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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.

\bigskip

\begin{center}
On the decision for the article

``Multiround Distributed Lifetime Coverage  Optimization \\ Protocol in Wireless
Sensor Networks''\\
  
by Ali Kadhum Idrees, Karine Deschinkel, Michel Salomon, and Raph\"ael Couturier

\medskip

\end{center}

\noindent Dear Editor,

After a careful reading of your  last decision letter, we are quite disappointed
by  the  rejection  of  our article  named:  ``Multiround  Distributed  Lifetime
Coverage  Optimization Protocol  in  Wireless Sensor  Networks'', submitted  for
publication  in  the AD  HOC  NETWORKS  journal.  Indeed,  we have  started  the
submission  process in  September 2014  and obtained  the comments  of only  ONE
reviewer during July 2015. Its suggestion  were very helpful and we incorporated
them in the revised article submitted in September 2015.

In particular,  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, as it  was suggested by the reviewer.  We made our
best to carefully address the issues raised  by the referee and revise our paper
accordingly.  So we  would like  to clarify  some of  the points  raised by  the
reviewer, since some them seem not to be not relevant or fair.

\noindent {\bf 1.}   The authors have partially taken into  account the comments
of my  previous review. Additional content  has been added, but  these additions
are sometime confusing.\\

\textcolor{blue}{\textbf{\textsc{Answer:} The reviewer does not clearly indicate
    which addition is confusing.}}\\

\noindent {\bf  2.} The  answer that  the authors have  provided to  my comments
should have been inserted into the paper,  this is not always the case (i.e., my
comment about the duration of the rounds).\\

\textcolor{blue}{\textbf{\textsc{Answer:}  We clearly  indicated in  Section~3.2
    that the rounds  are of equal duration and we  explained that this parameter
    should be set according to the types  of application (see our answer in part
    ``minor comments'' in our previous answer).}}\\

\noindent {\bf  3.} In Section~3.1,  all nodes  are assumed to  be ``homogeneous
from  the  point of  view  of  energy provision''.  Why  is  such an  hypothesis
necessary?   This assumption  is likely  to be  satisfied only  when the  WSN is
deployed for the first  time, with new sensors. But after  using the network for
the first  time, the  aforementioned hypothesis  is not  likely to  be satisfied
again.\\

\textcolor{blue}{\textbf{\textsc{Answer:} Maybe  the honorable  reviewer misread
    the  sentence  in   Section~3.1:  ``We  assume  that  all   nodes  are  {\bf
      homogeneous} in  terms of  communication and processing  capabilities, and
    {\bf heterogeneous} from the point of view of energy provision.'' }}\\

\noindent {\bf  4.}  The  last paragraph  of Section 3.1  is very  confusing. It
seems  that the  author  attempt  to propose  area  coverage  instead of  target
coverage,  but instead  of defining  ``primary points''  inside the  area to  be
covered, they  define points inside the  sensing range of the  sensors, that are
obviously covered when the corresponding sensor is active. There exists works in
the literature for area coverage, the authors should read them.\\

\textcolor{blue}{\textbf{\textsc{Answer:}  This remark is rather  offensive. Of
    course we read  literature for area coverage.  We use  the metric ``Coverage
    Ratio'' (defined  in Section~4.3) to measure  how much the area  is covered.
    But the optimization process to decide which  sensor has to be active or not
    in each  round is based on  the coverage of  only a specified set  of points
    called primary points. So the area  coverage problem is transformed into the
    target coverage problem.}}\\

\noindent {\bf 5.} In Section 3.2, the reason why a subregion is defined in such
a way that  the distance between any  two sensors in the same  subregion is less
than 3 hops  is not justified. The  reader is not told if  the proposed protocol
works better  when the  number of subregions  is low or  high. No  algorithm for
defining the subregions is given. It pertains to a clustering problem, for which
a large number of algorithms exists, but without a sound definition of what is a
'good'  partitioning for  the  proposed  protocol, the  reader  cannot select  a
clustering algorithm. \\

\textcolor{blue}{\textbf{\textsc{Answer:}   The  choice   of  the   number  of
    subregions  is  discussed  in  the   last  paragraph  of  Section~4.2.  More
    particularly, we explain that this parameter should be chosen by taking into
    account  the  trade-off between  the  benefit  of the  optimization  problem
    induced by the number of sensors in a subregion and the time needed to solve
    it.  As said  at  the beginning  of  Section~3.2, the  area  of interest  is
    ``divided   into    regular   homogeneous   subregions   using    a   simple
    divide-and-conquer algorithm.''}}\\

\noindent {\bf  6.} The  ILP of  Section 3.5 aims  at addressing  a bi-objective
problem. Since  full coverage  is required,  the ILP  should first  ensure total
coverage,  and then  minimize  overcoverage. The  current ILP  is  not a  proper
formulation for reaching this objective,  as undercoverage can be compensated by
overcoverage.  The primary  and secondary  objective are  then mixed  up into  a
single objective function with no interpretable meaning. Of course, an objective
function value of 100  is better than an objective value of  101, but one cannot
tell if  a gap of 1  makes a major difference  or not. The objectives  should be
distinguished,  and  the  problem  should   be  addressed  as  a  multiobjective
optimization problem.\\

\textcolor{blue}{\textbf{\textsc{Answer:} As mentioned in the paper, the ILP of
    Section~3.5 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. The  originality of  the model  is to
    solve both  objectives in  a parallel fashion:  maximizing the  coverage and
    minimizing the  overcoverage. Nevertheless the weights  $w_\theta$ and $w_U$
    must be properly chosen  so as to guarantee that the  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.  It has been formally
    proven in the  paper mentioned above that this guarantee  is satisfied for a
    constant weighting $w_{U}$ greater  than $\left|P\right|$ (when $w_{\theta}$
    is fixed to 1).}}

\bigskip
\noindent  {\bf 6.}  The content  of Section  4.3, where  different metrics  are
proposed to assess the solution quality, is a sign of an ill formulated problem:
how to comment  on the performance of  an algorithm on a  criterion (say network
lifetime) if the ILP does not take this objective into account? The performances
with these  additional objectives  are likely  to be related  to the  ILP solver
used: many optimal solutions  to the ILP of Section 3 may  have a very different
impact  in  terms  of  these   additional  metrics.  Hence,  measuring  them  is
pointless.\\

\textcolor{blue}{\textbf{\textsc{Answer:} We disagree  this remark. It is quite
    possible to optimize  a criterion to have  an impact on another  one. In the
    problem formulation proposed here, the number of active sensors is minimized
    in each round for a maximal  level of coverage. Limiting the activation time
    of each sensor has  a direct impact on its lifetime  and consequently on the
    network lifetime, as shown in our experimental results. For example, such an
    idea is used in the models developed for brachytherapy treatment planning to
    improve the quality of a  dose distribution ("Comparison of inverse planning
    simulated annealing and geometrical optimization for prostate high-dose-rate
    brachytherapy", I-Chow J. Hsu1, E.   Lessard, V. Weinberg, J.  Pouliot, {\it
      Brachytherapy} Volume 3,  Issue 3, 2004, Pages 147-152):  the objective in
    the problem  formulation is to  minimize a  weighted sum of  the differences
    between prescribed  doses and  obtained doses  in reference  points, whereas
    many criterion (like dose-volume histograms,  conformal index COIN) are used
    for quantitative evaluation of dose plans.}}\\
%si vous avez d'autres exemples plus parlants?

We  hope  that  these  observations  will allow  you  to  revise  your  decision
concerning our  manuscript. If possible,  we would like  to have comments  of an
additional reviewer.

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Best regards\\
The authors
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\end{document}
