X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/LiCO.git/blobdiff_plain/ec9271bc457e5e1614e0f874a640c20351334c66..8274ac64b1e11ea5647ca1a0d1903038ac427f7a:/PeCO-EO/reponse.tex

diff --git a/PeCO-EO/reponse.tex b/PeCO-EO/reponse.tex
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--- a/PeCO-EO/reponse.tex
+++ b/PeCO-EO/reponse.tex
@@ -19,260 +19,514 @@
 \today
 \end{flushright}%
 
-\vspace{-0.5cm}\hspace{-2cm}FEMTO-ST Institute, UMR 6714
+\vspace{-0.5cm}\hspace{-2cm}FEMTO-ST Institute, UMR 6174 CNRS
 
-\hspace{-2cm}University of Franche-Comt\'e
+\hspace{-2cm}University Bourgogne Franche-Comt\'e
 
-\hspace{-2cm}IUT Belfort-MontbÃ©liard, BP 527, 90016 Belfort Cedex, France.
+\hspace{-2cm}IUT Belfort-Montb\'eliard, BP 527, 90016 Belfort Cedex, France.
 
 \bigskip
 
 \begin{center}
 Detailed changes and addressed issues in the revision of the article
 
-"Perimeter-based Coverage Optimization to Improve Lifetime in Wireless Sensor Networks"\\
+``Perimeter-based Coverage Optimization \\
+to Improve Lifetime in Wireless Sensor Networks''\\
 
-by Ali Kadhum Idrees, Karine Deschinkel Michel Salomon, Rapahel Couturier
+by Ali Kadhum Idrees, Karine Deschinkel, Michel Salomon and Raph\"ael Couturier
+
+\medskip
 
-\bigskip
 \end{center}
 Dear Editor and Reviewers,
 
-First of all, we would like to thank you very much for your kind help to improve our article named:
-"Perimeter-based Coverage Optimization to Improve Lifetime 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 of improvement 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 with our responses to the comments and the revision for the original manuscript. \\
+First of all, we would like to thank you very much for your kind help to improve
+our article  named: ``Perimeter-based Coverage Optimization  to Improve Lifetime
+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.
 
 %Journal: Engineering Optimization
 %Reviewer's Comment to the Author Manuscript id GENO-2015-0094
 %Title: \bf "Perimeter-based Coverage Optimization to Improve Lifetime in Wireless Sensor Networks"
 %Authors: Ali Kadhum Idrees, Karine Deschinkela, Michel Salomon and Raphael Couturier
 
-
 \section*{Response to Reviewer No. 1 Comments}
 
-This paper proposes a scheduling technique for WSN to maximize coverage and network lifetime. The novelty of this paper is the integration of an existing perimeter coverage measure with an existing integer linear programming model. Here are few comments:\\
-
-\noindent {\bf 1.} The paper makes use of the existing integer optimization model to govern the state of each sensor node within the WSN to maximize coverage and network lifetime. This formulation of the  coverage problem is different from the literature in the sense that they use the perimeter coverage measures to optimize coverage as opposed to the targets/points coverage. The methodology uses existing methods and the original contribution lies only in the application of these methods for the coverage scheduling problem.\\
-
-\textcolor{blue}{\textbf{\textsc{Answer:}                             }}.\\
-
-
-\noindent {\bf 2.} The theory seems mathematically sound. However, the assumption made on the selection criteria for the leader seems too vague.  \\
-
-\textcolor{blue}{\textbf{\textsc{Answer:}  The selection criteria for the leader inside each subregion is explained in page 8, lines 50-51. After information exchange among the sensor nodes in the subregion, each node will have all required information to decide if it is a leader or not. The decision is based on selecting the sensor node that have a larger number of one-hop neighbors. If there is more than one sensor node has the same number of one-hop neighbors, the node that has larger remaining energy will be selected as a leader. If there is more than one sensor node with the same number of neighbors and remaining energy, the sensor node that has larger index will be selected as a leader. In fact, we gave a high priority to the number of neighbors to reduce the communication energy consumption  }}.\\
-
-
-\noindent {\bf 3.} The communication and information sharing required to cooperate and make these
-decisions was not discussed.  \\
-
-\textcolor{blue}{\textbf{\textsc{Answer:}  The communication and information sharing required to cooperate and make these decisions was discussed in page 8, lines 48-49}}.\\
-
-
-
-\noindent {\bf 4.} The definitions of the undercoverage and overcoverage variables are not clear. I suggest
-adding some information about these values, since without it, you cannot understand how M and V are computed for the optimization problem.  \\
-
-\textcolor{blue}{\textbf{\textsc{Answer:}                    }}.\\
-
-
-
-\noindent {\bf 5.} Can you mathematically justify how you chose the values of alpha and beta? This is not
-very clear. I would suggest possibly adding more results showing how the algorithm performs with different alphas and betas.  \\
-
-\textcolor{blue}{\textbf{\textsc{Answer:}                }}.\\
-
-
-
-\noindent {\bf 6.} The authors have performed a thorough review of existing coverage methodologies.
-However, the clarity in the literature review is a little off. Some of the descriptions of the method
-s used are very vague and do not bring out their key contributions. Some references are not consistent and I suggest using the journals template to adjust them for overall consistency.   \\
-
-\textcolor{blue}{\textbf{\textsc{Answer:}                               }}.\\
-
-
-
-\noindent {\bf 7.} The methodology is implemented in OMNeT++ (network simulator) and tested against 2 existing algorithms and a previously developed method by the authors. The simulation results are thorough and show that the proposed method improves the coverage and network lifetime compared with the 3 existing methods. The results are similar to previous work done by their team.   \\
-
-\textcolor{blue}{\textbf{\textsc{Answer:}                             }}.\\
-
-
-\noindent {\bf 8.}  Since this paper is attacking the coverage problem, I would like to see more information on the amount of coverage the algorithm is achieving. It seems that there is a tradeoff in this algorithm that allows the network to increase its lifetime but does not improve the coverage ratio. This may be an issue if this approach is used in an application that requires high coverage ratio.   \\
-
-\textcolor{blue}{\textbf{\textsc{Answer:}                                 }}.\\
-
-%%%%%%%%%%%%%%%%%%%%%%  ENGLISH and GRAMMER %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-
-\noindent\textcolor{black}{\textbf{\Large English and Grammar:}} \\
-
-\noindent {\ding{90} The first paragraph of every section is not indented.  }  \\
-
-\textcolor{blue}{\textbf{\textsc{Answer:} Corrected. The first paragraph of every section is indented in the new version. }}.\\
-
-
-\noindent {\ding{90} You seem to be writing in the first person. I suggest rewriting sentences that include âweâ âourâ or âIâ in the third person. (There are too many instances to list them all. They are easily found using the find tool.)  }  \\
-
-\textcolor{blue}{\textbf{\textsc{Answer:}      }}.\\
-
-
-\noindent {\ding{90}  Run-on sentence: Page 2 lines 43-48}  \\
-
-\textcolor{blue}{\textbf{\textsc{Answer:}       }}.\\
-
-
+This paper  proposes a  scheduling technique  for WSN  to maximize  coverage and
+network lifetime.  The novelty of this  paper is the integration  of an existing
+perimeter  coverage   measure  with  an  existing   integer  linear  programming
+model. Here are few comments:\\
+
+\noindent {\bf  1.} The  paper makes  use of  the existing  integer optimization
+model  to govern  the state  of  each sensor  node  within the  WSN to  maximize
+coverage  and network  lifetime. This  formulation  of the  coverage problem  is
+different from the literature in the  sense that they use the perimeter coverage
+measures to  optimize coverage  as opposed to  the targets/points  coverage. The
+methodology uses existing methods and the original contribution lies only in the
+application of these methods for the coverage scheduling problem.\\
+
+\textcolor{blue}{\textbf{\textsc{Answer:}  To  the  best of  our  knowledge,  no
+    integer  linear programming  based on  perimeter coverage  has ever been  
+    proposed in the literature.  As specified in the paper, in  Section 4, it is
+    inspired from a model developed for brachytherapy  treatment planning for
+    optimizing dose distribution. In this  model the deviation between an actual
+    dose  distribution  and  a  required  dose distribution  in  each  organ  is
+    minimized. In  WSN the deviations between  the actual level of  coverage and
+    the required  level are minimized.  Outside this parallel between  these two
+    applications the mathematical formulation is completely different.}}\\
+
+\noindent  {\bf  2.}  The  theory   seems  mathematically  sound.  However,  the
+assumption made on the selection criteria for the leader seems too vague.  \\
+
+\textcolor{blue}{\textbf{\textsc{Answer:} The selection  criteria for the leader
+    inside each subregion is explained page~9, at the end of Section~3.3.  After
+    the information exchange among the sensor  nodes in the subregion, each node
+    will have all the  information needed to decide if it will  be the leader or
+    not. The decision is based on selecting  the sensor node that has the larger
+    number of one-hop neighbors. If this value is the same for many sensors, the
+    node that has the largest remaining energy will be selected as a leader.  If
+    there exists  sensors with the same  number of neighbors and  the same value
+    for the remaining energy, the sensor node that has the largest index will be
+    finally selected as a leader. }}\\
+
+%{\bf In fact, we gave a high priority to the number of neighbors to reduce the communication energy consumption - PAS CLAIR  }}.\\
+
+\noindent  {\bf  3.}  The  communication and  information  sharing  required  to
+cooperate and make these decisions was not discussed.\\
+
+\textcolor{blue}{\textbf{\textsc{Answer:}  The   communication  and  information
+    sharing required to  cooperate and make these decisions is  discussed at the
+    end of page 8.  Position coordinates,  remaining energy, sensor node ID, and
+    number of one-hop neighbors are exchanged.}}\\
+
+\noindent  {\bf  4.}  The  definitions  of  the undercoverage  and  overcoverage
+variables are not  clear. I suggest adding some information  about these values,
+since  without it,  you cannot  understand  how M  and  V are  computed for  the
+optimization problem.\\
+
+\textcolor{blue}{\textbf{\textsc{Answer:} The  perimeter of  each sensor  may be
+    cut in parts called coverage intervals (CI). The level of coverage of one CI
+    is defined as  the number of active sensors neighbors  covering this part of
+    the perimeter. If a given level of  coverage $l$ is required for one sensor,
+    the  sensor is  said to  be undercovered  (respectively overcovered)  if the
+    level  of coverage  of one  of its  CI is  less (respectively  greater) than
+    $l$. In  other terms, we  define undercoverage and overcoverage  through the
+    use of  variables $M_{i}^{j}$  and $V_{i}^{j}$  for one  sensor $j$  and its
+    coverage interval  $i$. If the sensor  $j$ is undercovered, there  exists at
+    least  one of  its CI  (say  $i$) for  which  the number  of active  sensors
+    (denoted by  $l^{i}$) covering this part  of the perimeter is  less than $l$
+    and in this  case : $M_{i}^{j}=l-l^{i}$, $V_{i}^{j}=0$. On  the contrary, if
+    the sensor $j$ is overcovered, there exists at least one of its CI (say $i$)
+    for which  the number of active  sensors (denoted by $l^{i}$)  covering this
+    part of the perimeter is greater than  $l$ and in this case : $M_{i}^{j}=0$,
+    $V_{i}^{j}=l^{i}-l$.   This  explanation  has  been  added in the penultimate
+    paragraph of Section~4.}}\\
+
+\noindent {\bf  5.} Can you mathematically  justify how you chose  the values of
+alpha and  beta? This is  not very clear. I  would suggest possibly  adding more
+results showing how the algorithm performs with different alphas and betas.\\
+
+\textcolor{blue}{\textbf{\textsc{Answer:}  To  discuss   this  point,  we  added
+    Section  5.2.5  in which  we  study  the protocol  performance,  considering
+    $Lifetime_{50}$ and $Lifetime_{95}$ metrics, for different couples of values
+    for alpha  and beta.   Table 4 presents  the results obtained  for a  WSN of
+    200~sensor nodes.  It explains the  value chosen for the simulation settings
+    in Table~2. \\ \indent The choice of alpha and beta should be made according
+    to the  needs of the  application. Alpha should  be large enough  to prevent
+    undercoverage and thus  to reach the highest possible  coverage ratio.  Beta
+    should  be large  enough  to prevent  overcoverage and  thus  to activate  a
+    minimum number of sensors.  The  values of $\alpha_{i}^{j}$ can be identical
+    for all coverage  intervals $i$ of one  sensor $j$ in order  to express that
+    the   perimeter  of   each   sensor  should   be   uniformly  covered,   but
+    $\alpha_{i}^{j}$ values can be differentiated  between sensors to force some
+    regions to be  better covered than others. The choice  of $\beta \gg \alpha$
+    prevents the overcoverage, and so limit  the activation of a large number of
+    sensors, but  as $\alpha$  is low,  some areas may  be poorly  covered. This
+    explains the results obtained for $Lifetime_{50}$ with $\beta \gg \alpha$: a
+    large number of  periods with low coverage ratio.  With  $\alpha \gg \beta$,
+    we favor  the coverage  even if  some areas  may be  overcovered, so  a high
+    coverage ratio  is reached, but a  large number of sensors  are activated to
+    achieve this goal.   Therefore the network lifetime is  reduced.  The choice
+    $\alpha=0.6$ and  $\beta=0.4$ seems to  achieve the best  compromise between
+    lifetime and coverage ratio.}}\\
+
+\noindent {\bf  6.} The  authors have  performed a  thorough review  of existing
+coverage  methodologies.  However,  the clarity  in the  literature review  is a
+little off. Some of the descriptions of the  method s used are very vague and do
+not bring out their key contributions.  Some references are not consistent and I
+suggest using the journals template to adjust them for overall consistency.\\
+
+\textcolor{blue}{\textbf{\textsc{Answer:} References have been carefully checked
+    and seem to be consistent with the journal template. In Section~2, ``Related
+    literature'',  we refer  to papers  dealing  with coverage  and lifetime  in
+    WSN. Each  paragraph of this section  discusses the literature related  to a
+    particular aspect of the problem : 1. types of coverage, 2. types of scheme,
+    3. centralized versus distributed protocols,  4. optimization method. At the
+    end of each  paragraph we position our  approach. We have also  added a last
+    paragraph  about  our  previous  work  on  DiLCO  protocol  to  explain  the
+    difference with PeCO. }}\\
+
+\noindent {\bf 7.} The methodology is implemented in OMNeT++ (network simulator)
+and tested  against 2 existing algorithms  and a previously developed  method by
+the authors.   The simulation results  are thorough  and show that  the proposed
+method improves the  coverage and network lifetime compared with  the 3 existing
+methods. The results are similar to previous work done by their team.\\
+
+\textcolor{blue}{\textbf{\textsc{Answer:} Although  the study conducted  in this
+    paper reuses the  same protocol presented in our previous  work, we focus in
+    this  paper on  the mathematical  optimization model  developed to  schedule
+    nodes  activities.   We deliberately  chose  to  keep the  same  performance
+    indicators to  compare the results  obtained with this new  formulation with
+    other existing algorithms.}}\\
+
+\noindent {\bf 8.}  Since this paper  is attacking the coverage problem, I would
+like  to  see more  information  on  the amount  of  coverage  the algorithm  is
+achieving. It seems that  there is a tradeoff in this  algorithm that allows the
+network to increase  its lifetime but does not improve  the coverage ratio. This
+may be an  issue if this approach  is used in an application  that requires high
+coverage ratio. \\
+
+\textcolor{blue}{\textbf{\textsc{Answer:} Your  remark is very interesting.  Indeed,
+    Figures 8(a) and (b) highlight this  result. The PeCO protocol allows to achieve
+    a coverage  ratio greater than $50\%$  for far more periods  than the others
+    three  methods, but  for applications  requiring  a high  level of  coverage
+    (greater than  $95\%$), the DiLCO method is  more efficient. It is  explained at
+    the end of Section 5.2.4.}}\\
+
+%%%%%%%%%%%%%%%%%%%%%%  ENGLISH and GRAMMAR %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\noindent\textcolor{black}{\textbf{\Large English and Grammar:}}\\
+
+\noindent {\ding{90} The first paragraph of every Section is not indented.}\\
+
+\textcolor{blue}{\textbf{\textsc{Answer:} Right,  fixed. The first  paragraph of
+    every Section is indented in the new version. }}\\
+
+\noindent  {\ding{90} You  seem to  be writing  in the  first person.  I suggest
+  rewriting sentences that include ``we'' ``our'' or ``I'' in the third person. (There
+  are too many instances to list them  all. They are easily found using the find
+  tool.)  }  \\
+
+\textcolor{blue}{\textbf{\textsc{Answer:} It  is very  common to  find sentences
+    with ``we''  and ``our'' in  scientific papers to explain  the work made  by the
+    authors. Nevertheless  we agree with  the reviewer and we  reformulated some
+    sentences in the paper to avoid too many uses of the first person. }}\\
+
+\noindent {\ding{90} Run-on sentence: Page 2 lines 43-48} \\
+
+\textcolor{blue}{\textbf{\textsc{Answer:}  We  rewrote   this  sentence  in  two
+    separated sentences.  }}\\
 
 \noindent {\ding{90} Add an âandâ after the comma on page 3 line 34.}  \\
 
-\textcolor{blue}{\textbf{\textsc{Answer:}   Corrected.  }}.\\
-
-
-\noindent {\ding{90}  âmodel asâ instead of âThanâ on page 10 line 12.}  \\
+\textcolor{blue}{\textbf{\textsc{Answer:} Right, fixed.}}\\
 
-\textcolor{blue}{\textbf{\textsc{Answer:} Corrected. }}.\\
+\noindent {\ding{90} âmodel asâ instead of âThanâ on page 10 line 12.}  \\
 
+\textcolor{blue}{\textbf{\textsc{Answer:} Right, fixed.}}\\
 
 \noindent {\ding{90} âno longerâ instead of âno moreâ on page 10 line 31.}  \\
 
-\textcolor{blue}{\textbf{\textsc{Answer:} Corrected }}.\\
-
+\textcolor{blue}{\textbf{\textsc{Answer:} Right, fixed.}}\\
 
 \noindent {\ding{90} âin the active stateâ add the on page 10 line 34. }  \\
 
-\textcolor{blue}{\textbf{\textsc{Answer:} Corrected }}.\\
-
-
-
-\noindent { \ding{90} Lots of English and grammar mistakes. I recommend rereading the paper line by line and adjusting the sentences that do not make sense.} \\
-
-\textcolor{blue}{\textbf{\textsc{Answer:}      }}.\\
-
+\textcolor{blue}{\textbf{\textsc{Answer:} Right, fixed.}}\\
 
+\noindent  {  \ding{90}  Lots  of  English and  grammar  mistakes.  I  recommend
+  rereading the paper line by line and  adjusting the sentences that do not make
+  sense.} \\
 
+\textcolor{blue}{\textbf{\textsc{Answer:}  The English  of  the  paper has  been
+    carefully revised  and the readability  improved.  The new version  has been
+    checked by an English teacher.}}\\
 
 \section*{Response to Reviewer No. 2 Comments}
-The paper entitled "Perimeter-based Coverage Optimization to Improve Lifetime in Wireless Sensor Networks", by Ali Kadhum Idrees, Karine Deschinkela, Michel Salomon and Raphael Couturier proposes a new protocol for Wireless Sensor Networks called PeCO (Perimeter-based Coverage Optimization protocol) that aims at optimizing the use of energy by conjointly exploiting a spatial and temporal subdivision. The protocol is based on solving a Mixed Integer Linear Program at each leader node, and at each iteration of the protocol. The results obtained by PeCO are compared with three other competitors.
-
-
-\noindent\textcolor{black}{\textbf{\Large MAJOR COMMENTS:}} \\
-
-\noindent {\ding{90} The protocol framework is not described in details. In particular, the spatial and temporal subdivision (page 2, line 11) that is at the core of PeCO, is not described nor justified in much detail. How to implement an efficient spatial subdivision? On page 10, line 11, the number of subdivisions is said to be equal to 16, but the clustering algorithm used is not mentioned. Is this number dependent of the size of the sensing area? Of the number of sensors? Of the sensing range? The proposed protocol cannot be adopted by practitioners if such an important step is not documented. Temporal subdivision suffers from the same lack of description and justification: why should time intervals have the same duration? If they have the same duration, how should this common duration should be chosen?   }  \\
-
-\textcolor{blue}{\textbf{\textsc{Answer:}                                 }}.\\
-
-
-\noindent {\ding{90}  Page 9, Section 4, is the Perimeter-based coverage problem NP-hard? This question is important for justifying the use of a Mixed Integer Linear Programming model. }  \\
-
-\textcolor{blue}{\textbf{\textsc{Answer:}                                       }}.\\
-
-
-\noindent {\ding{90}  Page 9, the major problem with the present paper is, in my opinion, the objective function of the Mixed Integer Linear Program (2). It is not described in the paper, and looks like an attempt to address a multiobjective problem (like minimizing overcoverage and undercoverage). However, using a weighted sum is well known not to be an efficient way to address biobjective problems. The introduction of various performance metrics in Section 5.1 also suggests that the authors have not decided exactly which objective function to use, and compare their protocols against competitors without mentioning the exact purpose of each of them. If the performance metrics list given in Section 5.1 is exhaustive, then the authors should mention at the beginning of the paper what are the aims of the protocol, and explain how the protocol is built to optimize these objectives. }  \\
-
-\textcolor{blue}{\textbf{\textsc{Answer:}                                           }}.\\
-
-
-\noindent {\ding{90} Page 11 Section 5.2, the sensor nodes are said to be based on Atmels AVR ATmega103L microcontroller. If I am not mistaken, these devices have 128 KBytes of memory, and I didn't find any clue that they can run an operating system like Linux. This point is of primary importance for the proposed protocol, since GLPK (a C API) is supposed to be executed by the cluster leader. In addition to that, GLPK requires a non negligible amount of memory to run properly, and the Atmels AVR ATmega103L microcontroller might be insufficient for that purpose. The authors are urged to provide references of previous works showing that these technical constraints are not preventing their protocol to be implemented on the aforementioned microcontroller. Then, on page 13, in Section "5.2.3 Energy Consumption", the estimation of $E_p^com$ for the considered microcontroller seems quite challenging and should be carefully documented. Indeed, this is a key point in providing a fair comparison of PeCO with its competitors.  }  \\
-
-\textcolor{blue}{\textbf{\textsc{Answer:}                                              }}.\\
-
-
-
-
-\noindent\textcolor{black}{\textbf{\Large MINOR COMMENTS:}} \\
-
-
-\noindent {\ding{90} Page 12, lines 7-15, the authors mention that DiLCO protocol is close to PeCO. This should be mentioned earlier in the paper, ideally in Section 2 (Related Literature), along with the detailed description of DESK and GAF, the competitors of the proposed protocol, PeCO.  }  \\
 
-\textcolor{blue}{\textbf{\textsc{Answer:}       }}.\\
-
-
-
-\noindent {\ding{90} Page 2, line 20, "An optimal scheduling" should be replaced with "An optimal schedule" }  \\
-
-\textcolor{blue}{\textbf{\textsc{Answer:} Corrected }}.\\
-
-
-
-\noindent {\ding{90}  Page 4, we first read (line 23) "we assume that each sensor node can directly transmit its measurements to a mobile sink", then on line 30, "We also assume that the communication range Rc satisfies $Rc >=2Rs$. In fact, Zhang and Hou (2005) proved that if the transmission range fulfills the previous hypothesis, the complete coverage of a convex area implies connectivity among active nodes.". These two assumptions seems redundant. }  \\
-
-\textcolor{blue}{\textbf{\textsc{Answer:}          }}.\\
-
-
-
-\noindent {\ding{90}   Page 4, line 37, a definition for k-covered is missing (the sentence is an equivalence property).}  \\
-
-\textcolor{blue}{\textbf{\textsc{Answer:}        }}.\\
-
-
-
-
-\noindent {\ding{90}  Page 5, lines 34 and 37, replace [0, $2\pi$] with [0, $2\pi$) }  \\
-
-\textcolor{blue}{\textbf{\textsc{Answer:} Corrected }}.\\
-
-
-
-
-\noindent {\ding{90}  Page 5, line 36 and 43, replace "figure 2" with "Figure 2" }  \\
-
-\textcolor{blue}{\textbf{\textsc{Answer:} Corrected }}.\\
+The paper  entitled ``Perimeter-based Coverage Optimization  to Improve Lifetime
+in Wireless Sensor  Networks'', by Ali Kadhum Idrees,  Karine Deschinkel, Michel
+Salomon, and  Rapha\"el Couturier  proposes a new  protocol for  Wireless Sensor
+Networks called PeCO (Perimeter-based  Coverage Optimization protocol) that aims
+at optimizing the use of energy  by conjointly exploiting a spatial and temporal
+subdivision. The protocol is based on  solving a Mixed Integer Linear Program at
+each leader node, and at each iteration of the protocol. The results obtained by
+PeCO are compared with three other competitors.\\
+
+\noindent\textcolor{black}{\textbf{MAJOR COMMENTS:}} \\
+
+\noindent {\bf  1.}  The  protocol framework  is not  described in  details.  In
+particular, the  spatial and temporal subdivision  (page 2, line 11)  that is at
+the  core of  PeCO,  is not  described  nor  justified in  much  detail. How  to
+implement an efficient spatial subdivision ? On  page 10, line 11, the number of
+subdivisions is said to be equal to 16, but the clustering algorithm used is not
+mentioned. Is  this number dependent  of the size of  the sensing area?   Of the
+number of sensors? Of the sensing range? The proposed protocol cannot be adopted
+by  practitioners  if  such  an  important step  is  not  documented.   Temporal
+subdivision suffers  from the  same lack of  description and  justification: why
+should time  intervals have the same  duration? If they have  the same duration,
+how should this common duration should be chosen?\\
+
+\textcolor{blue}{\textbf{\textsc{Answer:}  Spatial   and  temporal   choices  of
+    subdivision are not  the topics of the  paper. 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. Concerning the choice of the sensing period duration, 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.   Several explanations  on  these points  are  given throughout  the
+    paper. In particular, we discuss the number of subregions in Section 5.2 and
+    the sensing duration in the second paragraph of Section 5.1.}}\\
+
+\noindent {\bf  2.}Page 9,  Section 4, is  the Perimeter-based  coverage problem
+NP-hard? This  question is important for  justifying the use of  a Mixed Integer
+Linear Programming model.\\
+
+\textcolor{blue}{\textbf{\textsc{Answer:}  The   perimeter  scheduling  coverage
+    problem is  NP-hard in  general, it  has been proved  in the  paper entitled
+    ``Perimeter Coverage  Scheduling in  Wireless Sensor Networks  Using Sensors
+    with a Single  Continuous Cover Range'' from Ka-Shun Hung  and King-Shan Lui
+    (EURASIP Journal on Wireless Communications and Networking 2010, 2010:926075
+    doi:10.1155/2010/926075). In this  paper, authors study the  coverage of the
+    perimeter of  a large object  requiring to be  monitored. In our  study, the
+    large object  to be monitored  is the sensor  itself (or more  precisely its
+    sensing  area).   This  point  has  been highlighted  at  the  beginning  of
+    Section~4.}}\\
+
+\noindent {\bf 3.}  Page 9, the major  problem with the present paper  is, in my
+opinion, the objective  function of the Mixed Integer Linear  Program (2). It is
+not  described  in   the  paper,  and  looks  like  an   attempt  to  address  a
+multiobjective      problem      (like     minimizing      overcoverage      and
+undercoverage).  However, using  a  weighted sum  is  well known  not  to be  an
+efficient  way to  address  biobjective problems.  The  introduction of  various
+performance  metrics in  Section 5.1  also suggests  that the  authors have  not
+decided exactly  which objective  function to use,  and compare  their protocols
+against competitors without mentioning the exact purpose of each of them. If the
+performance metrics  list given in Section  5.1 is exhaustive, then  the authors
+should mention at the beginning of the  paper what are the aims of the protocol,
+and explain how the protocol is built to optimize these objectives.  \\
+
+\textcolor{blue}{\textbf{\textsc{Answer:}  Right.   The   Mixed  Integer  Linear
+    Program adresses  a multiobjective  problem, where the  goal is  to minimize
+    overcoverage and  undercoverage for each  coverage interval of a  sensor. To
+    the best of our knowledge, representing the objective function as a weighted
+    sum of criteria  to be minimized in case of  multicriteria optimization is a
+    classical method.   In Section 5, the  comparison of protocols with  a large
+    variety of performance metrics allows  to select the most appropriate method
+    according to the QoS requirement of the application.}}\\
+
+\noindent {\bf 4.} Page 11 Section 5.2, the sensor nodes are said to be based on
+Atmels AVR ATmega103L microcontroller. If I  am not mistaken, these devices have
+128 KBytes of memory, and I didn't find  any clue that they can run an operating
+system  like  Linux. This  point  is  of  primary  importance for  the  proposed
+protocol,  since GLPK  (a C  API)  is supposed  to  be executed  by the  cluster
+leader. In addition to that, GLPK requires  a non negligible amount of memory to
+run  properly,   and  the  Atmels   AVR  ATmega103L  microcontroller   might  be
+insufficient for  that purpose. The authors  are urged to provide  references of
+previous works showing that these technical constraints are not preventing their
+protocol to be implemented on  the aforementioned microcontroller. Then, on page
+13, in Section "5.2.3 Energy Consumption", the estimation of $E_p^{com}$ for the
+considered  microcontroller  seems quite  challenging  and  should be  carefully
+documented. Indeed, this is  a key point in providing a  fair comparison of PeCO
+with its competitors.\\
+
+\textcolor{blue}{\textbf{\textsc{Answer 1:}
+To implement PeCO on real sensors nodes with limited memories capacities, we can act on :
+\begin{itemize}
+\item  the solver  : GLPK  is  memory consuming  for the  resolution of  integer
+  programming    (IP)   compared    with   other    commercial   solvers    like
+  CPLEX\textregistered.  Commercial  solvers  generally outperform  open  source
+  solvers (See  the report : ``Analysis of commercial  and free and  open source
+  solvers  for linear  optimization problems"  by B.  Meindl and  M. Templ  from
+  Vienna  University  of  Technology).  Memory  use depends  on  the  number  of
+  variables and number  of constraints.  For linear programs  (LP), a reasonable
+  estimate of memory use with CPLEX \textregistered~is to allow one megabyte per
+  thousand constraints.  For integer  programs, no  simple formula  exists since
+  memory use depends so heavily on the size of the branch and bound tree (B \& B
+  tree). But, the estimate for linear  programs still provides a lower bound. In
+  our  case,  the  characteristics  of  the  integer  programming  (2)  are  the
+  following:
+\begin{itemize}
+\item number of variables : $S* (2*I+1)$
+\item number of constraints : $2* I *S$
+\item number of non-zero coefficients : $2* I *S * B$
+\item number of parameters (in the objective function) : $2* I *S$
+\end{itemize}
+where $S$ denotes the number of sensors in the subregion, $I$ the average number
+of cover intervals per  sensor, $B$ the average number of  sensors involved in a
+coverage interval. The  following table gives the memory use  with GLPK to solve
+the integer  program (column 3) and  its LP-relaxation (column 4)  for different
+problem  sizes. The  sixth  column gives  an  estimate of  the  memory use  with
+CPLEX\textregistered  to solve  the  LP-relaxation according  to  the number  of
+constraints.
+\medskip \\
+\begin{tabular}{|c|c|c|c|c|c|r|}
+\hline
+Total number & S & I & GLPK IP & GLPK LP & nodes&CPLEX\\
+of nodes &&&&relaxation &B\&B tree &\\
+\hline
+100 & 6.25& 5&0.2 MB & 0.2 MB &1 &  64 KB\\
+\hline
+200 & 12.5& 11&1.7 MB & 1.6 MB &1 & 281 KB\\
+\hline
+300 &18.5 & 17&3.6 MB & 3.5 MB & 3 &644 KB\\
+\hline
+\end{tabular}
+\medskip  \\ It  is noteworthy  that  the difference  of memory  used with  GLPK
+between the resolution  of the IP and  its LP-relaxation is very  weak (not more
+than  0.1  MB). The  size  of  the  branch and  bound  tree  does not  exceed  3
+nodes.  This   result  leads   one  to   believe  that   the  memory   use  with
+CPLEX\textregistered for  solving the  IP would  be very close  to that  for the
+LP-relaxation, that is to say less than 300 KB for a subregion containing $S=12$
+sensors.  Moreover  the IP seems to  have some specifities that  encourage us to
+develop our own solver (coefficents matrix is very sparse) or to use an existing
+heuristic to find  good approximate solutions (Reference :  ``A feasibility pump
+heuristic  for  general  mixed-integer  problems",  Livio  Bertacco  and  Matteo
+Fischetti and Andrea Lodi, Discrete Optimization, issn 1572-5286).
+\item  the subdivision  of the  region of  interest. To  make the  resolution of
+  integer programming tractable by a leader  sensor, we need to limit the number
+  of nodes  in each subregion  (the number of  variables and constraints  of the
+  integer  programming  directly  depends  on  the  number  of  nodes  and
+  neigbors). It is therefore necessary to  adapt the subdvision according to the
+  number of sensors deployed in the area  and their sensing range (impact on the
+  number of coverage intervals).
+\end{itemize}
+A discussion about memory consumption has been added in Section 5.2}}
+\bigskip \\
+\indent \textcolor{blue}{\textbf{\textsc{Answer 2:} In Section 5.2  we give a table with
+    the  power  consumption  values  which   are  used  to  compute  the  energy
+    consumption. These ones are  based on the energy model of  (Vu et al. 2006).
+}}
 
+\bigskip
 
+\noindent\textcolor{black}{\textbf{MINOR COMMENTS:}} \\
 
+\noindent  {\ding{90}  Page 12,  lines  7-15,  the  authors mention  that  DiLCO
+  protocol is  close to  PeCO. This  should be mentioned  earlier in  the paper,
+  ideally in Section 2 (Related Literature), along with the detailed description
+  of DESK and GAF, the competitors of the proposed protocol, PeCO.  }  \\
 
-\noindent {\ding{90}  Page 5, line 50, replace "section 4" with "Section 4" }  \\
+\textcolor{blue}{\textbf{\textsc{Answer:} Right. This observation has been added
+    at the end of the introduction.}}\\
 
-\textcolor{blue}{\textbf{\textsc{Answer:} Corrected }}.\\
+\noindent  {\ding{90}  Page 2,  line  20,  ``An  optimal scheduling"  should  be
+  replaced with ``An optimal schedule" } \\
 
+\textcolor{blue}{\textbf{\textsc{Answer:} Right, fixed.}}\\
 
-\noindent {\ding{90}   Page 5, line 51, replace "figure 3" with "Figure 3"}  \\
+\noindent  {\ding{90} Page  4, we  first read  (line 23)  ``we assume  that each
+  sensor node can directly transmit its  measurements to a mobile sink", then on
+  line  30, "We  also assume  that the  communication range  $Rc$ satisfies  $Rc
+  >=2Rs$. In  fact, Zhang and Hou  (2005) proved that if  the transmission range
+  fulfills  the previous  hypothesis, the  complete  coverage of  a convex  area
+  implies  connectivity  among  active  nodes.".  These  two  assumptions  seems
+  redundant.}  \\
 
-\textcolor{blue}{\textbf{\textsc{Answer:} Corrected }}.\\
+\textcolor{blue}{\textbf{\textsc{Answer:}  Yes, you  are  right  and we  removed
+    sentences about the sink. Indeed we consider multi-hop communication.}}\\
 
+\noindent {\ding{90} Page 4, line 37, a definition for k-covered is missing (the
+  sentence is an equivalence property).}  \\
 
-\noindent {\ding{90}  Page 7, line 20 "regular homogeneous subregions" is too vague. }  \\
+\textcolor{blue}{\textbf{\textsc{Answer:} Right.   A network area is  said to be
+    $k$-covered if every point in the area  is covered by at least k sensors. We
+    added this definition in the paper.}}\\
 
-\textcolor{blue}{\textbf{\textsc{Answer:}           }}.\\
+\noindent  {\ding{90} Page  5, lines  34 and  37, replace  [0, $2\pi$]  with [0,
+    $2\pi$) } \\
 
+\textcolor{blue}{\textbf{\textsc{Answer:} Right, fixed.}}\\
 
-\noindent {\ding{90}   Page 7, line 24, replace "figure 4" with "Figure 4"}  \\
+\noindent {\ding{90} Page 5, line 36 and  43, replace ``figure 2" with ``Figure 2"
+} \\
 
-\textcolor{blue}{\textbf{\textsc{Answer:} Corrected }}.\\
+\textcolor{blue}{\textbf{\textsc{Answer:} Right, fixed.}}\\
 
+\noindent {\ding{90}  Page 5, line 50, replace ``section 4" with ``Section 4" }  \\
 
-\noindent {\ding{90}  Page 7, line 47, replace "Five status" with "Five statuses" }  \\
+\textcolor{blue}{\textbf{\textsc{Answer:} Right, fixed.}}\\
 
-\textcolor{blue}{\textbf{\textsc{Answer:} Corrected }}.\\
+\noindent {\ding{90}   Page 5, line 51, replace ``figure 3" with ``Figure 3"}  \\
 
+\textcolor{blue}{\textbf{\textsc{Answer:} Right, fixed.}}\\
 
+\noindent {\ding{90}  Page 7, line 20 ``regular homogeneous subregions" is too vague. }  \\
 
-\noindent {\ding{90}  Page 9, the constraints of the Mixed Integer Linear Program (2) are not numbered. There are two inequalities for overcoverage and undercoverage that are used to define Mij and Vij. Why not using replacing these inequalities by equalities? }  \\
+\textcolor{blue}{\textbf{\textsc{Answer:} As  mentioned in the  previous remark,
+    the spatial subdivision  was not clearly explained in the  paper. We added a
+    discussion about  this question in  the article. Thank you  for highlighting
+    it. }}\\
 
-\textcolor{blue}{\textbf{\textsc{Answer:}           }}.\\
+\noindent {\ding{90} Page 7, line 24, replace ``figure 4" with ``Figure 4"}  \\
 
+\textcolor{blue}{\textbf{\textsc{Answer:} Right, fixed.}}\\
 
-\noindent {\ding{90}  Page 10, line 50, "or if the network is no more connected". In order to assess this, the communication range should be known, but it is not given in Table 2. }  \\
 
-\textcolor{blue}{\textbf{\textsc{Answer:}                    }}.\\
+\noindent {\ding{90}  Page 7, line 47, replace ``Five status" with ``Five statuses" }  \\
 
+\textcolor{blue}{\textbf{\textsc{Answer:} Right, fixed.}}\\
 
-\noindent {\ding{90}  Page 10, line 53, the "Coverage ratio" definition is provided for a given period p? Then in the formula on top of page 11, N is set to 51 times 26, why? Is it somehow related to the sensing area having size 50 times 25? }  \\
+\noindent {\ding{90} Page 9, the constraints of the Mixed Integer Linear Program
+  (2)  are  not  numbered.  There  are two  inequalities  for  overcoverage  and
+  undercoverage that  are used to  define Mij and  Vij. Why not  using replacing
+  these inequalities by equalities? }  \\
 
-\textcolor{blue}{\textbf{\textsc{Answer:} Yes, the "Coverage ratio" definition is provided for a given period p. N is set to 51 times 26 = 1326 grid points because  we discretized the sensing field as a regular grid. Yes, it is related to the sensing area having size 50 times 25. }}.\\
+\textcolor{blue}{\textbf{\textsc{Answer:} For minimizing the objective function,
+    $M_{i}^{j}$ and  $V_{i}^{j}$ should  be set to  the smallest  possible value
+    such that  the inequalities are satisfied.  It is explained in  answer 4
+    for reviewer  1.  But,  at optimality,  constraints  are not  necessary
+    satisfied with equality. For instance, if a sensor $j$ is overcovered, there
+    exists at least one of its coverage  interval (say $i$) for which the number
+    of active sensors  (denoted by $l^{i}$) covering this part  of the perimeter
+    is greater than  $l$. In this case,  $M_{i}^{j}=0$, $V_{i}^{j}=l^{i}-l$, the
+    corresponding inequality $\sum_{k \in A} ( a^j_{ik} ~ X_{k}) + M^j_i \geq l$
+    is a  strict inequality since  $\sum_{k \in A}  ( a^j_{ik} ~  X_{k})=l^{i} >
+    l$. }}\\
 
+\noindent  {\ding{90}  Page  10,  line  50,  ``or if  the  network  is  no  more
+  connected". In order to assess this,  the communication range should be known,
+  but it is not given in Table 2. }  \\
 
-\noindent {\ding{90}  Page 11, line 17 in the formula of ASR, |S| should be replaced with J (where J is defined page 4 line 16). }  \\
+\textcolor{blue}{\textbf{\textsc{Answer:} Right, fixed.}}\\
 
-\textcolor{blue}{\textbf{\textsc{Answer:} Corrected }}.\\
+\noindent  {\ding{90} Page  10, line  53,  the ``Coverage  ratio" definition  is
+  provided for a given period p? Then in the formula on top of page 11, N is set
+  to 51 times 26, why? Is it somehow  related to the sensing area having size 50
+  times 25? } \\
 
+\textcolor{blue}{\textbf{\textsc{Answer:} Yes, the  ``Coverage ratio" definition
+    is provided for a given period p. N is set to 51 times 26 = 1326 grid points
+    because we discretized the  sensing field as a regular grid,  a point on the
+    contour and  a point  every meter. Yes,  it is related  to the  sensing area
+    having size 50 meters times 25 meters.}}\\
 
-\noindent {\ding{90}  Page 13, line 41 and 43, replace "figure 8" with "Figure 8" }  \\
+\noindent {\ding{90}  Page 11,  line 17  in the  formula of  ASR, |S|  should be
+  replaced with J (where J is defined page 4 line 16). }  \\
 
-\textcolor{blue}{\textbf{\textsc{Answer:} Corrected }}.\\
+\textcolor{blue}{\textbf{\textsc{Answer:} Right, fixed.}}\\
 
+\noindent {\ding{90} Page 13, line 41 and 43, replace ``figure 8" with ``Figure 8"
+} \\
 
+\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.
+We are very grateful to the  reviewers who, by their recommendations, allowed us
+to improve the quality of our article.
 
 \begin{flushright}
 Best regards\\
