modif biblio, article, reponse

diff --git a/PeCO-EO/articleeo.aux b/PeCO-EO/articleeo.aux
index d9dd4147fd233b19a7a4c49f6b9f27cc9d491af1..c627b72d10c75c6d2bef52136068c2f27d2e7ceb 100644 (file)
--- a/PeCO-EO/articleeo.aux
+++ b/PeCO-EO/articleeo.aux
@@ -44,6 +44,8 @@
 \@writefile{toc}{\contentsline {subsection}{\numberline {3.2}The Main Idea}{7}}
 \newlabel{figure4}{{4}{8}}
 \@writefile{toc}{\contentsline {subsection}{\numberline {3.3}PeCO Protocol Algorithm}{8}}
 \@writefile{toc}{\contentsline {subsection}{\numberline {3.2}The Main Idea}{7}}
 \newlabel{figure4}{{4}{8}}
 \@writefile{toc}{\contentsline {subsection}{\numberline {3.3}PeCO Protocol Algorithm}{8}}

+\citation{doi:10.1155/2010/926075}
+\citation{doi:10.1155/2010/926075}

 \newlabel{alg:PeCO}{{{1}}{9}}
 \@writefile{toc}{\contentsline {section}{\numberline {4}Perimeter-based Coverage Problem Formulation}{9}}
 \newlabel{cp}{{4}{9}}
 \newlabel{alg:PeCO}{{{1}}{9}}
 \@writefile{toc}{\contentsline {section}{\numberline {4}Perimeter-based Coverage Problem Formulation}{9}}
 \newlabel{cp}{{4}{9}}


@@ -52,7 +54,7 @@
 \@writefile{toc}{\contentsline {section}{\numberline {5}Performance Evaluation and Analysis}{10}}
 \newlabel{sec:Simulation Results and Analysis}{{5}{10}}
 \@writefile{toc}{\contentsline {subsection}{\numberline {5.1}Simulation Settings}{10}}
 \@writefile{toc}{\contentsline {section}{\numberline {5}Performance Evaluation and Analysis}{10}}
 \newlabel{sec:Simulation Results and Analysis}{{5}{10}}
 \@writefile{toc}{\contentsline {subsection}{\numberline {5.1}Simulation Settings}{10}}

-\newlabel{table3}{{2}{10}}
+\newlabel{table3}{{2}{11}}

 \citation{varga}
 \citation{AMPL}
 \citation{glpk}
 \citation{varga}
 \citation{AMPL}
 \citation{glpk}


@@ -62,20 +64,21 @@
 \citation{idrees2014coverage}
 \@writefile{toc}{\contentsline {subsection}{\numberline {5.2}Simulation Results}{12}}
 \@writefile{toc}{\contentsline {subsubsection}{\numberline {5.2.1}\bf  Coverage Ratio}{12}}
 \citation{idrees2014coverage}
 \@writefile{toc}{\contentsline {subsection}{\numberline {5.2}Simulation Results}{12}}
 \@writefile{toc}{\contentsline {subsubsection}{\numberline {5.2.1}\bf  Coverage Ratio}{12}}

-\@writefile{toc}{\contentsline {subsubsection}{\numberline {5.2.2}\bf  Active Sensors Ratio}{12}}

 \newlabel{figure5}{{5}{13}}
 \newlabel{figure5}{{5}{13}}

+\@writefile{toc}{\contentsline {subsubsection}{\numberline {5.2.2}\bf  Active Sensors Ratio}{13}}

 \newlabel{figure6}{{6}{13}}
 \newlabel{figure6}{{6}{13}}

-\@writefile{toc}{\contentsline {subsubsection}{\numberline {5.2.3}\bf  Energy Consumption}{13}}
-\@writefile{toc}{\contentsline {subsubsection}{\numberline {5.2.4}\bf  Network Lifetime}{13}}
+\@writefile{toc}{\contentsline {subsubsection}{\numberline {5.2.3}\bf  Energy Consumption}{14}}

 \newlabel{figure7}{{7}{14}}
 \newlabel{figure7}{{7}{14}}

-\@writefile{toc}{\contentsline {subsubsection}{\numberline {5.2.5}\bf  Impact of $\alpha $ and $\beta $ on PeCO's performance}{14}}
+\@writefile{toc}{\contentsline {subsubsection}{\numberline {5.2.4}\bf  Network Lifetime}{14}}

 \newlabel{figure8}{{8}{15}}
 \newlabel{figure8}{{8}{15}}

-\newlabel{figure9}{{9}{15}}
-\@writefile{toc}{\contentsline {section}{\numberline {6}Conclusion and Future Works}{15}}
-\newlabel{sec:Conclusion and Future Works}{{6}{15}}
+\@writefile{toc}{\contentsline {subsubsection}{\numberline {5.2.5}\bf  Impact of $\alpha $ and $\beta $ on PeCO's performance}{15}}

 \bibstyle{gENO}
 \bibdata{biblio}
 \bibcite{akyildiz2002wireless}{{1}{2002}{{Akyildiz et~al.}}{{Akyildiz, Su, Sankarasubramaniam, and Cayirci}}}
 \bibstyle{gENO}
 \bibdata{biblio}
 \bibcite{akyildiz2002wireless}{{1}{2002}{{Akyildiz et~al.}}{{Akyildiz, Su, Sankarasubramaniam, and Cayirci}}}

+\newlabel{figure9}{{9}{16}}
+\newlabel{my-labelx}{{3}{16}}
+\@writefile{toc}{\contentsline {section}{\numberline {6}Conclusion and Future Works}{16}}
+\newlabel{sec:Conclusion and Future Works}{{6}{16}}

 \bibcite{anastasi2009energy}{{2}{2009}{{Anastasi et~al.}}{{Anastasi, Conti, Di~Francesco, and Passarella}}}
 \bibcite{berman04}{{3}{2004}{{Berman and Calinescu}}{{}}}
 \bibcite{cardei2005improving}{{4}{2005}{{Cardei and Du}}{{}}}
 \bibcite{anastasi2009energy}{{2}{2009}{{Anastasi et~al.}}{{Anastasi, Conti, Di~Francesco, and Passarella}}}
 \bibcite{berman04}{{3}{2004}{{Berman and Calinescu}}{{}}}
 \bibcite{cardei2005improving}{{4}{2005}{{Cardei and Du}}{{}}}


@@ -84,39 +87,39 @@
 \bibcite{Deng2012}{{7}{2012}{{Deng, Jiguo~Yu, and Chen}}{{}}}
 \bibcite{deschinkel2012column}{{8}{2012}{{Deschinkel}}{{}}}
 \bibcite{AMPL}{{9}{November 12, 2002}{{Fourer, Gay, and Kernighan}}{{}}}
 \bibcite{Deng2012}{{7}{2012}{{Deng, Jiguo~Yu, and Chen}}{{}}}
 \bibcite{deschinkel2012column}{{8}{2012}{{Deschinkel}}{{}}}
 \bibcite{AMPL}{{9}{November 12, 2002}{{Fourer, Gay, and Kernighan}}{{}}}

-\newlabel{my-labelx}{{3}{16}}

 \bibcite{HeShibo}{{10}{2014}{{He et~al.}}{{He, Gong, Zhang, Chen, and Sun}}}
 \bibcite{Huang:2003:CPW:941350.941367}{{11}{2005{a}}{{Huang and Tseng}}{{}}}
 \bibcite{huang2005coverage}{{12}{2005{b}}{{Huang and Tseng}}{{}}}
 \bibcite{HeShibo}{{10}{2014}{{He et~al.}}{{He, Gong, Zhang, Chen, and Sun}}}
 \bibcite{Huang:2003:CPW:941350.941367}{{11}{2005{a}}{{Huang and Tseng}}{{}}}
 \bibcite{huang2005coverage}{{12}{2005{b}}{{Huang and Tseng}}{{}}}

-\bibcite{idrees2014coverage}{{13}{2014}{{Idrees et~al.}}{{Idrees, Deschinkel, Salomon, and Couturier}}}
-\bibcite{Idrees2}{{14}{2015}{{Idrees et~al.}}{{Idrees, Deschinkel, Salomon, and Couturier}}}
-\bibcite{jaggi2006}{{15}{2006}{{Jaggi and Abouzeid}}{{}}}
-\bibcite{kim2013maximum}{{16}{2013}{{Kim and Cobb}}{{}}}
-\bibcite{0031-9155-44-1-012}{{17}{1999}{{Lee et~al.}}{{Lee, Gallagher, Silvern, Wuu, and Zaider}}}
-\bibcite{li2013survey}{{18}{2013}{{Li and Vasilakos}}{{}}}
-\bibcite{ling2009energy}{{19}{2009}{{Ling and Znati}}{{}}}
-\bibcite{glpk}{{20}{2012}{{Makhorin}}{{}}}
-\bibcite{Misra}{{21}{2011}{{Misra, Kumar, and Obaidat}}{{}}}
-\bibcite{pc10}{{22}{2010}{{Padmavathy and Chitra}}{{}}}
-\bibcite{puccinelli2005wireless}{{23}{2005}{{Puccinelli and Haenggi}}{{}}}
-\bibcite{pujari2011high}{{24}{2011}{{Pujari}}{{}}}
-\bibcite{qu2013distributed}{{25}{2013}{{Qu and Georgakopoulos}}{{}}}
-\bibcite{rault2014energy}{{26}{2014}{{Rault, Bouabdallah, and Challal}}{{}}}
-\bibcite{doi:10.1080/0305215X.2012.687732}{{27}{2013}{{Singh, Rossi, and Sevaux}}{{}}}
-\bibcite{Tian02}{{28}{2002}{{Tian and Georganas}}{{}}}
-\bibcite{varga}{{29}{2003}{{Varga}}{{}}}
-\bibcite{ChinhVu}{{30}{2006}{{Vu et~al.}}{{Vu, Gao, Deshmukh, and Li}}}
-\bibcite{chin2007}{{31}{2009}{{Vu}}{{}}}
-\bibcite{wang2011coverage}{{32}{2011}{{Wang}}{{}}}
-\bibcite{5714480}{{33}{2010}{{Xing, Li, and Wang}}{{}}}
-\bibcite{xu2001geography}{{34}{2001}{{Xu, Heidemann, and Estrin}}{{}}}
-\bibcite{yan2008design}{{35}{2008}{{Yan et~al.}}{{Yan, Gu, He, and Stankovic}}}
-\bibcite{yang2014novel}{{36}{2014{a}}{{Yang and Chin}}{{}}}
-\bibcite{yangnovel}{{37}{2014{b}}{{Yang and Chin}}{{}}}
-\bibcite{Yang2014}{{38}{2014}{{Yang and Liu}}{{}}}
-\bibcite{yick2008wireless}{{39}{2008}{{Yick, Mukherjee, and Ghosal}}{{}}}
-\bibcite{Zhang05}{{40}{2005}{{Zhang and Hou}}{{}}}
-\bibcite{zhou2009variable}{{41}{2009}{{Zhou, Das, and Gupta}}{{}}}
-\bibcite{zorbas2010solving}{{42}{2010}{{Zorbas et~al.}}{{Zorbas, Glynos, Kotzanikolaou, and Douligeris}}}
-\endpage{18}
+\bibcite{doi:10.1155/2010/926075}{{13}{2010}{{Hung and Lui}}{{}}}
+\bibcite{idrees2014coverage}{{14}{2014}{{Idrees et~al.}}{{Idrees, Deschinkel, Salomon, and Couturier}}}
+\bibcite{Idrees2}{{15}{2015}{{Idrees et~al.}}{{Idrees, Deschinkel, Salomon, and Couturier}}}
+\bibcite{jaggi2006}{{16}{2006}{{Jaggi and Abouzeid}}{{}}}
+\bibcite{kim2013maximum}{{17}{2013}{{Kim and Cobb}}{{}}}
+\bibcite{0031-9155-44-1-012}{{18}{1999}{{Lee et~al.}}{{Lee, Gallagher, Silvern, Wuu, and Zaider}}}
+\bibcite{li2013survey}{{19}{2013}{{Li and Vasilakos}}{{}}}
+\bibcite{ling2009energy}{{20}{2009}{{Ling and Znati}}{{}}}
+\bibcite{glpk}{{21}{2012}{{Makhorin}}{{}}}
+\bibcite{Misra}{{22}{2011}{{Misra, Kumar, and Obaidat}}{{}}}
+\bibcite{pc10}{{23}{2010}{{Padmavathy and Chitra}}{{}}}
+\bibcite{puccinelli2005wireless}{{24}{2005}{{Puccinelli and Haenggi}}{{}}}
+\bibcite{pujari2011high}{{25}{2011}{{Pujari}}{{}}}
+\bibcite{qu2013distributed}{{26}{2013}{{Qu and Georgakopoulos}}{{}}}
+\bibcite{rault2014energy}{{27}{2014}{{Rault, Bouabdallah, and Challal}}{{}}}
+\bibcite{doi:10.1080/0305215X.2012.687732}{{28}{2013}{{Singh, Rossi, and Sevaux}}{{}}}
+\bibcite{Tian02}{{29}{2002}{{Tian and Georganas}}{{}}}
+\bibcite{varga}{{30}{2003}{{Varga}}{{}}}
+\bibcite{ChinhVu}{{31}{2006}{{Vu et~al.}}{{Vu, Gao, Deshmukh, and Li}}}
+\bibcite{chin2007}{{32}{2009}{{Vu}}{{}}}
+\bibcite{wang2011coverage}{{33}{2011}{{Wang}}{{}}}
+\bibcite{5714480}{{34}{2010}{{Xing, Li, and Wang}}{{}}}
+\bibcite{xu2001geography}{{35}{2001}{{Xu, Heidemann, and Estrin}}{{}}}
+\bibcite{yan2008design}{{36}{2008}{{Yan et~al.}}{{Yan, Gu, He, and Stankovic}}}
+\bibcite{yang2014novel}{{37}{2014{a}}{{Yang and Chin}}{{}}}
+\bibcite{yangnovel}{{38}{2014{b}}{{Yang and Chin}}{{}}}
+\bibcite{Yang2014}{{39}{2014}{{Yang and Liu}}{{}}}
+\bibcite{yick2008wireless}{{40}{2008}{{Yick, Mukherjee, and Ghosal}}{{}}}
+\bibcite{Zhang05}{{41}{2005}{{Zhang and Hou}}{{}}}
+\bibcite{zhou2009variable}{{42}{2009}{{Zhou, Das, and Gupta}}{{}}}
+\bibcite{zorbas2010solving}{{43}{2010}{{Zorbas et~al.}}{{Zorbas, Glynos, Kotzanikolaou, and Douligeris}}}
+\endpage{19}

 \questionmark{}
 \questionmark{}

diff --git a/PeCO-EO/articleeo.bbl b/PeCO-EO/articleeo.bbl
index a03bf2ad12bea0cab70542ada6e52cf02365fa07..b052e269e092b2cd9b7f32cfd98714130bcddd1e 100644 (file)
--- a/PeCO-EO/articleeo.bbl
+++ b/PeCO-EO/articleeo.bbl
@@ -1,4 +1,4 @@
-\begin{thebibliography}{42}
+\begin{thebibliography}{43}

 \newcommand{\enquote}[1]{``#1''}
 \providecommand{\natexlab}[1]{#1}
 \providecommand{\url}[1]{\normalfont{#1}}
 \newcommand{\enquote}[1]{``#1''}
 \providecommand{\natexlab}[1]{#1}
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@@ -75,6 +75,12 @@ Huang, Chi-Fu, and Yu-Chee Tseng. 2005{\natexlab{b}}. ``The coverage problem in
   a wireless sensor network.'' \emph{Mobile Networks and Applications} 10 (4):
   519--528.
 
   a wireless sensor network.'' \emph{Mobile Networks and Applications} 10 (4):
   519--528.
 

+\bibitem[Hung and Lui(2010)]{doi:10.1155/2010/926075}
+Hung, Ka-Shun, and King-Shan Lui. 2010. ``Perimeter Coverage Scheduling in
+  Wireless Sensor Networks Using Sensors with a Single Continuous Cover
+  Range.'' \emph{EURASIP Journal on Wireless Communications and Networking}
+  2010.
+

 \bibitem[Idrees et~al.(2014)Idrees, Deschinkel, Salomon, and
   Couturier]{idrees2014coverage}
 Idrees, Ali~Kadhum, Karine Deschinkel, Michel Salomon, and Rapha{\"e}l
 \bibitem[Idrees et~al.(2014)Idrees, Deschinkel, Salomon, and
   Couturier]{idrees2014coverage}
 Idrees, Ali~Kadhum, Karine Deschinkel, Michel Salomon, and Rapha{\"e}l


@@ -153,9 +159,9 @@ Rault, Tifenn, Abdelmadjid Bouabdallah, and Yacine Challal. 2014. ``Energy
   Networks} 67: 104--122.
 
 \bibitem[Singh, Rossi, and Sevaux(2013)]{doi:10.1080/0305215X.2012.687732}
   Networks} 67: 104--122.
 
 \bibitem[Singh, Rossi, and Sevaux(2013)]{doi:10.1080/0305215X.2012.687732}

-Singh, Alok, André Rossi, and Marc Sevaux. 2013. ``Matheuristic approaches for
-  Q-coverage problem versions in wireless sensor networks.'' \emph{Engineering
-  Optimization} 45 (5): 609--626.
+Singh, Alok, André Rossi, and Marc Sevaux. 2013. ``Metaheuristic approaches
+  for Q-coverage problem versions in wireless sensor networks.''
+  \emph{Engineering Optimization} 45 (5): 609--626.

 
 \bibitem[Tian and Georganas(2002)]{Tian02}
 Tian, Di, and Nicolas~D. Georganas. 2002. ``A coverage-preserving node
 
 \bibitem[Tian and Georganas(2002)]{Tian02}
 Tian, Di, and Nicolas~D. Georganas. 2002. ``A coverage-preserving node

diff --git a/PeCO-EO/articleeo.blg b/PeCO-EO/articleeo.blg
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+ 48196 string characters out of 3182031
+ 114324 words of memory out of 3000000
+ 6820 multiletter control sequences out of 15000+200000

  14560 words of font info for 56 fonts, out of 3000000 for 9000
  14 hyphenation exceptions out of 8191
  14560 words of font info for 56 fonts, out of 3000000 for 9000
  14 hyphenation exceptions out of 8191

- 41i,14n,27p,748b,327s stack positions out of 5000i,500n,10000p,200000b,50000s
+ 41i,14n,27p,839b,355s stack positions out of 5000i,500n,10000p,200000b,50000s

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@@ -1172,11 +1187,12 @@ exmf-dist/fonts/type1/public/amsfonts/cm/cmsy6.pfb></usr/share/texlive/texmf-di
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-c/amsfonts/cm/cmti8.pfb>
-Output written on articleeo.pdf (18 pages, 737681 bytes).
+c/amsfonts/cm/cmti8.pfb></usr/share/texlive/texmf-dist/fonts/type1/public/amsfo
+nts/symbols/msbm10.pfb>
+Output written on articleeo.pdf (19 pages, 743136 bytes).

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diff --git a/PeCO-EO/articleeo.pdf b/PeCO-EO/articleeo.pdf
index 81c171e06d3a709a15720c725ad00d53d91dd9c1..54c4d6d97393adc8599062445ae6c69f3f007e86 100644 (file)
Binary files a/PeCO-EO/articleeo.pdf and b/PeCO-EO/articleeo.pdf differ

diff --git a/PeCO-EO/articleeo.tex b/PeCO-EO/articleeo.tex
index 0927d21b2c9a3624d1e5bc011b674eb35374b612..215576a0d37a700c4de1cd15a701bea12c2f052b 100644 (file)
--- a/PeCO-EO/articleeo.tex
+++ b/PeCO-EO/articleeo.tex
@@ -91,8 +91,7 @@ This paper makes the following contributions.
   simulator OMNeT++, to demonstrate the  efficiency of our protocol. We have compared
   our   PeCO   protocol   to   two   approaches   found   in   the   literature:
   DESK~\citep{ChinhVu} and  GAF~\citep{xu2001geography}, and also to  our previous
   simulator OMNeT++, to demonstrate the  efficiency of our protocol. We have compared
   our   PeCO   protocol   to   two   approaches   found   in   the   literature:
   DESK~\citep{ChinhVu} and  GAF~\citep{xu2001geography}, and also to  our previous

-  work published in~\citep{Idrees2} which is  based on another optimization model
-  for sensor scheduling.
+  protocol DilCO published in~\citep{Idrees2}. DilCO uses the same framework as PeCO but is  based on another optimization model for sensor scheduling.

 \end{enumerate}
 
 
 \end{enumerate}
 
 


@@ -197,7 +196,7 @@ used~\citep{castano2013column,doi:10.1080/0305215X.2012.687732,deschinkel2012col
 
 
 
 
 
 

-The authors in \citep{Idrees2} propose a Distributed Lifetime Coverage Optimization (DiLCO) protocol, maintains the coverage and improves the lifetime in WSNs. It is  an improved version
+The authors in \citep{Idrees2} propose a Distributed Lifetime Coverage Optimization (DiLCO) protocol, which maintains the coverage and improves the lifetime in WSNs. It is  an improved version

 of a research work they presented in~\citep{idrees2014coverage}.  First, they partition the area of interest into subregions using a divide-and-conquer method. DiLCO protocol is then distributed on the sensor nodes in each subregion in a second step. DiLCO protocol combines two techniques: a leader election in each subregion, followed by an optimization-based node activity scheduling performed by each elected leader. The proposed DiLCO protocol is a periodic protocol where each period is decomposed into 4 phases: information exchange, leader election, decision, and sensing. The simulations show that DiLCO is able to increase the WSN lifetime and provides improved coverage performance. {\it  In the PeCO
   protocol, We have proposed a new mathematical optimization model. Instead of trying to
 cover a set of specified points/targets as in DiLCO protocol, we formulate an integer program based
 of a research work they presented in~\citep{idrees2014coverage}.  First, they partition the area of interest into subregions using a divide-and-conquer method. DiLCO protocol is then distributed on the sensor nodes in each subregion in a second step. DiLCO protocol combines two techniques: a leader election in each subregion, followed by an optimization-based node activity scheduling performed by each elected leader. The proposed DiLCO protocol is a periodic protocol where each period is decomposed into 4 phases: information exchange, leader election, decision, and sensing. The simulations show that DiLCO is able to increase the WSN lifetime and provides improved coverage performance. {\it  In the PeCO
   protocol, We have proposed a new mathematical optimization model. Instead of trying to
 cover a set of specified points/targets as in DiLCO protocol, we formulate an integer program based


@@ -209,11 +208,11 @@ on perimeter coverage of each sensor. The model involves integer variables to ca
 \section{ The P{\scshape e}CO Protocol Description}
 \label{sec:The PeCO Protocol Description}
 
 \section{ The P{\scshape e}CO Protocol Description}
 \label{sec:The PeCO Protocol Description}
 

-In  this  section,  the Perimeter-based  Coverage
-Optimization protocol is decribed in details.  First we present the  assumptions we made and the models
-we considered (in particular the perimeter coverage one), second we describe the
-background idea of our protocol, and third  we give the outline of the algorithm
-executed by each node.
+%In  this  section,  the Perimeter-based  Coverage
+%Optimization protocol is decribed in details.  First we present the  assumptions we made and the models
+%we considered (in particular the perimeter coverage one), second we describe the
+%background idea of our protocol, and third  we give the outline of the algorithm
+%executed by each node.

 
 
 \subsection{Assumptions and Models}
 
 
 \subsection{Assumptions and Models}


@@ -278,7 +277,7 @@ The arc on the perimeter of~$u$ defined by the angular interval $[\pi
 Every couple of intersection points is placed on the angular interval $[0,2\pi)$
 in  a  counterclockwise manner,  leading  to  a  partitioning of  the  interval.
 Figure~\ref{figure1}(a)  illustrates  the arcs  for  the  nine neighbors  of
 Every couple of intersection points is placed on the angular interval $[0,2\pi)$
 in  a  counterclockwise manner,  leading  to  a  partitioning of  the  interval.
 Figure~\ref{figure1}(a)  illustrates  the arcs  for  the  nine neighbors  of

-sensor $0$ and  Figure~\ref{figure2} gives the position of  the corresponding arcs
+sensor $0$ and  table~\ref{my-label} gives the position of  the corresponding arcs

 in  the interval  $[0,2\pi)$. More  precisely, the  points are
 ordered according  to the  measures of  the angles  defined by  their respective
 positions. The intersection points are  then visited one after another, starting
 in  the interval  $[0,2\pi)$. More  precisely, the  points are
 ordered according  to the  measures of  the angles  defined by  their respective
 positions. The intersection points are  then visited one after another, starting


@@ -336,7 +335,7 @@ above is thus given by the sixth line of the table.
 
 
 In the PeCO  protocol, the scheduling of the sensor  nodes' activities is formulated  with an
 
 
 In the PeCO  protocol, the scheduling of the sensor  nodes' activities is formulated  with an

-integer program  based on  coverage intervals. The  formulation of  the coverage
+mixed-doi:10.1155/2010/926075integer program  based on  coverage intervals. The  formulation of  the coverage

 optimization problem is  detailed in~Section~\ref{cp}.  Note that  when a sensor
 node  has a  part of  its sensing  range outside  the WSN  sensing field,  as in
 Figure~\ref{figure3}, the maximum coverage level for  this arc is set to $\infty$
 optimization problem is  detailed in~Section~\ref{cp}.  Note that  when a sensor
 node  has a  part of  its sensing  range outside  the WSN  sensing field,  as in
 Figure~\ref{figure3}, the maximum coverage level for  this arc is set to $\infty$


@@ -357,7 +356,7 @@ optimization algorithm.
 The  WSN area of  interest is, in a  first step, divided  into regular
 homogeneous subregions  using a divide-and-conquer  algorithm. In a  second step
 our  protocol  will  be  executed  in   a  distributed  way  in  each  subregion
 The  WSN area of  interest is, in a  first step, divided  into regular
 homogeneous subregions  using a divide-and-conquer  algorithm. In a  second step
 our  protocol  will  be  executed  in   a  distributed  way  in  each  subregion

-simultaneously to schedule nodes' activities for one sensing period.
+simultaneously to schedule nodes' activities for one sensing period. In the study, sensors are assumed to be deployed almost uniformly over the region. The regular subdivision is made such that the number of hops between any pairs of sensors inside a subregion is less than or equal to 3. 

 
 As  shown in  Figure~\ref{figure4}, node  activity  scheduling is  produced by  our
 protocol in a periodic manner. Each period is divided into 4 stages: Information
 
 As  shown in  Figure~\ref{figure4}, node  activity  scheduling is  produced by  our
 protocol in a periodic manner. Each period is divided into 4 stages: Information


@@ -375,7 +374,7 @@ taken  into  account since  the  sensors  can  update  and then  exchange  their
 information (including their  residual energy) at the beginning  of each period.
 However, the pre-sensing  phases (INFO Exchange, Leader  Election, and Decision)
 are energy consuming, even for nodes that will not join the set cover to monitor
 information (including their  residual energy) at the beginning  of each period.
 However, the pre-sensing  phases (INFO Exchange, Leader  Election, and Decision)
 are energy consuming, even for nodes that will not join the set cover to monitor

-the area.
+the area. Sensing period duration is adapted according to the QoS requirements of the application.

 
 \begin{figure}[t!]
 \centering
 
 \begin{figure}[t!]
 \centering


@@ -476,8 +475,9 @@ construct the set of active sensors in the sensing stage.
 \section{Perimeter-based Coverage Problem Formulation}
 \label{cp}
 
 \section{Perimeter-based Coverage Problem Formulation}
 \label{cp}
 

-In this  section, the coverage model is  mathematically formulated. The following
-notations are used  throughout the
+In this  section, the perimeter-based coverage problem is  mathematically formulated. It has been proved to be a NP-hard problem by\citep{doi:10.1155/2010/926075}. Authors study the coverage of the perimeter of a large object requiring to be monitored. For the proposed formulation in this paper, the large object to be monitored is the sensor itself (or more precisely its sensing area).
+
+The following notations are used  throughout the

 section.\\
 First, the following sets:
 \begin{itemize}
 section.\\
 First, the following sets:
 \begin{itemize}


@@ -500,16 +500,16 @@ a^j_{ik} = \left \{
 \end{equation}
 Note that $a^k_{ik}=1$ by definition of the interval.
 
 \end{equation}
 Note that $a^k_{ik}=1$ by definition of the interval.
 

-Second, several binary  and integer  variables are defined.  Hence,  each binary
+Second, several variables are defined.  Hence,  each binary

 variable $X_{k}$  determines the activation of  sensor $k$ in the  sensing phase
 variable $X_{k}$  determines the activation of  sensor $k$ in the  sensing phase

-($X_k=1$ if  the sensor $k$  is active or 0  otherwise).  $M^j_i$ is  an integer
+($X_k=1$ if  the sensor $k$  is active or 0  otherwise).  $M^j_i$ is  a

 variable  which  measures  the  undercoverage  for  the  coverage  interval  $i$
 corresponding to  sensor~$j$. In  the same  way, the  overcoverage for  the same
 coverage interval is given by the variable $V^j_i$.
 
 variable  which  measures  the  undercoverage  for  the  coverage  interval  $i$
 corresponding to  sensor~$j$. In  the same  way, the  overcoverage for  the same
 coverage interval is given by the variable $V^j_i$.
 

-If we decide to sustain a level of coverage equal to $l$ all along the perimeter
-of sensor  $j$, we have  to ensure  that at least  $l$ sensors involved  in each
-coverage  interval $i  \in I_j$  of  sensor $j$  are active.   According to  the
+To sustain a level of coverage equal to $l$ all along the perimeter
+of sensor  $j$, at least  $l$ sensors involved  in each
+coverage  interval $i  \in I_j$  of  sensor $j$ have to be active.   According to  the

 previous notations, the number of active sensors in the coverage interval $i$ of
 sensor $j$  is given by  $\sum_{k \in A} a^j_{ik}  X_k$.  To extend  the network
 lifetime,  the objective  is to  activate a  minimal number  of sensors  in each
 previous notations, the number of active sensors in the coverage interval $i$ of
 sensor $j$  is given by  $\sum_{k \in A} a^j_{ik}  X_k$.  To extend  the network
 lifetime,  the objective  is to  activate a  minimal number  of sensors  in each


@@ -525,7 +525,7 @@ to reach a coverage level as close as possible to the desired one.
 
 
 
 
 
 

-Our coverage optimization problem can then be mathematically expressed as follows: 
+The coverage optimization problem can then be mathematically expressed as follows: 

 
 \begin{equation} 
 \left \{
 
 \begin{equation} 
 \left \{


@@ -534,25 +534,28 @@ Our coverage optimization problem can then be mathematically expressed as follow
 \textrm{subject to :}&\\
 \sum_{k \in A} ( a^j_{ik} ~ X_{k}) + M^j_i  \geq l \quad \forall i \in I_j, \forall j \in S\\
 \sum_{k \in A} ( a^j_{ik} ~ X_{k}) - V^j_i  \leq l \quad \forall i \in I_j, \forall j \in S\\
 \textrm{subject to :}&\\
 \sum_{k \in A} ( a^j_{ik} ~ X_{k}) + M^j_i  \geq l \quad \forall i \in I_j, \forall j \in S\\
 \sum_{k \in A} ( a^j_{ik} ~ X_{k}) - V^j_i  \leq l \quad \forall i \in I_j, \forall j \in S\\

-X_{k} \in \{0,1\}, \forall k \in A
+X_{k} \in \{0,1\}, \forall k \in A \\

 M^j_i, V^j_i \in  \mathbb{R}^{+}
 \end{array}
 \right.
 \end{equation}
 
 M^j_i, V^j_i \in  \mathbb{R}^{+}
 \end{array}
 \right.
 \end{equation}
 

+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 $l$. 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 : $M_{i}^{j}=l-l^{i}$, $V_{i}^{j}=0$. In 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 : $M_{i}^{j}=0$, $V_{i}^{j}=l^{i}-l$.  
+

 $\alpha^j_i$ and $\beta^j_i$  are nonnegative weights selected  according to the
 relative importance of satisfying the associated level of coverage. For example,
 weights associated with  coverage intervals of a specified part  of a region may
 be  given by a  relatively larger  magnitude than  weights associated  with another
 $\alpha^j_i$ and $\beta^j_i$  are nonnegative weights selected  according to the
 relative importance of satisfying the associated level of coverage. For example,
 weights associated with  coverage intervals of a specified part  of a region may
 be  given by a  relatively larger  magnitude than  weights associated  with another

-region. This  kind of integer program  is inspired from the  model developed for
+region. This  kind of mixed-integer program  is inspired from the  model developed for

 brachytherapy treatment planning  for optimizing dose  distribution
 brachytherapy treatment planning  for optimizing dose  distribution

-\citep{0031-9155-44-1-012}. The integer  program must be solved by  the leader in
+\citep{0031-9155-44-1-012}.  The choice of variables $\alpha$ and $\beta$ should be made according to the needs of the application. $\alpha$ should be enough large to prevent undercoverage and so to reach the highest possible coverage ratio. $\beta$ should be enough large to prevent overcoverage and so to activate a minimum number of sensors. 
+The mixed-integer  program must be solved by  the leader in

 each subregion at the beginning of  each sensing phase, whenever the environment
 has  changed (new  leader,  death of  some  sensors). Note  that  the number  of
 constraints in the model is constant  (constraints of coverage expressed for all
 sensors), whereas the number of variables $X_k$ decreases over periods, since 
 only alive  sensors (sensors with enough energy to  be alive during one
 each subregion at the beginning of  each sensing phase, whenever the environment
 has  changed (new  leader,  death of  some  sensors). Note  that  the number  of
 constraints in the model is constant  (constraints of coverage expressed for all
 sensors), whereas the number of variables $X_k$ decreases over periods, since 
 only alive  sensors (sensors with enough energy to  be alive during one

-sensing phase) are considered in the model.
+sensing phase) are considered in the model. 

 
 \section{Performance Evaluation and Analysis}  
 \label{sec:Simulation Results and Analysis}
 
 \section{Performance Evaluation and Analysis}  
 \label{sec:Simulation Results and Analysis}


@@ -798,8 +801,8 @@ ratio greater than 50\%, we can  see on Figure~\ref{figure8}(b) that the lifetim
 is about twice longer with  PeCO compared to DESK protocol.  The performance
 difference    is    more    obvious   in    Figure~\ref{figure8}(b)    than    in
 Figure~\ref{figure8}(a) because the gain induced  by our protocols increases with
 is about twice longer with  PeCO compared to DESK protocol.  The performance
 difference    is    more    obvious   in    Figure~\ref{figure8}(b)    than    in
 Figure~\ref{figure8}(a) because the gain induced  by our protocols increases with

- time, and the lifetime with a coverage  of 50\% is far  longer than with
-95\%.
+ time, and the lifetime with a coverage  over 50\% is far  longer than with
+95\%. 

 
 \begin{figure}[h!]
   \centering
 
 \begin{figure}[h!]
   \centering


@@ -834,7 +837,8 @@ not ineffective for the smallest network sizes.
 
 
 \subsubsection{\bf Impact of $\alpha$ and $\beta$ on PeCO's performance}
 
 
 \subsubsection{\bf Impact of $\alpha$ and $\beta$ on PeCO's performance}

-Table~\ref{my-labelx} explains all possible network lifetime result of the relation between the different values of $\alpha$ and $\beta$, and for a network size equal to 200 sensor nodes. As can be seen in Table~\ref{my-labelx},  it is obvious and clear that when $\alpha$ decreased and $\beta$ increased by any step, the network lifetime for $Lifetime_{50}$ increased and the $Lifetime_{95}$ decreased. Therefore, selecting the values of $\alpha$ and $\beta$ depend on the application type used in the sensor nework. In PeCO protocol, $\alpha$ and $\beta$ are chosen based on the largest value of network lifetime for $Lifetime_{95}$.
+Table~\ref{my-labelx} shows network lifetime results for the different values of $\alpha$ and $\beta$, and for a network size equal to 200 sensor nodes. 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 {\it Lifetime50} with $\beta \gg \alpha$: a large number of periods with low coverage ratio. With $\alpha \gg \beta$, we priviligie the coverage even if some areas may be overcovered, so high coverage ratio is reached, but a large number of sensors are activated to achieve this goal. Therefore network lifetime is reduced. The choice $\alpha=0.6$ and $\beta=0.4$ seems to achieve the best compromise between lifetime and coverage ratio.     
+%As can be seen in Table~\ref{my-labelx},  it is obvious and clear that when $\alpha$ decreased and $\beta$ increased by any step, the network lifetime for $Lifetime_{50}$ increased and the $Lifetime_{95}$ decreased. Therefore, selecting the values of $\alpha$ and $\beta$ depend on the application type used in the sensor nework. In PeCO protocol, $\alpha$ and $\beta$ are chosen based on the largest value of network lifetime for $Lifetime_{95}$.

 
 \begin{table}[h]
 \centering
 
 \begin{table}[h]
 \centering


@@ -849,7 +853,7 @@ $\alpha$ & $\beta$ & $Lifetime_{50}$ & $Lifetime_{95}$ \\ \hline
 0.3 & 0.7 & 134 & 0 \\ \hline
 0.4 & 0.6 & 125 & 0 \\ \hline
 0.5 & 0.5 & 118 & 30 \\ \hline
 0.3 & 0.7 & 134 & 0 \\ \hline
 0.4 & 0.6 & 125 & 0 \\ \hline
 0.5 & 0.5 & 118 & 30 \\ \hline

-0.6 & 0.4 & 94 & 57 \\ \hline
+{\bf 0.6} & {\bf 0.4} & {\bf 94} & {\bf 57} \\ \hline

 0.7 & 0.3 & 97 & 49 \\ \hline
 0.8 & 0.2 & 90 & 52 \\ \hline
 0.9 & 0.1 & 77 & 50 \\ \hline
 0.7 & 0.3 & 97 & 49 \\ \hline
 0.8 & 0.2 & 90 & 52 \\ \hline
 0.9 & 0.1 & 77 & 50 \\ \hline

diff --git a/PeCO-EO/articleeo.tex~ b/PeCO-EO/articleeo.tex~
index 96b4465cc70683363758f94036cda1a65c9a3c78..215576a0d37a700c4de1cd15a701bea12c2f052b 100644 (file)
--- a/PeCO-EO/articleeo.tex~
+++ b/PeCO-EO/articleeo.tex~
@@ -91,8 +91,7 @@ This paper makes the following contributions.
   simulator OMNeT++, to demonstrate the  efficiency of our protocol. We have compared
   our   PeCO   protocol   to   two   approaches   found   in   the   literature:
   DESK~\citep{ChinhVu} and  GAF~\citep{xu2001geography}, and also to  our previous
   simulator OMNeT++, to demonstrate the  efficiency of our protocol. We have compared
   our   PeCO   protocol   to   two   approaches   found   in   the   literature:
   DESK~\citep{ChinhVu} and  GAF~\citep{xu2001geography}, and also to  our previous

-  work published in~\citep{Idrees2} which is  based on another optimization model
-  for sensor scheduling.
+  protocol DilCO published in~\citep{Idrees2}. DilCO uses the same framework as PeCO but is  based on another optimization model for sensor scheduling.

 \end{enumerate}
 
 
 \end{enumerate}
 
 


@@ -197,7 +196,7 @@ used~\citep{castano2013column,doi:10.1080/0305215X.2012.687732,deschinkel2012col
 
 
 
 
 
 

-The authors in \citep{Idrees2} propose a Distributed Lifetime Coverage Optimization (DiLCO) protocol, maintains the coverage and improves the lifetime in WSNs. It is  an improved version
+The authors in \citep{Idrees2} propose a Distributed Lifetime Coverage Optimization (DiLCO) protocol, which maintains the coverage and improves the lifetime in WSNs. It is  an improved version

 of a research work they presented in~\citep{idrees2014coverage}.  First, they partition the area of interest into subregions using a divide-and-conquer method. DiLCO protocol is then distributed on the sensor nodes in each subregion in a second step. DiLCO protocol combines two techniques: a leader election in each subregion, followed by an optimization-based node activity scheduling performed by each elected leader. The proposed DiLCO protocol is a periodic protocol where each period is decomposed into 4 phases: information exchange, leader election, decision, and sensing. The simulations show that DiLCO is able to increase the WSN lifetime and provides improved coverage performance. {\it  In the PeCO
   protocol, We have proposed a new mathematical optimization model. Instead of trying to
 cover a set of specified points/targets as in DiLCO protocol, we formulate an integer program based
 of a research work they presented in~\citep{idrees2014coverage}.  First, they partition the area of interest into subregions using a divide-and-conquer method. DiLCO protocol is then distributed on the sensor nodes in each subregion in a second step. DiLCO protocol combines two techniques: a leader election in each subregion, followed by an optimization-based node activity scheduling performed by each elected leader. The proposed DiLCO protocol is a periodic protocol where each period is decomposed into 4 phases: information exchange, leader election, decision, and sensing. The simulations show that DiLCO is able to increase the WSN lifetime and provides improved coverage performance. {\it  In the PeCO
   protocol, We have proposed a new mathematical optimization model. Instead of trying to
 cover a set of specified points/targets as in DiLCO protocol, we formulate an integer program based


@@ -209,11 +208,11 @@ on perimeter coverage of each sensor. The model involves integer variables to ca
 \section{ The P{\scshape e}CO Protocol Description}
 \label{sec:The PeCO Protocol Description}
 
 \section{ The P{\scshape e}CO Protocol Description}
 \label{sec:The PeCO Protocol Description}
 

-In  this  section,  the Perimeter-based  Coverage
-Optimization protocol is decribed in details.  First we present the  assumptions we made and the models
-we considered (in particular the perimeter coverage one), second we describe the
-background idea of our protocol, and third  we give the outline of the algorithm
-executed by each node.
+%In  this  section,  the Perimeter-based  Coverage
+%Optimization protocol is decribed in details.  First we present the  assumptions we made and the models
+%we considered (in particular the perimeter coverage one), second we describe the
+%background idea of our protocol, and third  we give the outline of the algorithm
+%executed by each node.

 
 
 \subsection{Assumptions and Models}
 
 
 \subsection{Assumptions and Models}


@@ -278,7 +277,7 @@ The arc on the perimeter of~$u$ defined by the angular interval $[\pi
 Every couple of intersection points is placed on the angular interval $[0,2\pi)$
 in  a  counterclockwise manner,  leading  to  a  partitioning of  the  interval.
 Figure~\ref{figure1}(a)  illustrates  the arcs  for  the  nine neighbors  of
 Every couple of intersection points is placed on the angular interval $[0,2\pi)$
 in  a  counterclockwise manner,  leading  to  a  partitioning of  the  interval.
 Figure~\ref{figure1}(a)  illustrates  the arcs  for  the  nine neighbors  of

-sensor $0$ and  Figure~\ref{figure2} gives the position of  the corresponding arcs
+sensor $0$ and  table~\ref{my-label} gives the position of  the corresponding arcs

 in  the interval  $[0,2\pi)$. More  precisely, the  points are
 ordered according  to the  measures of  the angles  defined by  their respective
 positions. The intersection points are  then visited one after another, starting
 in  the interval  $[0,2\pi)$. More  precisely, the  points are
 ordered according  to the  measures of  the angles  defined by  their respective
 positions. The intersection points are  then visited one after another, starting


@@ -336,7 +335,7 @@ above is thus given by the sixth line of the table.
 
 
 In the PeCO  protocol, the scheduling of the sensor  nodes' activities is formulated  with an
 
 
 In the PeCO  protocol, the scheduling of the sensor  nodes' activities is formulated  with an

-integer program  based on  coverage intervals. The  formulation of  the coverage
+mixed-doi:10.1155/2010/926075integer program  based on  coverage intervals. The  formulation of  the coverage

 optimization problem is  detailed in~Section~\ref{cp}.  Note that  when a sensor
 node  has a  part of  its sensing  range outside  the WSN  sensing field,  as in
 Figure~\ref{figure3}, the maximum coverage level for  this arc is set to $\infty$
 optimization problem is  detailed in~Section~\ref{cp}.  Note that  when a sensor
 node  has a  part of  its sensing  range outside  the WSN  sensing field,  as in
 Figure~\ref{figure3}, the maximum coverage level for  this arc is set to $\infty$


@@ -357,7 +356,7 @@ optimization algorithm.
 The  WSN area of  interest is, in a  first step, divided  into regular
 homogeneous subregions  using a divide-and-conquer  algorithm. In a  second step
 our  protocol  will  be  executed  in   a  distributed  way  in  each  subregion
 The  WSN area of  interest is, in a  first step, divided  into regular
 homogeneous subregions  using a divide-and-conquer  algorithm. In a  second step
 our  protocol  will  be  executed  in   a  distributed  way  in  each  subregion

-simultaneously to schedule nodes' activities for one sensing period.
+simultaneously to schedule nodes' activities for one sensing period. In the study, sensors are assumed to be deployed almost uniformly over the region. The regular subdivision is made such that the number of hops between any pairs of sensors inside a subregion is less than or equal to 3. 

 
 As  shown in  Figure~\ref{figure4}, node  activity  scheduling is  produced by  our
 protocol in a periodic manner. Each period is divided into 4 stages: Information
 
 As  shown in  Figure~\ref{figure4}, node  activity  scheduling is  produced by  our
 protocol in a periodic manner. Each period is divided into 4 stages: Information


@@ -375,7 +374,7 @@ taken  into  account since  the  sensors  can  update  and then  exchange  their
 information (including their  residual energy) at the beginning  of each period.
 However, the pre-sensing  phases (INFO Exchange, Leader  Election, and Decision)
 are energy consuming, even for nodes that will not join the set cover to monitor
 information (including their  residual energy) at the beginning  of each period.
 However, the pre-sensing  phases (INFO Exchange, Leader  Election, and Decision)
 are energy consuming, even for nodes that will not join the set cover to monitor

-the area.
+the area. Sensing period duration is adapted according to the QoS requirements of the application.

 
 \begin{figure}[t!]
 \centering
 
 \begin{figure}[t!]
 \centering


@@ -476,8 +475,9 @@ construct the set of active sensors in the sensing stage.
 \section{Perimeter-based Coverage Problem Formulation}
 \label{cp}
 
 \section{Perimeter-based Coverage Problem Formulation}
 \label{cp}
 

-In this  section, the coverage model is  mathematically formulated. The following
-notations are used  throughout the
+In this  section, the perimeter-based coverage problem is  mathematically formulated. It has been proved to be a NP-hard problem by\citep{doi:10.1155/2010/926075}. Authors study the coverage of the perimeter of a large object requiring to be monitored. For the proposed formulation in this paper, the large object to be monitored is the sensor itself (or more precisely its sensing area).
+
+The following notations are used  throughout the

 section.\\
 First, the following sets:
 \begin{itemize}
 section.\\
 First, the following sets:
 \begin{itemize}


@@ -500,16 +500,16 @@ a^j_{ik} = \left \{
 \end{equation}
 Note that $a^k_{ik}=1$ by definition of the interval.
 
 \end{equation}
 Note that $a^k_{ik}=1$ by definition of the interval.
 

-Second, several binary  and integer  variables are defined.  Hence,  each binary
+Second, several variables are defined.  Hence,  each binary

 variable $X_{k}$  determines the activation of  sensor $k$ in the  sensing phase
 variable $X_{k}$  determines the activation of  sensor $k$ in the  sensing phase

-($X_k=1$ if  the sensor $k$  is active or 0  otherwise).  $M^j_i$ is  an integer
+($X_k=1$ if  the sensor $k$  is active or 0  otherwise).  $M^j_i$ is  a

 variable  which  measures  the  undercoverage  for  the  coverage  interval  $i$
 corresponding to  sensor~$j$. In  the same  way, the  overcoverage for  the same
 coverage interval is given by the variable $V^j_i$.
 
 variable  which  measures  the  undercoverage  for  the  coverage  interval  $i$
 corresponding to  sensor~$j$. In  the same  way, the  overcoverage for  the same
 coverage interval is given by the variable $V^j_i$.
 

-If we decide to sustain a level of coverage equal to $l$ all along the perimeter
-of sensor  $j$, we have  to ensure  that at least  $l$ sensors involved  in each
-coverage  interval $i  \in I_j$  of  sensor $j$  are active.   According to  the
+To sustain a level of coverage equal to $l$ all along the perimeter
+of sensor  $j$, at least  $l$ sensors involved  in each
+coverage  interval $i  \in I_j$  of  sensor $j$ have to be active.   According to  the

 previous notations, the number of active sensors in the coverage interval $i$ of
 sensor $j$  is given by  $\sum_{k \in A} a^j_{ik}  X_k$.  To extend  the network
 lifetime,  the objective  is to  activate a  minimal number  of sensors  in each
 previous notations, the number of active sensors in the coverage interval $i$ of
 sensor $j$  is given by  $\sum_{k \in A} a^j_{ik}  X_k$.  To extend  the network
 lifetime,  the objective  is to  activate a  minimal number  of sensors  in each


@@ -525,7 +525,7 @@ to reach a coverage level as close as possible to the desired one.
 
 
 
 
 
 

-Our coverage optimization problem can then be mathematically expressed as follows: 
+The coverage optimization problem can then be mathematically expressed as follows: 

 
 \begin{equation} 
 \left \{
 
 \begin{equation} 
 \left \{


@@ -534,24 +534,28 @@ Our coverage optimization problem can then be mathematically expressed as follow
 \textrm{subject to :}&\\
 \sum_{k \in A} ( a^j_{ik} ~ X_{k}) + M^j_i  \geq l \quad \forall i \in I_j, \forall j \in S\\
 \sum_{k \in A} ( a^j_{ik} ~ X_{k}) - V^j_i  \leq l \quad \forall i \in I_j, \forall j \in S\\
 \textrm{subject to :}&\\
 \sum_{k \in A} ( a^j_{ik} ~ X_{k}) + M^j_i  \geq l \quad \forall i \in I_j, \forall j \in S\\
 \sum_{k \in A} ( a^j_{ik} ~ X_{k}) - V^j_i  \leq l \quad \forall i \in I_j, \forall j \in S\\

-X_{k} \in \{0,1\}, \forall k \in A
+X_{k} \in \{0,1\}, \forall k \in A \\
+M^j_i, V^j_i \in  \mathbb{R}^{+}

 \end{array}
 \right.
 \end{equation}
 
 \end{array}
 \right.
 \end{equation}
 

+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 $l$. 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 : $M_{i}^{j}=l-l^{i}$, $V_{i}^{j}=0$. In 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 : $M_{i}^{j}=0$, $V_{i}^{j}=l^{i}-l$.  
+

 $\alpha^j_i$ and $\beta^j_i$  are nonnegative weights selected  according to the
 relative importance of satisfying the associated level of coverage. For example,
 weights associated with  coverage intervals of a specified part  of a region may
 be  given by a  relatively larger  magnitude than  weights associated  with another
 $\alpha^j_i$ and $\beta^j_i$  are nonnegative weights selected  according to the
 relative importance of satisfying the associated level of coverage. For example,
 weights associated with  coverage intervals of a specified part  of a region may
 be  given by a  relatively larger  magnitude than  weights associated  with another

-region. This  kind of integer program  is inspired from the  model developed for
+region. This  kind of mixed-integer program  is inspired from the  model developed for

 brachytherapy treatment planning  for optimizing dose  distribution
 brachytherapy treatment planning  for optimizing dose  distribution

-\citep{0031-9155-44-1-012}. The integer  program must be solved by  the leader in
+\citep{0031-9155-44-1-012}.  The choice of variables $\alpha$ and $\beta$ should be made according to the needs of the application. $\alpha$ should be enough large to prevent undercoverage and so to reach the highest possible coverage ratio. $\beta$ should be enough large to prevent overcoverage and so to activate a minimum number of sensors. 
+The mixed-integer  program must be solved by  the leader in

 each subregion at the beginning of  each sensing phase, whenever the environment
 has  changed (new  leader,  death of  some  sensors). Note  that  the number  of
 constraints in the model is constant  (constraints of coverage expressed for all
 sensors), whereas the number of variables $X_k$ decreases over periods, since 
 only alive  sensors (sensors with enough energy to  be alive during one
 each subregion at the beginning of  each sensing phase, whenever the environment
 has  changed (new  leader,  death of  some  sensors). Note  that  the number  of
 constraints in the model is constant  (constraints of coverage expressed for all
 sensors), whereas the number of variables $X_k$ decreases over periods, since 
 only alive  sensors (sensors with enough energy to  be alive during one

-sensing phase) are considered in the model.
+sensing phase) are considered in the model. 

 
 \section{Performance Evaluation and Analysis}  
 \label{sec:Simulation Results and Analysis}
 
 \section{Performance Evaluation and Analysis}  
 \label{sec:Simulation Results and Analysis}


@@ -797,8 +801,8 @@ ratio greater than 50\%, we can  see on Figure~\ref{figure8}(b) that the lifetim
 is about twice longer with  PeCO compared to DESK protocol.  The performance
 difference    is    more    obvious   in    Figure~\ref{figure8}(b)    than    in
 Figure~\ref{figure8}(a) because the gain induced  by our protocols increases with
 is about twice longer with  PeCO compared to DESK protocol.  The performance
 difference    is    more    obvious   in    Figure~\ref{figure8}(b)    than    in
 Figure~\ref{figure8}(a) because the gain induced  by our protocols increases with

- time, and the lifetime with a coverage  of 50\% is far  longer than with
-95\%.
+ time, and the lifetime with a coverage  over 50\% is far  longer than with
+95\%. 

 
 \begin{figure}[h!]
   \centering
 
 \begin{figure}[h!]
   \centering


@@ -833,7 +837,8 @@ not ineffective for the smallest network sizes.
 
 
 \subsubsection{\bf Impact of $\alpha$ and $\beta$ on PeCO's performance}
 
 
 \subsubsection{\bf Impact of $\alpha$ and $\beta$ on PeCO's performance}

-Table~\ref{my-labelx} explains all possible network lifetime result of the relation between the different values of $\alpha$ and $\beta$, and for a network size equal to 200 sensor nodes. As can be seen in Table~\ref{my-labelx},  it is obvious and clear that when $\alpha$ decreased and $\beta$ increased by any step, the network lifetime for $Lifetime_{50}$ increased and the $Lifetime_{95}$ decreased. Therefore, selecting the values of $\alpha$ and $\beta$ depend on the application type used in the sensor nework. In PeCO protocol, $\alpha$ and $\beta$ are chosen based on the largest value of network lifetime for $Lifetime_{95}$.
+Table~\ref{my-labelx} shows network lifetime results for the different values of $\alpha$ and $\beta$, and for a network size equal to 200 sensor nodes. 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 {\it Lifetime50} with $\beta \gg \alpha$: a large number of periods with low coverage ratio. With $\alpha \gg \beta$, we priviligie the coverage even if some areas may be overcovered, so high coverage ratio is reached, but a large number of sensors are activated to achieve this goal. Therefore network lifetime is reduced. The choice $\alpha=0.6$ and $\beta=0.4$ seems to achieve the best compromise between lifetime and coverage ratio.     
+%As can be seen in Table~\ref{my-labelx},  it is obvious and clear that when $\alpha$ decreased and $\beta$ increased by any step, the network lifetime for $Lifetime_{50}$ increased and the $Lifetime_{95}$ decreased. Therefore, selecting the values of $\alpha$ and $\beta$ depend on the application type used in the sensor nework. In PeCO protocol, $\alpha$ and $\beta$ are chosen based on the largest value of network lifetime for $Lifetime_{95}$.

 
 \begin{table}[h]
 \centering
 
 \begin{table}[h]
 \centering


@@ -848,7 +853,7 @@ $\alpha$ & $\beta$ & $Lifetime_{50}$ & $Lifetime_{95}$ \\ \hline
 0.3 & 0.7 & 134 & 0 \\ \hline
 0.4 & 0.6 & 125 & 0 \\ \hline
 0.5 & 0.5 & 118 & 30 \\ \hline
 0.3 & 0.7 & 134 & 0 \\ \hline
 0.4 & 0.6 & 125 & 0 \\ \hline
 0.5 & 0.5 & 118 & 30 \\ \hline

-0.6 & 0.4 & 94 & 57 \\ \hline
+{\bf 0.6} & {\bf 0.4} & {\bf 94} & {\bf 57} \\ \hline

 0.7 & 0.3 & 97 & 49 \\ \hline
 0.8 & 0.2 & 90 & 52 \\ \hline
 0.9 & 0.1 & 77 & 50 \\ \hline
 0.7 & 0.3 & 97 & 49 \\ \hline
 0.8 & 0.2 & 90 & 52 \\ \hline
 0.9 & 0.1 & 77 & 50 \\ \hline

diff --git a/PeCO-EO/biblio.bib b/PeCO-EO/biblio.bib
index b342afa5b332eb458cd8f2f09cf7a18398da4d85..5c93e97a67fa8aaff896fc592efc8afbf9b53cf6 100644 (file)
--- a/PeCO-EO/biblio.bib
+++ b/PeCO-EO/biblio.bib
@@ -1028,7 +1028,7 @@ year = {2012},
 
 @article{doi:10.1080/0305215X.2012.687732,
 author = {Singh, Alok and Rossi, André and Sevaux, Marc},
 
 @article{doi:10.1080/0305215X.2012.687732,
 author = {Singh, Alok and Rossi, André and Sevaux, Marc},

-title = {Matheuristic approaches for Q-coverage problem versions in wireless sensor networks},
+title = {Metaheuristic approaches for Q-coverage problem versions in wireless sensor networks},

 journal = {Engineering Optimization},
 volume = {45},
 number = {5},
 journal = {Engineering Optimization},
 volume = {45},
 number = {5},


@@ -1036,4 +1036,13 @@ pages = {609-626},
 year = {2013}
 }
 
 year = {2013}
 }
 

+@article{doi:10.1155/2010/926075,
+author = {Hung,  Ka-Shun and Lui, King-Shan},
+title = {Perimeter Coverage Scheduling in Wireless Sensor Networks Using Sensors with a Single Continuous Cover Range},
+journal = {EURASIP Journal on Wireless Communications and Networking },
+volume = {2010},
+year = {2010}
+}
+
+

 
 

diff --git a/PeCO-EO/reponse.tex b/PeCO-EO/reponse.tex
index 4965597e9a7bee070b0095bd5b03148d96d34332..b00dd1d194dfe02e47b11e0a3069363f5fb1e3f4 100644 (file)
--- a/PeCO-EO/reponse.tex
+++ b/PeCO-EO/reponse.tex
@@ -101,9 +101,9 @@ s used are very vague and do not bring out their key contributions. Some referen
 
 \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.   \\
 
 
 \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 interesting. Indeed, figures 8(a) and (b) highlight this result. PeCO methods allows to achieve a coverage ratio greater than $50\%$ for many more periods than the others three methods, but for applications requiring an high level of coverage (greater than $95\%$), DilCO method is more efficient.                                 }}\\
+\textcolor{blue}{\textbf{\textsc{Answer:}  Your remark is interesting. Indeed, figures 8(a) and (b) highlight this result. PeCO methods allows to achieve a coverage ratio greater than $50\%$ for many more periods than the others three methods, but for applications requiring an high level of coverage (greater than $95\%$), DilCO method is more efficient. It is explained at the end of section 5.2.4.                                }}\\

 
 

-%%%%%%%%%%%%%%%%%%%%%%  ENGLISH and GRAMMER %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%%%%%%%%%%%%%%%%%%%%%%  ENGLISH and GRAMMAR %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

 
 \noindent\textcolor{black}{\textbf{\Large English and Grammar:}} \\
 
 
 \noindent\textcolor{black}{\textbf{\Large English and Grammar:}} \\
 


@@ -170,7 +170,7 @@ The paper entitled "Perimeter-based Coverage Optimization to Improve Lifetime in
 
 \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.  \\
 
 
 \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:}  As far as we know, representing the objective function as a weighted sum of criteria to be minimized in case of multicriteria optimization is a classical method.                                        }}\\
+\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 for each sensor. As far as we know, 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.    \\
 
 
 \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.    \\


@@ -179,14 +179,15 @@ The paper entitled "Perimeter-based Coverage Optimization to Improve Lifetime in
 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
 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 CPLE\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:
+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}
 \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 used 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 used with CPLEX to solves the LP-relaxation according to the number of constraints.
+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.

 \\
 \begin{tabular}{|c|c|c|c|c|c|r|}
 \hline
 \\
 \begin{tabular}{|c|c|c|c|c|c|r|}
 \hline


@@ -200,7 +201,8 @@ of nodes &&&&relaxation &B\&B tree &\\
 300 &18.5 & 17&3.6 Mb & 3.5 Mb & 3 &644 Kb\\
 \hline
 \end{tabular}
 300 &18.5 & 17&3.6 Mb & 3.5 Mb & 3 &644 Kb\\
 \hline
 \end{tabular}

-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 dos not exceed 3 nodes. This result leads one to believe the memory used with CPLEX for solving the IP would be very close to that for the LP-relaxation, that is to say around 100 Kb for a subregion containing $S=10$ 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).
+\\
+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 dos 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 around 100 Kb for a subregion containing $S=10$ 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 is directly depending 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}}}\\
 
 \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 is directly depending 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}}}\\
 


@@ -212,7 +214,7 @@ It is noteworthy that the difference of memory used with GLPK between the resolu
 
 \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 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:}       }}.\\
+\textcolor{blue}{\textbf{\textsc{Answer:} Right. This observation has been added at the end of the introduction}}.\\

 
 
 
 
 
 


@@ -261,7 +263,7 @@ It is noteworthy that the difference of memory used with GLPK between the resolu
 
 \noindent {\ding{90}  Page 7, line 20 "regular homogeneous subregions" is too vague. }  \\
 
 
 \noindent {\ding{90}  Page 7, line 20 "regular homogeneous subregions" is too vague. }  \\
 

-\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. A FAIRE          }}.\\
+\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. }}.\\

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