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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

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

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

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Detailed changes and addressed issues in the revision of the article

"Perimeter-based Coverage Optimization to Improve Lifetime in Wireless Sensor Networks"\\

by Ali Kadhum Idrees, Karine Deschinkel Michel Salomon, Rapahel 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:
"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. \\


%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 “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:}      }}.\\


\noindent {\ding{90}  Run-on sentence: Page 2 lines 43-48}  \\

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



\noindent {\ding{90} Add an “and” after the comma on page 3 line 34.}  \\

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


\noindent {\ding{90}  “model as” instead of “Than” on page 10 line 12.}  \\

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


\noindent {\ding{90} “no longer” instead of “no more” on page 10 line 31.}  \\

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


\noindent {\ding{90} “in the active state” 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:}      }}.\\




\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 }}.\\




\noindent {\ding{90}  Page 5, line 50, replace "section 4" with "Section 4" }  \\

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


\noindent {\ding{90}   Page 5, line 51, replace "figure 3" with "Figure 3"}  \\

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


\noindent {\ding{90}  Page 7, line 20 "regular homogeneous subregions" is too vague. }  \\

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


\noindent {\ding{90}   Page 7, line 24, replace "figure 4" with "Figure 4"}  \\

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


\noindent {\ding{90}  Page 7, line 47, replace "Five status" with "Five statuses" }  \\

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



\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:}           }}.\\


\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 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. Yes, it is related to the sensing area having size 50 times 25. }}.\\


\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 }}.\\


\noindent {\ding{90}  Page 13, line 41 and 43, replace "figure 8" with "Figure 8" }  \\

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



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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