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%\title{Response to the reviewers of \bf "Perimeter-based Coverage Optimization to Improve Lifetime in Wireless Sensor Networks"}
%\author{Ali Kadhum Idrees, Karine Deschinkela, Michel Salomon and Raphael Couturier}

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\vspace{-0.5cm}\hspace{-2cm}FEMTO-ST Institute, UMR 6714 CNRS

\hspace{-2cm}University Bourgogne Franche-Comt\'e

\hspace{-2cm}IUT Belfort-Montb\'eliard, BP 527, 90016 Belfort Cedex, France.

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Detailed changes and addressed issues in the revision of the article

``Multiround Distributed Lifetime Coverage Optimization \\
 Protocol in Wireless Sensor Networks''\\
  

by Ali Kadhum Idrees, Karine Deschinkel, Michel Salomon, and Raph\"ael Couturier

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Dear Editor and Reviewers,

First of all, we would like to thank you very much for your kind help to improve
our article  named: `` Multiround Distributed Lifetime Coverage Optimization
Protocol in Wireless Sensor Networks
''.  We  highly  appreciate the  detailed  valuable
comments of the reviewers on our  article. The suggestions are quite helpful for
us and we incorporate them in the revised article. We are happy to submit to you
a revised version that considers most of your remarks and suggestions to improve
the quality of our article.

As below, we  would like to clarify  some of the points raised  by the reviewers
and we hope the reviewers and the  editors will be satisfied by our responses to
the comments and the revision for the original manuscript.



\section*{Response to Reviewer No. 1 Comments}

The paper entitled "Multiround Distributed Lifetime Coverage Optimization
Protocol in Wireless Sensor Networks" introduces MuDiLCO, a distributed protocol
to enhance the use of WSN by splitting the network lifetime into periods, and by
breaking each sensing activity of a period into a series of rounds. A sensor
called the leader is elected, and based on local data, solves a Mixed Integer
Linear Program in order to schedule the activity of its neighbors over the
sensing rounds of the current period.

The contribution of this paper is interesting, but probably needs to be deepened
in order to reach the standards of a publication in Ad Hoc Networks.\\


\noindent\textcolor{black}{\textbf{MAJOR COMMENTS:}} \\

\noindent {\bf  1.}     Page 6, Section 3.2
The author didn't explain how subregions are created. This is an important
point, as clustering may have a significant impact on solution quality. Not only
the size of the subregion should be discussed and analyzed, but also the
clustering strategy.\\

\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
The objective function (5) of the Mixed Integer Linear Program appears to be
very questionable. Indeed overcoverage and undercoverage may compensate each
other, so the same objective value may represent two incomparable situations. It
seems that the semantic of the objective function is not well defined, as one
may wonder what exactly is (quantitatively speaking) the problem objective.
Coverage breach is obviously an issue in WSN, but why penalizing overcoverage? A
two-phase approach where breach is minimized first, and then overcoverage is
minimized would probably make more sense.
    \\

\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.  }}\\



\noindent {\bf 3.}   Page 9
In the MILP formulation, it is possible that some point p is never covered at
all, which means that some part of the area to monitor may never be monitored by
the WSN. The authors are referred to "alpha-coverage to extend network lifetime
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:} 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
The criterion "Energy Consumption" is the average consumption per round. But the
duration of a round is a feature that can be arbitrarily set in the algorithm.
Computing the average energy consumption per unit of time over the network
lifetime would be better, as it is independent from the number and duration of
rounds.  \\

\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.}}



\noindent {\bf 5.}    Page 15-18
Figures 2-6 mention four different versions of MuDiLCO. The performance of these
different versions should be analyzed with more details for each figure.
Alternatively, the authors may remove some versions of MuDiLCO if they do not
bring any valuable insight. \\


\textcolor{blue}{\textbf{\textsc{Answer :}        }}


\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
efficient as other versions. Why not using a heuristic (or a metaheuristic) for
addressing the problem instead of using an exact solver? A straightforward and
easily implementable idea to cut CPU time would be to return the best feasible
solution found by the solver after a given time threshold for example. Doing so
is very likely to save time and energy, and to improve the results of MuDiLCO-7
in particular.  \\


\textcolor{blue}{\textbf{\textsc{Answer :}        }}


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\noindent\textcolor{black}{\textbf{MINOR COMMENTS:}} \\

\noindent  {\ding{90}    Page 2
The paragraph that begins with "The remainder of the paper is organized as
follows" should mention the content of Section 5.    }  \\

\textcolor{blue}{\textbf{\textsc{Answer:}  Right, fixed.  Section 5 is included as a subsection 4.4 within section 4.    }}\\

\noindent  {\ding{90}   Page 3
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
very popular in WSN.     } \\

\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:}          }}\\

\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:} 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 $W_\theta$
              } \\

\textcolor{blue}{\textbf{\textsc{Answer:} Right, fixed }}.\\

\noindent {\ding{90}    Page 12
Don't italicize "mW" in "equal to 02575 mW"            } \\

\textcolor{blue}{\textbf{\textsc{Answer:} Right, fixed }}.\\

\noindent {\ding{90}  Page 14
ML is not defined (see the denominator of the large, unnumbered formula that
defines EC).          }  \\

\textcolor{blue}{\textbf{\textsc{Answer:} Right, fixed }}.\\

\noindent {\ding{90}  Page 19 Section 6

"Sensing phase itself divided into T rounds" -> T should be italic.           } 
\\

\textcolor{blue}{\textbf{\textsc{Answer:} Right, fixed }}.\\

\noindent {\ding{90}  Page 18 Section 5.5
The name of the solver used to solve the Mixed Integer Linear Program should be
given.   }  \\

\textcolor{blue}{\textbf{\textsc{Answer:}   Right, fixed         }}.\\


We are very grateful to the  reviewers who, by their recommendations, allowed us
to improve the quality of our article.
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Best regards\\
The authors
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