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13 %\title{Response to the reviewers of \bf "Perimeter-based Coverage Optimization to Improve Lifetime in Wireless Sensor Networks"}
14 %\author{Ali Kadhum Idrees, Karine Deschinkela, Michel Salomon and Raphael Couturier}
22 \vspace{-0.5cm}\hspace{-2cm}FEMTO-ST Institute, UMR 6714 CNRS
24 \hspace{-2cm}University Bourgogne Franche-Comt\'e
26 \hspace{-2cm}IUT Belfort-Montb\'eliard, BP 527, 90016 Belfort Cedex, France.
31 Detailed changes and addressed issues in the revision of the article
33 ``Multiround Distributed Lifetime Coverage Optimization \\
34 Protocol in Wireless Sensor Networks''\\
36 by Ali Kadhum Idrees, Karine Deschinkel, Michel Salomon, and Raph\"ael Couturier
42 Dear Editor and Reviewers,
44 First of all, we would like to thank you very much for your kind help in
45 improving our article named: `` Multiround Distributed Lifetime Coverage
46 Optimization Protocol in Wireless Sensor Networks ''. We highly appreciate the
47 detailed and valuable comments of the reviewers on our article. The suggestions
48 have been very helpful to us and we have incorporated them in the revised
49 article. We are happy to submit to you a revised version that considers most of
50 your remarks and suggestions to improve the quality of our article.
52 Below, we would like to clarify some of the points raised by the reviewers
53 and we hope the reviewers and the editors will be satisfied by our responses to
54 the comments and the revision for the original manuscript.
56 \section*{Response to Reviewer No. 1 Comments}
58 The paper entitled ``Multiround Distributed Lifetime Coverage Optimization
59 Protocol in Wireless Sensor Networks'' introduces MuDiLCO, a distributed
60 protocol to enhance the use of WSN by splitting the network lifetime into
61 periods, and by breaking each sensing activity of a period into a series of
62 rounds. A sensor called the leader is elected, and based on local data, solves
63 a Mixed Integer Linear Program in order to schedule the activity of its
64 neighbors over the sensing rounds of the current period.
66 The contribution of this paper is interesting, but probably needs to be deepened
67 in order to reach the standards of a publication in Ad Hoc Networks.\\
69 \noindent\textcolor{black}{\textbf{MAJOR COMMENTS:}}\\
71 \noindent {\bf 1.} Page 6, Section 3.2 The author didn't explain how subregions
72 are created. This is an important point, as clustering may have a significant
73 impact on solution quality. Not only the size of the subregion should be
74 discussed and analyzed, but also the clustering strategy.\\
76 \textcolor{blue}{\textbf{\textsc{Answer:} In our work, we assume that the
77 sensors are deployed almost uniformly and with high density over the region.
78 So we only need to fix a regular division of the region into subregions to
79 make the problem tractable. The subdivision has been made so that the number of
80 hops between any pairs of sensors inside a subregion is less than or equal
82 % In particular, we discuss the number of subregions in......
85 \noindent {\bf 2.} Page 8 The objective function (5) of the Mixed Integer Linear
86 Program appears to be very questionable. Indeed overcoverage and undercoverage
87 may compensate each other, so the same objective value may represent two
88 incomparable situations. It seems that the semantic of the objective function is
89 not well defined, as one may wonder what exactly is (quantitatively speaking)
90 the problem objective. Coverage breach is obviously an issue in WSN, but why
91 penalizing overcoverage? A two-phase approach where breach is minimized first,
92 and then overcoverage is minimized would probably make more sense.\\
94 \textcolor{blue}{\textbf{\textsc{Answer:} As mentioned in the paper the integer
95 program is based on the model proposed by F. Pedraza, A. L. Medaglia, and
96 A. Garcia (``Efficient coverage algorithms for wireless sensor networks'')
97 with some modifications. Their initial approach consisted first in finding
98 the maximum coverage obtainable using the available sensors and then in using
99 this information as input to the problem of minimizing the overcoverage. But
100 this two-steps approach is time consuming. The originality of the model is
101 to solve both objectives in a parallel fashion. Nevertheless the weights
102 $W_\theta$ and $W_U$ must be properly chosen so as to guarantee that the
103 maximum number of points which are covered during each round is maximum. By
104 choosing $W_{U}$ much larger than $W_{\theta}$, the coverage of a
105 maximum of primary points is ensured. Then for the same number of covered
106 primary points, the solution with a minimal number of active sensors is
109 \noindent {\bf 3.} Page 9 In the MILP formulation, it is possible that some
110 point p is never covered at all, which means that some part of the area to
111 monitor may never be monitored by the WSN. The authors are referred to
112 ``$\alpha$-coverage to extend network lifetime on wireless sensor networks'',
113 Optim. Lett. 7, No. 1, 157-172 (2013) by Gentilli et al to enforce a constraint
114 on the minimum coverage of each point.\\
116 \textcolor{blue}{\textbf{\textsc{Answer:} As previously explained, the model
117 with the appropriate weights ensures that a maximum number of points are
118 covered by the set of still alive sensors. The coverage is measured through
119 the performance metrics ``coverage ratio''. This one remains around 100\% as
120 long as possible (as long as there are enough alive sensors to cover all
121 primary points) and then decreases. The problem introduced in
122 ``$alpha$-coverage to extend network lifetime on wireless sensor networks''
123 by Gentilli is quite different. In this problem, the coverage ratio is fixed
124 to a predetermined value ($\alpha$) and the amount of time during which the
125 network can satisfy a target coverage greater than $\alpha$ is
128 \noindent {\bf 4.} Page 13 The criterion ``Energy Consumption'' is the average
129 consumption per round. But the duration of a round is a feature that can be
130 arbitrarily set in the algorithm. Computing the average energy consumption per
131 unit of time over the network lifetime would be better, as it is independent
132 from the number and duration of rounds.\\
134 \textcolor{blue}{\textbf{\textsc{Answer :} Yes, you are right. It is possible to
135 obtain the average energy consumption per unit of time by dividing the
136 criterion defined in section~4.3 by the round duration.}}
138 \noindent {\bf 5.} Page 15-18 Figures 2-6 mention four different versions of
139 MuDiLCO. The performance of these different versions should be analyzed with
140 more details for each figure. Alternatively, the authors may remove some
141 versions of MuDiLCO if they do not bring any valuable insight. \\
143 \textcolor{blue}{\textbf{\textsc{Answer :} Right. Therefore we have completely
144 re-written section 5 to highlight the most significant results.}}
147 \noindent {\bf 6.} Page 19 (most major point) The authors state that solving
148 the Mixed Integer Linear Program is time-consuming, and use this point for
149 explaining why MuDiLCO-7 is not as efficient as other versions. Why not using a
150 heuristic (or a metaheuristic) for addressing the problem instead of using an
151 exact solver? A straightforward and easily implementable idea to cut CPU time
152 would be to return the best feasible solution found by the solver after a given
153 time threshold for example. Doing so is very likely to save time and energy, and
154 to improve the results of MuDiLCO-7 in particular.\\
156 \textcolor{blue}{\textbf{\textsc{Answer :} Your remark is very interesting. We
157 have observed that the optimal solution of the integer program is often
158 obtained after the exploration of very few nodes of the Branch-and-Bound
159 tree. Therefore we conducted new simulations by applying your idea. That is
160 to say we have stopped the resolution of the Branch-and-Bound method after a
161 time threshold empirically defined and we retain the best feasible solution
162 found by the solver. This approach allows to significantly improve the
163 results with multirounds, especially for MuDiLCO-7, as shown in the paper.}}
167 \noindent\textcolor{black}{\textbf{MINOR COMMENTS:}} \\
169 \noindent {\ding{90} Page 2 The paragraph that begins with ``The remainder of
170 the paper is organized as follows'' should mention the content of Section 5.
173 \textcolor{blue}{\textbf{\textsc{Answer:} Right, fixed.}}\\
175 \noindent {\ding{90} Page 3 The sentence ``the centralized approaches usually
176 suffer from the scalability problem, making them less competitive as the
177 network size increase'' should probably be tempered: heuristics and
178 metaheuristics can handle very large and centralized problems (even if exact
179 approaches can't), and these approaches are empirically very popular in
182 \textcolor{blue}{\textbf{\textsc{Answer:} Right, fixed.}}\\
184 \noindent {\ding{90} Page 5 ``The choice of number and locations of primary
185 points is the subject of another study not presented here''. The authors
186 should provide at least one reference about the aforementioned study.}\\
188 \textcolor{blue}{\textbf{\textsc{Answer:} Right. We have included a section
189 (section~5.1) dedicated to the choice and the number of primary points.}}\\
191 \noindent {\ding{90} Page 6, Figure 1: All rounds seem to have the same
192 duration. This should be stated explicitly, and justified (in column
193 generation based approaches, ``rounds'' do not have the same duration).}\\
195 \textcolor{blue}{\textbf{\textsc{Answer:} All rounds have the same duration. It
196 is explicitly explained in the second paragraph of section~3.2. This
197 assumption leads to an integer formulation of the optimization problem. The
198 decision variables are binary variables, $X_{t,j}$ for the activation
199 ($X_{t,j}=1$) or not ($X_{t,j}=0$) of the sensor $j$ during round $t$.
200 Column generation based approaches can be applied when the decision
201 variables of the optimization problem are continuous. In this case the
202 variables are the time intervals during which the sensors of a cover set
203 (not necessarily disjoint) are active. The time intervals are not equal.
204 Concerning the choice of round duration of equal length, it is correlated
205 with the types of applications, with the amount of initial energy in sensors
206 batteries, and also with the duration of the exchange phase. All
207 applications do not have the same Quality of Service requirements. In our
208 case, the information exchange is executed every hour, but the length of the
209 sensing period could be reduced and adapted dynamically. On the one hand, a
210 small sensing period would allow the network to be more reliable but would
211 have higher communication costs. On the other hand, the choice of a long
212 duration may cause problems in case of node failures during the sensing
215 \noindent {\ding{90} Page 11 in Table 1 $W_\Theta$ should be replaced with
218 \textcolor{blue}{\textbf{\textsc{Answer:} Right, fixed.}}\\
220 \noindent {\ding{90} Page 12 Don't italicize ``mW'' in ``equal to 02575 mW'' }\\
222 \textcolor{blue}{\textbf{\textsc{Answer:} Right, fixed.}}\\
224 \noindent {\ding{90} Page 14 ML is not defined (see the denominator of the
225 large, unnumbered formula that defines EC).}\\
227 \textcolor{blue}{\textbf{\textsc{Answer:} Right, fixed.}}\\
229 \noindent {\ding{90} Page 19 Section 6 ``Sensing phase itself divided into T
230 rounds'' -> T should be italic.}\\
232 \textcolor{blue}{\textbf{\textsc{Answer:} Right, fixed.}}\\
234 \noindent {\ding{90} Page 18 Section 5.5
235 The name of the solver used to solve the Mixed Integer Linear Program should be
238 \textcolor{blue}{\textbf{\textsc{Answer:} Right, fixed.}}\\
240 We are very grateful to the reviewers who, by their recommendations, allowed us
241 to improve the quality of our article.
