X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/Sensornets15.git/blobdiff_plain/30623c88a2804ea8abf07dd5b15eeacdcd39a33d..d7d5c33508ae16b9109c73481cb704710c4007c8:/reponse.tex?ds=sidebyside

diff --git a/reponse.tex b/reponse.tex
index 4b131be..ac9ba0a 100644
--- a/reponse.tex
+++ b/reponse.tex
@@ -77,6 +77,7 @@ The paper present a new system to optimize sensord detections. The work present
 
 
 \textcolor{blue}{\textbf{\textsc{Answer:} Right.  We  have  included a  paragraph on the examples and practical applications of WSNs in section~1. }}
+\textcolor{red}{Je pense que la question porte sur un exemple d'application de notre protocole?}
 
 
 \section*{Response to Reviewer $\#$3 Comments}
@@ -84,90 +85,122 @@ This work proposed a distributed lifetime coverage optimization (DiLCO) protocol
 sub-areas, and assigning a single cluster head in each sub-area to achieve more balanced energy dissipation. Hence, I suggest that the authors could clearly state the differences and benefits between their leader selection technique and the methods of cluster head election in LEACH or other distributed protocols. Moreover, they used the two protocols, DESK and GAF, for assessing the performance of their protocols is not convincible. The authors may include more well-known or recently developed protocols for comparison. 
 
 
-\textcolor{blue}{\textbf{\textsc{Answer :}  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.   \\\\
+\textcolor{green}{\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 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. }}
 
 
 
 
-The following improvements may be suggested to make it even better:\\
+\noindent The following improvements may be suggested to make it even better:\\
 \noindent {\bf 1. What is the "new idea" or contribution of this work?}    \\
 \textcolor{blue}{\textbf{\textsc{Answer :}       
 The contribution of this work is to design a protocol that focuses on the area coverage problem with the objective of maximizing the network lifetime. Our proposition, the Distributed Lifetime Coverage Optimization
-(DiLCO) protocol, maintains the coverage and improves the lifetime in WSNs. Our protocol combines two energy efficient mechanisms: leader election and sensor activity scheduling based optimization to optimize the coverage and the network lifetime inside each subregion. we strengthen our simulations by taking into account the characteristics of a Medusa II sensor (Raghunathan et al., 2002) to measure the energy consumption and the computation time. We have implemented two other existing distributed approaches: DESK (Vu et al., 2006) and GAF (Xu et al., 2001)) in order to compare their performances with our approach. 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. }    \\
-\textcolor{blue}{\textbf{\textsc{Answer :}       }}
+\textcolor{blue}{\textbf{\textsc{Answer :} All special characters and symbols have been carefully checked : they were always described and defined in the text, except for $E_{th}$ in algorithm 1. So we added a description in section 3.2 before its use in the algorithm.}}\\
 
 \noindent {\bf 3. From their simulations using the five versions: DiLCO-2, DiLCO-4, DiLCO-8, DiLCO-16, and DiLCO-32. The authors concluded that the more subregions enable the extension of the network lifetime. From their experimental simulations, the subdivision in 16 subregions seems to be the most relevant. However, I was wondering if this was possible to derive an expression for the real optimal number of subregions. In general, the optimal number of subregions depends on the size of sensor field and the location of base station.}  \\
-\textcolor{blue}{\textbf{\textsc{Answer :}  In fact, the optimal number of subregions depends on the area of interest size, sensing range of sensor, and the location of base station. The optimal number of subregions will be investigated in future. }}
-
-\noindent {\bf 4. The authors should try to indicate which parameters are critical to performance, is there a significant parameter difference, $w_u$ and $w_\Theta$ in Eq. (4) for example, when the protocol is applied of different WSNs? }    \\
-\textcolor{blue}{\textbf{\textsc{Answer :}  The number of primary points $P$ parameter has a significant impact on the performance of DiLCO protocol. When the WSN size increases the network lifetime decreases when number of primary points increases because the energy required for the computation of the optimization algorithm. }}
+\textcolor{blue}{\textbf{\textsc{Answer :}  In fact, the optimal number of subregions depends on the area of interest size, sensing range of sensor, and the location of base station. The optimal number of subregions will be investigated in future. }}\\
+
+\noindent {\bf 4. The authors should try to indicate which parameters are critical to performance, is there a significant parameter difference, $w_U$ and $w_\Theta$ in Eq. (4) for example, when the protocol is applied of different WSNs? }    \\
+\textcolor{blue}{\textbf{\textsc{Answer :}  As mentioned in the paper, the integer
+    program is based  on the model proposed  by F. Pedraza, A.  L. Medaglia, and
+    A. Garcia  (``Efficient coverage algorithms for  wireless sensor networks'')
+    with some modifications.   The originality of  the model is
+    to solve  both objectives  in a parallel  fashion : maximizing the coverage and minimizing the overcoverage. Nevertheless  the weights
+    $w_\theta$ and  $w_U$ must be  properly chosen so  as to guarantee  that the
+    maximum number of points which are  covered during each round is maximum. By
+    choosing  $w_{U}$ much  larger than $w_{\theta}$,  the coverage  of a
+    maximum of  primary points  is ensured.  Then for the  same number  of covered
+    primary points,  the solution  with a  minimal number  of active  sensors is
+    preferred. It has been proved in the paper mentioned above that this guarantee is satisfied for a weighting constant $w_{U}$ greater than $P$ (when $w_{\theta}$ is fixed to 1). }}\\
 
 \noindent {\bf 5. It is unclear whether the parameters of the other two protocols were optimized at all. If they were not, as I suspect, there is no way of knowing whether, indeed, the proposed protocol outperforms the other two on the simulations of WSNs reported in the paper. All experiments would have to be made replicable and the comparisons with other protocols should be fair and crystal clear.}    \\
-\textcolor{blue}{\textbf{\textsc{Answer :}   The parameters of the other two protocols were optimized at all as well as we used the same energy consumption model of  one of them with slight modification for ensuring fair comparison.   }}
+\textcolor{blue}{\textbf{\textsc{Answer :}   The parameters of the other two protocols were optimized at all as well as we used the same energy consumption model of  one of them with slight modification for ensuring fair comparison.   }}\\
 
 \noindent {\bf 6. I think the authors have a not too bad work here in hands, but the resulting paper is lacking some of convincible originality.}    \\
-\textcolor{blue}{\textbf{\textsc{Answer :}  To the best of our knowledge, no hybrid coverage optimization protocol (as our DiLCO protocol) that globally distributed on the subregions and locally centralized using optimization has ever been proposed in the literature. DiLCO protocol 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. 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.  }}\\
 
 \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  - 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 monitoring the area of interest using as less energy as possible.   }}
-
-\noindent {\bf  - 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 :} 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  - in line 42 of section  3, why  do we need Rc $\geq$ 2Rs ? 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 also assume that the communication range Rc satisfies Rc $\geq$ 2Rs. In fact, Zhang and Hou (2005) proved that if the transmission range fulfills the previous hypothesis, the complete coverage of a convex area implies connectivity among active nodes.}}\\
-
-\noindent {\bf  - 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 in the subsection 3.2.     }}
-
-\noindent {\bf  - 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 :}   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 explained that in subsection 5.1.  }}
-
-\noindent {\bf  - about the information collected (line 36-38) , what are they used for ?}    \\
-\textcolor{blue}{\textbf{\textsc{Answer :}  They used for leader election and decision phases.   }}
-
-\noindent {\bf  - 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 :}   It is sure that 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). The sensor node participates in the competition with energy enough for nearly one hour. }}
-
-\noindent {\bf  - 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 :}       }}
-
-\noindent {\bf  - 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, we give a high value to $ w_U $ because of giving more importance to prevent the undercoverage.   }}
-
-\noindent {\bf  - in table 2, the "listening" and the "computation" status are both (ON, ON, ON), is that correct ?}    \\
-\textcolor{blue}{\textbf{\textsc{Answer :}  Yes, because of both cases continue their processing, communication, and sensing tasks.     }}
-
-\noindent {\bf  - in line 60-61, you choose active energy as reference, is that sufficient for the computation ?}    \\
-\textcolor{blue}{\textbf{\textsc{Answer :}   Yes, it is sufficient for the computation.    }}
-
-\noindent {\bf  - The equation of EC has the communication energy duplicated}    \\
+\noindent {\bf  1. The concept of efficiency is not clearly stated, is it the amount of energy used by the protocol or the time it takes to completion ? (line 52 of the introduction "most efficient")}    \\
+\textcolor{blue}{\textbf{\textsc{Answer :} The concept of efficiency refers to the ability of maintaining the best coverage as long as possible. As  previously explained,  the  model with the  appropriate weights ensures  that a  maximum number of  points are
+    covered by the set of still  alive sensors. The efficiency is measured through
+    the performance metrics "coverage ratio" and "network lifetime". Coverage ratio remains around 100\% as
+    long as  possible (as long  as there are enough  alive sensors to  cover all
+    primary   points)   and   then   decreases. Network Lifetime is defined as the time until the coverage ratio drops below a predefined threshold.  }}\\
+
+\noindent {\bf  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. Communication range is comprised between 30 and 300 meters. And the sensing range does not exceed 30m. \textcolor{red}{In the case of MEDUSA II sensor node,...........}}}\\
+
+\noindent {\bf  4. In line 63 of subsection 3.2, it is not clear why the periodic scheduling is in favor of a more robust network. Please, explain.}    \\
+\textcolor{blue}{\textbf{\textsc{Answer :}  We explain it in the subsection 3.2. : " A periodic  scheduling  is
+interesting  because it  enhances the  robustness  of the  network against  node failures. First,  a node  that has not  enough energy  to complete a  period, or
+which fails before  the decision is taken, will be  excluded from the scheduling
+process. Second,  if a node  fails later, whereas  it was supposed to  sense the
+region of  interest, it will only affect  the quality of the  coverage until the
+definition of  a new  cover set  in the next  period. "    }}\\
+
+\noindent {\bf  5. The next sentence mention "enough energy to complete a period". This is another point where the author could be more rigorous. Indeed, how accurate is the evaluation of the required energy for a period ?}    \\
+\textcolor{blue}{\textbf{\textsc{Answer :}  The evaluation of the required energy to complete a period takes into account the energy consumed for information exchange with neigbors inside a subregion and the energy needed to stay active during the sensing period. Here, the sensing period duration is equal to one hour but may adapted dynamically according to the QoS requirements. The threshold value $E_{th}$ has been fixed to 36 Joules. This value has been computed by multiplying the energy consumed in the active state (9.72 mW) by the time in second for one period (3600 seconds), and adding the energy for the pre-sensing phases. We explain that in subsection 5.1. In our simulation, the time computation required by a leader to solve the integer program does not exceed 1000 seconds regardless the size of the network and the number of subregions (see figure 4), except the case with two subregions (DilCO-2) where the times computation become much too long as the network size increases. So the energy required for computation $E^{comp}$, estimated to 26.83 mW per second, will never exceed 26.83 Joules. All sensors whose remaining energy is greater than $E_{th}=36$ Joules are potential leaders. Once a leader is selected, it will be itself included in the coverage problem formulation only if its remaining energy before computation is greater than $E_{th}+E^{comp}$. We added a sentence in section 3.2. before the description of the algorithm to clarify this point. Recall that $E^{comp}>E_{th}$ makes no sense. In such a case, the energy required for the decision phase would be greater than the energy required for the sensing phase.}}\\
+
+\noindent {\bf  6. About the information collected (line 36-38) , what are they used for ?}    \\
+\textcolor{blue}{\textbf{\textsc{Answer :}   The information collected is used for leader election and decision phases. Details on the INFO packet have been added at the end of section~3.2. After
+    the information exchange among the sensor  nodes in the subregion, each node
+    will have all the  information needed to decide if it will  be the leader or
+    not. The decision is based on selecting  the sensor node that has the larger
+    number of one-hop neighbors. If this value is the same for many sensors, the
+    node that has the largest remaining energy will be selected as a leader.  If
+    there exists  sensors with the same  number of neighbors and  the same value
+    for the remaining energy, the sensor node that has the largest index will be
+    finally selected as a leader. }}\\
+
+\noindent {\bf  7. The way the leader is elected could emphasize first on the remaining energy.  Is it sure that the remaining energy will be sufficient to solve the integer program algorithm ?}    \\
+\textcolor{blue}{\textbf{\textsc{Answer :}   You are right. We have answered this question in previous comments. Remaining energy for DiLCO-4, DiLCO-8, DiLCO-16, and DiLCO-32 protocol versions will be sufficient to solve the integer program algorithm (see Figure 4: Execution time in seconds) in so far as the time computation does not exceed 1000 seconds. Therefore the energy required for computation $E^{comp}$, estimated to 26.83 mW per second, will never exceed 26.83 Joules. However only sensors able to be alive during one sensing period will be included in the coverage problem formulation. To sum up, a sensor may be elected as a leader only if its remaining energy is greater than $E^{comp}$, a leader may participate in the sensing phase only if its remaining energy is greater than $E_{th}+E^{comp}$. Recall that $E_{th}>E^{comp}$.}}\\
+
+\noindent {\bf  8. Regarding the MIP formulation at the end of section 4, the first constraint does not appear as a constraint for me as it is an invariant (as shown on top)}    \\
+\textcolor{blue}{\textbf{\textsc{Answer :} This constraint is essential to make the integer program consistent. Whithout this constraint, one optimal solution may be $\theta_p=0 \quad \forall p \in P$, and $U_p=0 \quad \forall p \in P$, whatever the values of $X_j$. And no real optimization is performed. }}\\
+
+\noindent {\bf  9. How $ w_\theta $ and $ w_U $ are chosen ? (end of section 4). How dependent if the method toward these parameters ?}    \\
+\textcolor{blue}{\textbf{\textsc{Answer :}   Both weights $ w_\theta $ and $ w_U $ must be carefully chosen in order to guarantee that the maximum number of points are covered during each period. In fact, $ w_U $ should  be large enough compared to $w_{\Theta}$ to prevent overcoverage and so to activate a minimum  number of sensors. We discuss this point in our answer for question 4 of reviewer 3.}}\\
+
+\noindent {\bf  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 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
-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. }}
+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  - figure 2 should be discussed including the initial energy and the topology of the graph}    \\
+\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. The topology of the graph is uniform graph with high density  }}
+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  - you mention a DELL laptop. How this could be assimilated to a sensor ?}    \\
-\textcolor{blue}{\textbf{\textsc{Answer :}   In fact, The execution times are obtained as shown 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.}}\\
 
-\noindent {\bf  - in figure 4, what makes the execution times different ?}    \\
-\textcolor{blue}{\textbf{\textsc{Answer :}  The WSN size  makes the execution times different.    }}
+\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  - 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  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  - the connectivity among subregion should be studied too.}    \\
-\textcolor{blue}{\textbf{\textsc{Answer :}  Yes you are right, we will investigated in future.     }}
+\noindent {\bf  17. The connectivity among subregion should be studied too.}    \\
+\textcolor{blue}{\textbf{\textsc{Answer :}  Yes you are right, we will investigated it more precisely in future. Up to now, we make the assumption that the communication range $R_c$ satisfies the condition $Rc \geq 2R_s$. In fact, Zhang and Hou ("Maintaining Sensing Coverage and. Connectivity in Large Sensor Networks",2005) proved that if the transmission range fulfills the previous hypothesis, the complete coverage of a convex area implies connectivity among active nodes. Therefore, as long as the coverage ratio is greater than $95\%$, we can assume that the connectivity is maintained. And we check it this hypothesis by simulation with OMNET++.}}\\\\
 
 
 
