\documentclass[14]{article}
\usepackage{epsfig}
\usepackage{subfigure}
\usepackage{calc}
\usepackage{amssymb}
\usepackage{amstext}
\usepackage{amsmath}
\usepackage{amsthm}
\usepackage{multicol}
\usepackage{pslatex}
\usepackage{apalike}

\usepackage[small]{caption}
\usepackage{color}
\usepackage{times}
\usepackage{titlesec}
\usepackage{pifont}
\usepackage[linesnumbered,ruled,vlined,commentsnumbered]{algorithm2e}
\usepackage{mathtools}  
\usepackage{color}
\usepackage{times}
\usepackage{titlesec}
\usepackage{pifont}
%\usepackage[T1]{fontenc}
%\usepackage[latin1]{inputenc}

\renewcommand{\labelenumii}{\labelenumi\arabic{enumii}}
%\titleformat*{\section}{\Large\bfseries}

%\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}

\begin{document}

\begin{flushright}
\today
\end{flushright}%

\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}
Detailed changes and addressed issues in the revision of the article

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

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

\medskip

\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: `` 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 $\#$1 Comments}

The paper present a new system to optimize sensord detections. The work present the algorithm in a cleare and well descrived way. The main problem is connected with the luck of examples and also on the practical applications. I suggest in future to make a more formal description of the process.\\


\textcolor{blue}{\textbf{\textsc{Answer:} Right.  We  have  included a  paragraph on the examples and practical applications of WSNs in section~1. }}
\textcolor{red}Je pense que la question porte sur un exemple d'application de notre protocole?}


\section*{Response to Reviewer $\#$3 Comments}
This work proposed a distributed lifetime coverage optimization (DiLCO) protocol to apply to predefined subregions, which are generated from the area of interest using a classical divide-and-conquer method, to improve the lifetime of a wireless sensor network. Their proposed protocol is devised with a two-step process, including a leader election technique in each subregion and a sensor's activity scheduling by each elected leader. In general, it is a good idea to pre-divide the network domain into several sub-areas, and assign a single cluster head in each sub-area for achieving more balanced energy dissipation for the wireless sensor network. As we known, Heinzelman et al. (2000) first proposed a clustering protocol called LEACH for periodical data-gathering applications. Also many variants of LEACH protocol or a variety of distributed protocols had proposed enhanced energy efficient adaptive clustering protocols by pre-dividing the network domain into several
sub-areas, and assigning a single cluster head in each sub-area to achieve more balanced energy dissipation. Hence, I suggest that the authors could clearly state the differences and benefits between their leader selection technique and the methods of cluster head election in LEACH or other distributed protocols. Moreover, they used the two protocols, DESK and GAF, for assessing the performance of their protocols is not convincible. The authors may include more well-known or recently developed protocols for comparison. 


\textcolor{blue}{\textbf{\textsc{Answer :}  The difference between our leader selection technique and the methods of cluster head election in LEACH or other distributed protocols in that our approach  assumes  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 is made using divide-and-conquer concept such that the number of hops between any pairs  of sensors inside a subregion is  less than or equal to~3. The sensors inside each subregion cooperate to elect one leader. Leader applies sensor activity scheduling based optimization to provide the schedule to the sensor nodes in the subregion. The advantage of our approach is to minimize the energy consumption required for communication. The sensors only require to communicate with the other sensors inside the subregion to elect the leader instead of communicating with other nodes in the WSN. \\Whereas in LEACH and other cluster head election methods, the cluster heads are elected in distributed way where sensors  elect  themselves  to  be local cluster-heads  at any  given time  with  a  certain  probability. These cluster-head  nodes  broadcast  their  status  to  the  other  sensors  in the network.  Each sensor node determines to which cluster it wants to belong by choosing the cluster-head that requires the minimum communication energy. Once all the nodes are organized into clusters, each cluster-head creates a schedule for the nodes in its cluster.   \\\\
In fact, GAF algorithm is chosen for comparison as a competitor because it is famous and easy to implement, as well as many authors referred to it in many publications. DESK algorithm is also selected as competitor in the comparison because it works into rounds fashion (network lifetime divided into rounds) similar to our approaches, as well as DESK is a full distributed coverage approach. }}




The following improvements may be suggested to make it even better:\\
\noindent {\bf 1. What is the "new idea" or contribution of this work?}    \\
\textcolor{blue}{\textbf{\textsc{Answer :}       
The contribution of this work is to design a protocol that focuses on the area coverage problem with the objective of maximizing the network lifetime. Our proposition, the Distributed Lifetime Coverage Optimization
(DiLCO) protocol, maintains the coverage and improves the lifetime in WSNs. Our protocol combines two energy efficient mechanisms: leader election and sensor activity scheduling based optimization to optimize the coverage and the network lifetime inside each subregion. we strengthen our simulations by taking into account the characteristics of a Medusa II sensor (Raghunathan et al., 2002) to measure the energy consumption and the computation time. We have implemented two other existing distributed approaches: DESK (Vu et al., 2006) and GAF (Xu et al., 2001)) in order to compare their performances with our approach. We also focus on performance analysis based on the number of subregions.
}}

\noindent {\bf 2. There are many parameters (listed in Page 5) that must be predefined before the proposed method begins. The reviewer suggests that the all special characters and symbols should be described or defined in the text. }    \\
\textcolor{blue}{\textbf{\textsc{Answer :}       }}

\noindent {\bf 3. From their simulations using the five versions: DiLCO-2, DiLCO-4, DiLCO-8, DiLCO-16, and DiLCO-32. The authors concluded that the more subregions enable the extension of the network lifetime. From their experimental simulations, the subdivision in 16 subregions seems to be the most relevant. However, I was wondering if this was possible to derive an expression for the real optimal number of subregions. In general, the optimal number of subregions depends on the size of sensor field and the location of base station.}  \\
\textcolor{blue}{\textbf{\textsc{Answer :}  In fact, the optimal number of subregions depends on the area of interest size, sensing range of sensor, and the location of base station. The optimal number of subregions will be investigated in future. }}

\noindent {\bf 4. The authors should try to indicate which parameters are critical to performance, is there a significant parameter difference, $w_u$ and $w_\Theta$ in Eq. (4) for example, when the protocol is applied of different WSNs? }    \\
\textcolor{blue}{\textbf{\textsc{Answer :}  The number of primary points $P$ parameter has a significant impact on the performance of DiLCO protocol. When the WSN size increases the network lifetime decreases when number of primary points increases because the energy required for the computation of the optimization algorithm. }}

\noindent {\bf 5. It is unclear whether the parameters of the other two protocols were optimized at all. If they were not, as I suspect, there is no way of knowing whether, indeed, the proposed protocol outperforms the other two on the simulations of WSNs reported in the paper. All experiments would have to be made replicable and the comparisons with other protocols should be fair and crystal clear.}    \\
\textcolor{blue}{\textbf{\textsc{Answer :}   The parameters of the other two protocols were optimized at all as well as we used the same energy consumption model of  one of them with slight modification for ensuring fair comparison.   }}

\noindent {\bf 6. I think the authors have a not too bad work here in hands, but the resulting paper is lacking some of convincible originality.}    \\
\textcolor{blue}{\textbf{\textsc{Answer :}  To the best of our knowledge, no hybrid coverage optimization protocol (as our DiLCO protocol) that globally distributed on the subregions and locally centralized using optimization has ever been proposed in the literature. DiLCO protocol based on combination of two energy efficient mechanisms: leader election and sensor activity scheduling based optimization so as to optimize the coverage and the network lifetime in each subregion.  }}

\section*{Response to Reviewer $\#$5 Comments}
The paper addresses the problem of lifetime coverage in wireless sensor networks. The main issue here is the energy to maintain full coverage of the network while achieving sensing, communication,  and computation tasks. The author suggest a new protocol, named DiLCO, aiming at solving the aforementioned objective using a discrete optimization approach. The focus of the paper is clear and the basic idea looks attractive. However, from my opinion, number of clarifications are needed in order for me to be able to validate the whole contribution of the authors. Some of them include:

\noindent {\bf  - the concept of efficiency is not clearly stated, is it the amount of energy used by the protocol or the time it takes to completion ? (line 52 of the introduction "most efficient")}    \\
\textcolor{blue}{\textbf{\textsc{Answer :} The concept of efficiency refers to monitoring the area of interest using as less energy as possible.   }}

\noindent {\bf  - the topology of the graph is not considered in the paper. Isn't it important ?  In which class of graphs the author think they will perform better ? are there some disadvantageous topologies ?}    \\
\textcolor{blue}{\textbf{\textsc{Answer :} Uniform graph partition is used by subdividing the sensing field into smaller subgraphs (subregion) using divide-and-conquer concept. The subgraph consists of sensor nodes which are previously deployed over the sensing field uniformly with high density to ensure that any primary point on the sensing field is covered by at least one sensor node. The graph partition problem has gained importance due to its application for clustering. The topology of the graph has important impact on the protocol performance. Random graph has negative  effect on our DiLCO protocol because we suppose that the sensing field is subdivided uniformly.  }}

\noindent {\bf  - in line 42 of section  3, why  do we need Rc $\geq$ 2Rs ? Isn't it sufficient to have Rc $ > $ Rs ? what is the implication of a stronger hypothesis ? how realistic is it ? again, this raised the question of the topology.}    \\

\textcolor{blue}{\textbf{\textsc{Answer :}   We also assume that the communication range Rc satisfies Rc $\geq$ 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.}}\\

\noindent {\bf  - line 63 of subsection 3.2, it is not clear why the periodic scheduling is in favor of a more robust network. Please, explain.}    \\
\textcolor{blue}{\textbf{\textsc{Answer :}  We explain in the subsection 3.2.     }}

\noindent {\bf  - the next sentence mention "enough energy to complete a period". This is another point where the author could be more rigorous. Indeed, how accurate is the evaluation of the required energy for a period ?}    \\
\textcolor{blue}{\textbf{\textsc{Answer :}   This value has been computed by multiplying the energy consumed in the active state (9.72 mW) by the time in second for one period (3600 seconds), and adding the energy for the pre-sensing phases. We explained that in subsection 5.1.  }}

\noindent {\bf  - about the information collected (line 36-38) , what are they used for ?}    \\
\textcolor{blue}{\textbf{\textsc{Answer :}  They used for leader election and decision phases.   }}

\noindent {\bf  - the way the leader is elected could emphasize first on the remaining energy.  Is it sure that the remaining energy will be sufficient to solve the integer program algorithm ?}    \\
\textcolor{blue}{\textbf{\textsc{Answer :}   It is sure that remaining energy for DiLCO-4, DiLCO-8, DiLCO-16, and DiLCO-32 protocol versions will be sufficient to solve the integer program algorithm (see Figure 4: Execution time in seconds). The sensor node participates in the competition with energy enough for nearly one hour. }}

\noindent {\bf  - regarding the MIP formulation at the end of section 4, the first constraint does not appear as a constraint for me as it is an invariant (as shown on top)}    \\
\textcolor{blue}{\textbf{\textsc{Answer :}       }}

\noindent {\bf  - how $ w_\theta $ and $ w_U $ are chosen ? (end of section 4). How dependent if the method toward these parameters ?}    \\
\textcolor{blue}{\textbf{\textsc{Answer :}   Both weights $ w_\theta $ and $ w_U $ must be carefully chosen in order to guarantee that the maximum number of points are covered during each period. In fact, we give a high value to $ w_U $ because of giving more importance to prevent the undercoverage.   }}

\noindent {\bf  - in table 2, the "listening" and the "computation" status are both (ON, ON, ON), is that correct ?}    \\
\textcolor{blue}{\textbf{\textsc{Answer :}  Yes, because of both cases continue their processing, communication, and sensing tasks.     }}

\noindent {\bf  - in line 60-61, you choose active energy as reference, is that sufficient for the computation ?}    \\
\textcolor{blue}{\textbf{\textsc{Answer :}   Yes, it is sufficient for the computation.    }}

\noindent {\bf  - The equation of EC has the communication energy duplicated}    \\
\textcolor{blue}{\textbf{\textsc{Answer :}   In fact, there is no duplication.  The  first   one,  denoted   $E^{\scriptsize  \mbox{com}}_m$, represents  the  energy  consumption  spent   by  all  the  nodes  for  wireless
communications  during period  $m$. The second, $E^{\scriptsize \mbox{comp}}_m$  refers to the  energy needed by all  the leader nodes  to solve the  integer program  during a  period. }}

\noindent {\bf  - figure 2 should be discussed including the initial energy and the topology of the graph}    \\
\textcolor{blue}{\textbf{\textsc{Answer :}   Each node has an initial energy level, in Joules, which is randomly drawn in $[500-700]$. If its energy provision reaches a value below the threshold $E_{th}$ = 36 Joules, the minimum energy
needed for a node to stay active during one period, it will no longer take part in the coverage task. The topology of the graph is uniform graph with high density  }}

\noindent {\bf  - you mention a DELL laptop. How this could be assimilated to a sensor ?}    \\
\textcolor{blue}{\textbf{\textsc{Answer :}   In fact, The execution times are obtained as shown in subsection 5.2.3.    }}

\noindent {\bf  - in figure 4, what makes the execution times different ?}    \\
\textcolor{blue}{\textbf{\textsc{Answer :}  The WSN size  makes the execution times different.    }}

\noindent {\bf  - why is it important to mention a divide-and-conquer approach (conclusion)}    \\
\textcolor{blue}{\textbf{\textsc{Answer :}   it is important to mention a divide-and-conquer approach because of the subdivision of the sensing field is based on this concept.   }}

\noindent {\bf  - the connectivity among subregion should be studied too.}    \\
\textcolor{blue}{\textbf{\textsc{Answer :}  Yes you are right, we will investigated in future.     }}






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


\end{document}
