the size of the subregion should be discussed and analyzed, but also the
clustering strategy.\\
-\textcolor{blue}{\textbf{\textsc{Answer:} }}\\
+\textcolor{blue}{\textbf{\textsc{Answer:} In the study, we assume that
+ the deployment of sensors is almost uniform 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 such that the number of hops
+ between any pairs of sensors inside a subregion is less than or equal
+ to~3. In particular, we discuss the number of subregions in......}}\\
\noindent {\bf 2.} Page 8
minimized would probably make more sense.
\\
-\textcolor{blue}{\textbf{\textsc{Answer:} }}\\
+\textcolor{blue}{\textbf{\textsc{Answer:} As mentioned in the paper the integer program is based on the model proposed by F. Pedraza and A. L. Medaglia and A. Garcia ("Efficient coverage algorithms for wireless sensor networks") with some modifications. Their initial approach consisted in first finding the maximum coverage obtainable from available sensors to then use this information as input to the problem of minimizing the overcoverage. But this two-steps approach is time consuming. The originality of the model is to solve both objectives in a parallel fashion. Nevertheless the weights $W_\theta$ and $W_U$ must be properly chosen so as to guarantee that the maximum number of points are covered during each round. By choosing $W_{U}$ very
+large compared to $W_{\theta}$, the coverage of a maximum of primary points is ensured. Then for a same number of covered points, solution with a minimal number of active sensors is preferred. }}\\
on wireless sensor networks", Optim. Lett. 7, No. 1, 157-172 (2013) by Gentilli
et al to enforce a constraint on the minimum coverage of each point. \\
-\textcolor{blue}{\textbf{\textsc{Answer:} }}\\
+\textcolor{blue}{\textbf{\textsc{Answer:} As previously explained, the model with the appropriate weights ensures that a maximum number of points are covered for the set of still alive sensors. The coverage is measured through the performance metrics "coverage ratio". 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. The problem introduced in "alpha-coverage to extend network lifetime
+on wireless sensor networks" by Gentilli is quite different. In this problem, the coverage ratio is fixed to a predetermined value ($\alpha$) and the amount of time during which the network can satisfy a target coverage greater than $\alpha$ is maximized. }}\\
\noindent {\bf 4.} Page 13
lifetime would be better, as it is independent from the number and duration of
rounds. \\
-\textcolor{blue}{\textbf{\textsc{Answer :} }}
+\textcolor{blue}{\textbf{\textsc{Answer :} Yes, you are right. It is possible to obtain the average energy consumption per unit of time by dividing the criterion defined in section .... by the round duration.}}
bring any valuable insight. \\
-\textcolor{blue}{\textbf{\textsc{Answer :} }}
+\textcolor{blue}{\textbf{\textsc{Answer :} Right. We have completely re-written section 5 to highlight the most significant results. }}
+\bigskip
\noindent {\bf 6.} Page 19 (most major point)
The authors state that solving the Mixed Integer Linear Program is
time-consuming, and use this point for explaining why MuDiLCO-7 is not as
in particular. \\
-\textcolor{blue}{\textbf{\textsc{Answer :} }}
+\textcolor{blue}{\textbf{\textsc{Answer :} Your remark is very interesting. We have observed that the optimal solution of the integer program is often obtained after the exploration of very few nodes of the Branch-and-Bound-tree. Therefore we conducted new simulations by applying your idea. That is to say we have stopped the resolution of the Branch-and-Bound method after a time threshold empirically defined and we retain the best feasible
+solution found by the solver. This approach allows to improve significantly the results with multirounds, especially for MuDiLCO-7.}}
\bigskip
The sentence "the centralized approaches usually suffer from the scalability
problem, making them less competitive as the network size increase" should
probably be tempered: heuristics and metaheuristics can handle very large and
-centralized problems (even if exact approaches can't), and these approaches are
+centralized problems (even if exact approaches can't), and these approaches areempirically
very popular in WSN. } \\
-\textcolor{blue}{\textbf{\textsc{Answer:} }}\\
+\textcolor{blue}{\textbf{\textsc{Answer:} Right, fixed }}\\
\noindent {\ding{90} Page 5
"The choice of number and locations of primary points is the subject of another
study not presented here". The authors should provide at least one reference
about the aforementioned study. } \\
-\textcolor{blue}{\textbf{\textsc{Answer:} }}\\
+\textcolor{blue}{\textbf{\textsc{Answer:} Right. We have included a section (section ...) dedicated to the choice and the number of primary points. }}\\
\noindent {\ding{90} Page 6, Figure 1:
All rounds seem to have the same duration. This should be stated explicitly, and
justified (in column generation based approaches, "rounds" to not have the same
duration). } \\
-\textcolor{blue}{\textbf{\textsc{Answer:} }}\\
+\textcolor{blue}{\textbf{\textsc{Answer:} All rounds have the same duration. It is explicitly explained
+ in paragraph ... in section .... This assumption leads to an integer formulation of the optimization problem. The decision variables are binary variables, $X_{t,j}$ for the activation ($X_{t,j}=1$) or not ($X_{t,j}=0$) of the sensor $j$ during the round $t$. Column generation based approaches can be applied when the decision variables of the optimization problem are continuous. In this case the variables are the time intervals during which the sensors of a cover set (not necessarily disjoint) are active. The time intervals are not equal. Concerning the choice of round duration of equal length, 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, 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 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. }}\\
\noindent {\ding{90} Page 11 in Table 1
$W_\Theta$ should be replaced with $W_\theta$
