398,9 +400,14 @@ X_{j} \in \{0,1\}, &\forall j \in J
 \end{array}
 \right.
 \end{equation}
 \end{array}
 \right.
 \end{equation}

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

 % MODIF - END
 
 
 % MODIF - END
 
 

diff --git a/reponse.tex b/reponse.tex
index 1c2ffde06ea6d1050bb8e64e09e96fd2ec05a0f9..afa144f570a13085c4cb3be56e656bc90bdbdb23 100644 (file)
--- a/reponse.tex
+++ b/reponse.tex
@@ -95,7 +95,7 @@ In fact, GAF algorithm is chosen for comparison as a competitor because it is fa
 \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
 \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. We also focus on performance analysis based on the number of subregions.
+(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. }    \\
 }}\\
 
 \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. }    \\


@@ -105,7 +105,7 @@ The contribution of this work is to design a protocol that focuses on the area c
 \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 :}  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
+\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
     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


@@ -115,7 +115,7 @@ The contribution of this work is to design a protocol that focuses on the area c
     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. It has been proved in the paper mentioned above that this guarantee is satisfied for a weighting constant $w_{U}$ greater than $P$. }}\\
+    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 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.   }}\\


@@ -134,14 +134,14 @@ The paper addresses the problem of lifetime coverage in wireless sensor networks
     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 ?}    \\
     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 an highly dense network of sensors uniformly deployed in the area of interest. }}\\
+\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.}\\
 %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 (2005, "Maintaining Sensing Coverage and. Connectivity in Large Sensor Networks") 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. In the case of MEDUSA II sensor node,...........}}\\
+\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. In the case of MEDUSA II sensor node,...........}}\\

 
 \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 the subsection 3.2. " A periodic  scheduling  is
+\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
 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


@@ -149,7 +149,7 @@ 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 ?}    \\
 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 ?}    \\

-\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). 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 $E_{th}+E^{comp}$. 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 to 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. 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.}}\\

 
 \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
 
 \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


@@ -163,19 +163,19 @@ definition of  a new  cover set  in the next  period. "    }}\\
     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 ?}    \\
     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 ?}    \\

-\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..... 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 $E_{th}+E^{comp}$. }}\\
+\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  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 may be $\theta_p=0 \forall p \in P$, and $U_p=0 \forall p \in P$, whatever the values of $X_j$. And no real optimization is performed. }}\\
+\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  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 so 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  11. In line 60-61, you choose active energy as reference, is that sufficient for the computation ?}    \\
 
 \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  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 answer for question ? of reviewer ?.}}\\
+\textcolor{blue}{\textbf{\textsc{Answer :} We discuss this point in our answers for question 5 and 7.}}\\

 
 \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
 
 \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


@@ -183,7 +183,7 @@ communications  during period  $m$. The second, $E^{\scriptsize \mbox{comp}}_m$
 
 \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
 
 \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 ? for reviewer ? we consider an highly dense network of sensors uniformly deployed in the area of interest.}}\\
+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  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.}}\\


@@ -191,16 +191,16 @@ needed for a node to stay active during one period, it will no longer take part
 \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
 \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

-  $A \subseteq J$, and the number  of primary points
-  $P$.  Thus  the integer  program contains $A$  variables of  type $X_j$,
+  $J$, 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
   $P$ overcoverage variables and $P$  undercoverage variables. The number of

-  constraints  is equal  to $P$  (for constraints  (\ref{})).}}\\
+  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 of the subdivision of the sensing field is based on this concept.   }}\\
 
 \noindent {\bf  17. The connectivity among subregion should be studied too.}    \\
 
 \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  17. The connectivity among subregion should be studied too.}    \\

-\textcolor{blue}{\textbf{\textsc{Answer :}  Yes you are right, we will investigated in future.     }}
+\textcolor{blue}{\textbf{\textsc{Answer :}  Yes you are right, we will investigated in future.     }}\\\\