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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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\today
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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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\begin{center}
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  in
improving  our  article  named:  ``  Multiround  Distributed  Lifetime  Coverage
Optimization Protocol in Wireless Sensor  Networks ''.  We highly appreciate the
detailed and valuable comments of the  reviewers on our article. The suggestions
have  been very  helpful to  us and  we have  incorporated 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.

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  our  work,  we  assume  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 has been made so 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, A.  L. Medaglia, and
    A. Garcia  (``Efficient coverage algorithms for  wireless sensor networks'')
    with some modifications.  Their initial approach consisted  first in finding
    the maximum coverage obtainable using the  available sensors and then in using
    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 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.  }}\\

\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 by the set of still  alive sensors. The coverage is measured through
    the performance metrics ``coverage ratio''. This one 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~4.3 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 :}  Right. Therefore 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 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 :}  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   significantly improve the
    results with multirounds, especially for MuDiLCO-7, as shown in the paper.}}

\bigskip

\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.}}\\

\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  empirically 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:}  Right.  We  have  included a  section
    (section~5.1) 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'' do not have the same duration).}\\

\textcolor{blue}{\textbf{\textsc{Answer:} All rounds have  the same duration. It
    is  explicitly  explained in  the  second  paragraph of  section~3.2.   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  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, the 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 node  failures 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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