application of these methods for the coverage scheduling problem.\\
\textcolor{blue}{\textbf{\textsc{Answer:} To the best of our knowledge, no
- integer linear programming based on perimeter coverage has been already
+ integer linear programming based on perimeter coverage has ever been
proposed in the literature. As specified in the paper, in Section 4, it is
inspired from a model developed for brachytherapy treatment planning for
optimizing dose distribution. In this model the deviation between an actual
assumption made on the selection criteria for the leader seems too vague. \\
\textcolor{blue}{\textbf{\textsc{Answer:} The selection criteria for the leader
- inside each subregion is explained in page~9, at the end of Section~3.3
- After information exchange among the sensor nodes in the subregion, each
- node will have all the information needed to decide if it will the leader or
+ inside each subregion is explained page~9, at the end of Section~3.3
+ 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
coverage interval $i$. If the sensor $j$ is undercovered, there exists at
least one of its CI (say $i$) for which the number of active sensors
(denoted by $l^{i}$) covering this part of the perimeter is less than $l$
- and in this case : $M_{i}^{j}=l-l^{i}$, $V_{i}^{j}=0$. In the contrary, if
+ and in this case : $M_{i}^{j}=l-l^{i}$, $V_{i}^{j}=0$. On the contrary, if
the sensor $j$ is overcovered, there exists at least one of its CI (say $i$)
for which the number of active sensors (denoted by $l^{i}$) covering this
part of the perimeter is greater than $l$ and in this case : $M_{i}^{j}=0$,
for alpha and beta. Table 4 presents the results obtained for a WSN of
200~sensor nodes. It explains the value chosen for the simulation settings
in Table~2. \\ \indent The choice of alpha and beta should be made according
- to the needs of the application. Alpha should be enough large to prevent
- undercoverage and so to reach the highest possible coverage ratio. Beta
- should be enough large to prevent overcoverage and so to activate a minimum
+ to the needs of the application. Alpha should be large enough to prevent
+ undercoverage and thus to reach the highest possible coverage ratio. Beta
+ should be enough large to prevent overcoverage and thus to activate a minimum
number of sensors. The values of $\alpha_{i}^{j}$ can be identical for all
coverage intervals $i$ of one sensor $j$ in order to express that the
perimeter of each sensor should be uniformly covered, but $\alpha_{i}^{j}$
as $\alpha$ is low, some areas may be poorly covered. This explains the
results obtained for $Lifetime_{50}$ with $\beta \gg \alpha$: a large number
of periods with low coverage ratio. With $\alpha \gg \beta$, we favor the
- coverage even if some areas may be overcovered, so high coverage ratio is
+ coverage even if some areas may be overcovered, so a high coverage ratio is
reached, but a large number of sensors are activated to achieve this goal.
- Therefore network lifetime is reduced. The choice $\alpha=0.6$ and
+ Therefore the network lifetime is reduced. The choice $\alpha=0.6$ and
$\beta=0.4$ seems to achieve the best compromise between lifetime and
coverage ratio.}}\\
WSN. Each paragraph of this Section discusses the literature related to a
particular aspect of the problem : 1. types of coverage, 2. types of scheme,
3. centralized versus distributed protocols, 4. optimization method. At the
- end of each paragraph we position our approach.}}\\
+ end of each paragraph we position our approach. We have also added a last paragraph about our previous work on DilCO protocol to explain the difference with PeCO. }}\\
\noindent {\bf 7.} The methodology is implemented in OMNeT++ (network simulator)
and tested against 2 existing algorithms and a previously developed method by
may be an issue if this approach is used in an application that requires high
coverage ratio. \\
-\textcolor{blue}{\textbf{\textsc{Answer:} Your remark is interesting. Indeed,
- Figures 8(a) and (b) highlight this result. PeCO protocol allows to achieve
+\textcolor{blue}{\textbf{\textsc{Answer:} Your remark is very interesting. Indeed,
+ Figures 8(a) and (b) highlight this result. The PeCO protocol allows to achieve
a coverage ratio greater than $50\%$ for far more periods than the others
three methods, but for applications requiring a high level of coverage
- (greater than $95\%$), DiLCO method is more efficient. It is explained at
+ (greater than $95\%$), the DiLCO method is more efficient. It is explained at
the end of Section 5.2.4.}}\\
%%%%%%%%%%%%%%%%%%%%%% ENGLISH and GRAMMAR %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
to~3. Concerning the choice of the sensing period duration, it is correlated
with the types of applications, with the amount of initial energy in sensors
batteries and also with the duration of the exchange phase. All applications
- do not have the same Quality of Service requirements. In our case
+ do not have the same Quality of Service requirements. In our case,
information exchange is executed every hour, but the length of the sensing
- period could be reduced and adapted dynamically. On the one hand a small
- sensing period would allow to be more reliable but would have higher
- communication costs. On the other hand the choice of a long duration may
+ period could be reduced and adapted dynamically. On the one hand, a small
+ sensing period would allow the network to be more reliable but would have higher
+ communication costs. On the other hand, the choice of a long duration may
cause problems in case of nodes failure during the sensing period.
Several explanations on these points are given throughout the paper. In
particular, we discuss the number of subregions in Section 5.2 and the
\textcolor{blue}{\textbf{\textsc{Answer:} Right. The mixed Integer Linear
Program adresses a multiobjective problem, where the goal is to minimize
- overcoverage and undercoverage for each coverage interval of a sensor. As
- far as we know, representing the objective function as a weighted sum of
+ overcoverage and undercoverage for each coverage interval of a sensor. To the best of our knowledge, representing the objective function as a weighted sum of
criteria to be minimized in case of multicriteria optimization is a
classical method. In Section 5, the comparison of protocols with a large
variety of performance metrics allows to select the most appropriate method
\medskip \\
It is noteworthy that the difference of memory used with GLPK between the
resolution of the IP and its LP-relaxation is very weak (not more than 0.1
-MB). The size of the branch and bound tree dos not exceed 3 nodes. This result
+MB). The size of the branch and bound tree does not exceed 3 nodes. This result
leads one to believe that the memory use with CPLEX\textregistered for solving
the IP would be very close to that for the LP-relaxation, that is to say around
100 Kb for a subregion containing $S=10$ sensors. Moreover the IP seems to have
\item the subdivision of the region of interest. To make the resolution of
integer programming tractable by a leader sensor, we need to limit the number
of nodes in each subregion (the number of variables and constraints of the
- integer programming is directly depending on the number of nodes and
+ integer programming directly depends on the number of nodes and
neigbors). It is therefore necessary to adapt the subdvision according to the
number of sensors deployed in the area and their sensing range (impact on the
number of coverage intervals).
\textcolor{blue}{\textbf{\textsc{Answer:} For minimizing the objective function,
$M_{i}^{j}$ and $V_{i}^{j}$ should be set to the smallest possible value
- such that the inequalities are satisfied. It is explained in the answer 4
- for the reviewer 1. But, at optimality, constraints are not necessary
+ such that the inequalities are satisfied. It is explained in answer 4
+ for reviewer 1. But, at optimality, constraints are not necessary
satisfied with equality. For instance, if a sensor $j$ is overcovered, there
exists at least one of its coverage interval (say $i$) for which the number
of active sensors (denoted by $l^{i}$) covering this part of the perimeter
