Update by Ali

[JournalMultiPeriods.git] / article.tex

diff --git a/article.tex b/article.tex
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--- a/article.tex
+++ b/article.tex
@@ -67,21 +67,31 @@
 %% \address{Address\fnref{label3}}
 %% \fntext[label3]{}
 
 %% \address{Address\fnref{label3}}
 %% \fntext[label3]{}
 

-\title{Multiperiod Distributed Lifetime Coverage Optimization Protocol in Wireless Sensor Networks}
+\title{Multiround Distributed Lifetime Coverage Optimization Protocol in Wireless Sensor Networks}

 
 %% use optional labels to link authors explicitly to addresses:
 %% \author[label1,label2]{}
 %% \address[label1]{}
 %% \address[label2]{}
 
 %% use optional labels to link authors explicitly to addresses:
 %% \author[label1,label2]{}
 %% \address[label1]{}
 %% \address[label2]{}

-\author{Ali Kadhum Idrees, Karine Deschinkel, \\
-Michel Salomon, and Rapha\"el Couturier}
+%\author{Ali Kadhum Idrees, Karine Deschinkel, \\
+%Michel Salomon, and Rapha\"el Couturier}
+

 %\thanks{are members in the AND team - DISC department - FEMTO-ST Institute, University of Franche-Comt\'e, Belfort, France.
 % e-mail: ali.idness@edu.univ-fcomte.fr, $\lbrace$karine.deschinkel, michel.salomon, raphael.couturier$\rbrace$@univ-fcomte.fr.}% <-this % stops a space
 %\thanks{}% <-this % stops a space
  
 %\thanks{are members in the AND team - DISC department - FEMTO-ST Institute, University of Franche-Comt\'e, Belfort, France.
 % e-mail: ali.idness@edu.univ-fcomte.fr, $\lbrace$karine.deschinkel, michel.salomon, raphael.couturier$\rbrace$@univ-fcomte.fr.}% <-this % stops a space
 %\thanks{}% <-this % stops a space
  

-\address{FEMTO-ST Institute, University of Franche-Comt\'e, Belfort, France. \\ 
-e-mail: ali.idness@edu.univ-fcomte.fr, \\
-$\lbrace$karine.deschinkel, michel.salomon, raphael.couturier$\rbrace$@univ-fcomte.fr.}
+%\address{FEMTO-ST Institute, University of Franche-Comt\'e, Belfort, France. \\ 
+%e-mail: ali.idness@edu.univ-fcomte.fr, \\
+%$\lbrace$karine.deschinkel, michel.salomon, raphael.couturier$\rbrace$@univ-fcomte.fr.}
+
+
+\author{Ali Kadhum Idrees$^{a,b}$, Karine Deschinkel$^{a}$, \\
+Michel Salomon$^{a}$ and Rapha\"el Couturier $^{a}$ \\
+  $^{a}${\em{FEMTO-ST Institute, UMR 6174 CNRS, \\
+  University Bourgogne Franche-Comt\'e, Belfort, France}} \\ 
+  $^{b}${\em{Department of Computer Science, University of Babylon, Babylon, Iraq}}
+}  
+

 
 \begin{abstract}
 %One of  the fundamental challenges in Wireless Sensor Networks (WSNs)
 
 \begin{abstract}
 %One of  the fundamental challenges in Wireless Sensor Networks (WSNs)


@@ -89,11 +99,11 @@ $\lbrace$karine.deschinkel, michel.salomon, raphael.couturier$\rbrace$@univ-fcom
 %continuously  and  effectively  when  monitoring a  certain  area  (or
 %region) of  interest. 
 Coverage and  lifetime are  two paramount problems  in Wireless  Sensor Networks
 %continuously  and  effectively  when  monitoring a  certain  area  (or
 %region) of  interest. 
 Coverage and  lifetime are  two paramount problems  in Wireless  Sensor Networks

-(WSNs). In this paper, a method called Multiperiod Distributed Lifetime Coverage
+(WSNs). In this paper, a method called Multiround Distributed Lifetime Coverage

 Optimization  protocol (MuDiLCO)  is proposed  to maintain  the coverage  and to
 improve the lifetime in wireless sensor  networks. The area of interest is first
 divided  into subregions and  then the  MuDiLCO protocol  is distributed  on the
 Optimization  protocol (MuDiLCO)  is proposed  to maintain  the coverage  and to
 improve the lifetime in wireless sensor  networks. The area of interest is first
 divided  into subregions and  then the  MuDiLCO protocol  is distributed  on the

-sensor nodes in each subregion. The proposed MuDiLCO protocol works into periods
+sensor nodes in each subregion. The proposed MuDiLCO protocol works in periods

 during which sets of sensor nodes are scheduled to remain active for a number of
 rounds  during the  sensing phase,  to  ensure coverage  so as  to maximize  the
 lifetime of  WSN.  The decision process is  carried out by a  leader node, which
 during which sets of sensor nodes are scheduled to remain active for a number of
 rounds  during the  sensing phase,  to  ensure coverage  so as  to maximize  the
 lifetime of  WSN.  The decision process is  carried out by a  leader node, which


@@ -106,7 +116,7 @@ network lifetime and improve the coverage performance.
 \end{abstract}
 
 \begin{keyword}
 \end{abstract}
 
 \begin{keyword}

-Wireless   Sensor   Networks,   Area   Coverage,   Network   lifetime,
+Wireless   Sensor   Networks,   Area   Coverage,   Network   Lifetime,

 Optimization, Scheduling, Distributed Computation.
 
 \end{keyword}
 Optimization, Scheduling, Distributed Computation.
 
 \end{keyword}


@@ -117,24 +127,24 @@ Optimization, Scheduling, Distributed Computation.
  
 \indent  The   fast  developments  of  low-cost  sensor   devices  and  wireless
 communications have allowed the emergence of WSNs. A WSN includes a large number
  
 \indent  The   fast  developments  of  low-cost  sensor   devices  and  wireless
 communications have allowed the emergence of WSNs. A WSN includes a large number

-of small, limited-power sensors that can sense, process and transmit data over a
-wireless  communication. They  communicate with  each other  by  using multi-hop
+of small, limited-power sensors that  can sense, process, and transmit data over
+a wireless  communication. They communicate  with each other by  using multi-hop

 wireless communications and cooperate together  to monitor the area of interest,
 so that  each measured data can be  reported to a monitoring  center called sink
 wireless communications and cooperate together  to monitor the area of interest,
 so that  each measured data can be  reported to a monitoring  center called sink

-for  further analysis~\cite{Sudip03}.  There are  several fields  of application
+for further  analysis~\cite{Sudip03}.  There  are several fields  of application

 covering  a wide  spectrum for  a  WSN, including  health, home,  environmental,
 military, and industrial applications~\cite{Akyildiz02}.
 
 On the one hand sensor nodes run on batteries with limited capacities, and it is
 often  costly  or  simply  impossible  to  replace  and/or  recharge  batteries,
 especially in remote and hostile environments. Obviously, to achieve a long life
 covering  a wide  spectrum for  a  WSN, including  health, home,  environmental,
 military, and industrial applications~\cite{Akyildiz02}.
 
 On the one hand sensor nodes run on batteries with limited capacities, and it is
 often  costly  or  simply  impossible  to  replace  and/or  recharge  batteries,
 especially in remote and hostile environments. Obviously, to achieve a long life

-of the network  it is important to conserve  battery power.  Therefore, lifetime
+of the  network it is important  to conserve battery  power. Therefore, lifetime

 optimization is one of the most  critical issues in wireless sensor networks. On
 optimization is one of the most  critical issues in wireless sensor networks. On

-the other hand we must guarantee coverage over the area of interest.  To fulfill
+the other hand we must guarantee  coverage over the area of interest. To fulfill

 these two objectives, the main idea  is to take advantage of overlapping sensing
 regions to turn-off redundant sensor nodes  and thus save energy. In this paper,
 we concentrate  on the area coverage  problem, with the  objective of maximizing
 these two objectives, the main idea  is to take advantage of overlapping sensing
 regions to turn-off redundant sensor nodes  and thus save energy. In this paper,
 we concentrate  on the area coverage  problem, with the  objective of maximizing

-the network lifetime by using an optimized multirounds scheduling.
+the network lifetime by using an optimized multiround scheduling.

 
 % One of the major scientific research challenges in WSNs, which are addressed by a large number of literature during the last few years is to design energy efficient approaches for coverage and connectivity in WSNs~\cite{conti2014mobile}. The coverage problem is one  of the
 %fundamental challenges in WSNs~\cite{Nayak04} that consists in monitoring efficiently and continuously
 
 % One of the major scientific research challenges in WSNs, which are addressed by a large number of literature during the last few years is to design energy efficient approaches for coverage and connectivity in WSNs~\cite{conti2014mobile}. The coverage problem is one  of the
 %fundamental challenges in WSNs~\cite{Nayak04} that consists in monitoring efficiently and continuously


@@ -159,6 +169,8 @@ demonstrate  the  usefulness  of   the  proposed  approach.   Finally,  we  give
 concluding    remarks   and    some    suggestions   for    future   works    in
 Section~\ref{sec:conclusion}.
 
 concluding    remarks   and    some    suggestions   for    future   works    in
 Section~\ref{sec:conclusion}.
 

+
+%%RC : Related works good for a phd thesis but too long for a paper. Ali you  need to learn to .... summarize :-)

 \section{Related works} % Trop proche de l'etat de l'art de l'article de Zorbas ?
 \label{rw}
 
 \section{Related works} % Trop proche de l'etat de l'art de l'article de Zorbas ?
 \label{rw}
 


@@ -171,17 +183,122 @@ algorithms in WSNs according to several design choices:
 \item  Sensors   scheduling  algorithm  implementation,   i.e.   centralized  or
   distributed/localized algorithms.
 \item The objective of sensor coverage, i.e. to maximize the network lifetime or
 \item  Sensors   scheduling  algorithm  implementation,   i.e.   centralized  or
   distributed/localized algorithms.
 \item The objective of sensor coverage, i.e. to maximize the network lifetime or

-  to minimize the number of sensors during the sensing period.
+  to minimize the number of sensors during a sensing round.

 \item The homogeneous or heterogeneous nature  of the nodes, in terms of sensing
   or communication capabilities.
 \item The node deployment method, which may be random or deterministic.
 \item The homogeneous or heterogeneous nature  of the nodes, in terms of sensing
   or communication capabilities.
 \item The node deployment method, which may be random or deterministic.

-\item  Additional  requirements  for  energy-efficient  coverage  and  connected
-  coverage.
+\item  Additional  requirements  for  energy-efficient and  connected coverage.

 \end{itemize}
 
 The choice of non-disjoint or disjoint cover sets (sensors participate or not in
 many cover sets) can be added to the above list.
 % The independency in the cover set (i.e. whether the cover sets are disjoint or non-disjoint) \cite{zorbas2010solving} is another design choice that can be added to the above list.
 \end{itemize}
 
 The choice of non-disjoint or disjoint cover sets (sensors participate or not in
 many cover sets) can be added to the above list.
 % The independency in the cover set (i.e. whether the cover sets are disjoint or non-disjoint) \cite{zorbas2010solving} is another design choice that can be added to the above list.

+
+\subsection{Centralized approaches}
+
+The major approach  is to divide/organize the sensors into  a suitable number of
+cover sets where  each set completely covers an interest  region and to activate
+these cover sets successively.  The centralized algorithms always provide nearly
+or close  to optimal solution since the  algorithm has global view  of the whole
+network. Note that  centralized algorithms have the advantage  of requiring very
+low  processing  power  from  the  sensor  nodes,  which  usually  have  limited
+processing  capabilities. The  main drawback  of this  kind of  approach  is its
+higher cost in communications, since the  node that will make the decision needs
+information from all the  sensor nodes. Moreover, centralized approaches usually
+suffer from the scalability problem, making them less competitive as the network
+size increases.
+
+The first algorithms proposed in the literature consider that the cover sets are
+disjoint:  a  sensor  node  appears  in  exactly  one  of  the  generated  cover
+sets~\cite{abrams2004set,cardei2005improving,Slijepcevic01powerefficient}.     In
+the   case  of  non-disjoint   algorithms  \cite{pujari2011high},   sensors  may
+participate in  more than one  cover set.  In  some cases, this may  prolong the
+lifetime of the network in comparison  to the disjoint cover set algorithms, but
+designing  algorithms for  non-disjoint cover  sets generally  induces  a higher
+order  of complexity.   Moreover, in  case of  a sensor's  failure, non-disjoint
+scheduling  policies are less  resilient and  reliable because  a sensor  may be
+involved in more than one cover sets.
+%For instance, the proposed work in ~\cite{cardei2005energy, berman04}    
+
+In~\cite{yang2014maximum},  the  authors have  considered  a linear  programming
+approach  to select  the minimum  number of  working sensor  nodes, in  order to
+preserve a  maximum coverage  and to  extend lifetime of  the network.  Cheng et
+al.~\cite{cheng2014energy} have defined a  heuristic algorithm called Cover Sets
+Balance  (CSB), which  chooses  a set  of  active nodes  using  the tuple  (data
+coverage range, residual  energy).  Then, they have introduced  a new Correlated
+Node Set Computing (CNSC) algorithm to  find the correlated node set for a given
+node.   After that,  they  proposed a  High  Residual Energy  First (HREF)  node
+selection algorithm to minimize the number  of active nodes so as to prolong the
+network  lifetime.  Various  centralized  methods  based  on  column  generation
+approaches                    have                   also                   been
+proposed~\cite{castano2013column,rossi2012exact,deschinkel2012column}.
+
+\subsection{Distributed approaches}
+%{\bf Distributed approaches}
+In distributed  and localized coverage  algorithms, the required  computation to
+schedule the  activity of  sensor nodes  will be done  by the  cooperation among
+neighboring nodes. These  algorithms may require more computation  power for the
+processing by the cooperating sensor nodes, but they are more scalable for large
+WSNs.  Localized and distributed algorithms generally result in non-disjoint set
+covers.
+
+Many distributed algorithms have been  developed to perform the scheduling so as
+to          preserve         coverage,          see          for         example
+\cite{Gallais06,Tian02,Ye03,Zhang05,HeinzelmanCB02,       yardibi2010distributed,
+  prasad2007distributed,Misra}.   Distributed  algorithms  typically operate  in
+rounds for  a predetermined duration. At  the beginning of each  round, a sensor
+exchanges information with  its neighbors and makes a  decision to either remain
+turned on or  to go to sleep for  the round. This decision is  basically made on
+simple     greedy     criteria    like     the     largest    uncovered     area
+\cite{Berman05efficientenergy}      or       maximum      uncovered      targets
+\cite{lu2003coverage}.   The  Distributed  Adaptive Sleep  Scheduling  Algorithm
+(DASSA) \cite{yardibi2010distributed}  does not require  location information of
+sensors while  maintaining connectivity and  satisfying a user  defined coverage
+target.  In  DASSA, nodes use the  residual energy levels and  feedback from the
+sink for  scheduling the activity  of their neighbors.  This  feedback mechanism
+reduces  the randomness  in scheduling  that would  otherwise occur  due  to the
+absence of location information.  In  \cite{ChinhVu}, the author have designed a
+novel distributed heuristic,  called Distributed Energy-efficient Scheduling for
+k-coverage (DESK), which  ensures that the energy consumption  among the sensors
+is  balanced  and the  lifetime  maximized  while  the coverage  requirement  is
+maintained.   This heuristic  works in  rounds, requires  only  one-hop neighbor
+information, and each  sensor decides its status (active or  sleep) based on the
+perimeter coverage model from~\cite{Huang:2003:CPW:941350.941367}.
+
+%Our Work, which is presented in~\cite{idrees2014coverage} proposed a coverage optimization protocol to improve the lifetime in
+%heterogeneous energy wireless sensor networks. 
+%In this work, the coverage protocol distributed in each sensor node in the subregion but the optimization take place over the the whole subregion. We consider only distributing the coverage protocol over two subregions. 
+
+The  works presented  in  \cite{Bang, Zhixin,  Zhang}  focus on  coverage-aware,
+distributed energy-efficient,  and distributed clustering  methods respectively,
+which  aim at extending  the network  lifetime, while  the coverage  is ensured.
+More recently, Shibo et al.  \cite{Shibo} have expressed the coverage problem as
+a  minimum  weight submodular  set  cover  problem  and proposed  a  Distributed
+Truncated Greedy  Algorithm (DTGA) to solve  it.  They take  advantage from both
+temporal and spatial correlations between  data sensed by different sensors, and
+leverage prediction, to improve  the lifetime.  In \cite{xu2001geography}, Xu et
+al.  have  described an algorithm, called Geographical  Adaptive Fidelity (GAF),
+which uses geographic  location information to divide the  area of interest into
+fixed square grids.   Within each grid, it keeps only one  node staying awake to
+take the responsibility of sensing and communication.
+
+Some  other  approaches (outside  the  scope  of our  work)  do  not consider  a
+synchronized and  predetermined time-slot where  the sensors are active  or not.
+Indeed, each sensor  maintains its own timer and its  wake-up time is randomized
+\cite{Ye03} or regulated \cite{cardei2005maximum} over time.
+
+The MuDiLCO protocol (for  Multiround Distributed Lifetime Coverage Optimization
+protocol) presented  in this  paper is an  extension of the  approach introduced
+in~\cite{idrees2014coverage}.   In~\cite{idrees2014coverage},  the  protocol  is
+deployed over  only two  subregions. Simulation results  have shown that  it was
+more  interesting  to  divide  the  area  into  several  subregions,  given  the
+computation complexity. Compared to our previous paper, in this one we study the
+possibility of dividing  the sensing phase into multiple rounds  and we also add
+an  improved  model  of energy  consumption  to  assess  the efficiency  of  our
+approach. In fact, in this paper we make a multiround optimization, while it was
+a single round optimization in our previous work.
+
+\iffalse

    
 \subsection{Centralized Approaches}
 %{\bf Centralized approaches}
    
 \subsection{Centralized Approaches}
 %{\bf Centralized approaches}


@@ -199,25 +316,25 @@ size increases.
 
 The first algorithms proposed in the literature consider that the cover sets are
 disjoint: a sensor node appears in exactly one of the generated cover sets.  For
 
 The first algorithms proposed in the literature consider that the cover sets are
 disjoint: a sensor node appears in exactly one of the generated cover sets.  For

-instance, Slijepcevic  and Potkonjak \cite{Slijepcevic01powerefficient} proposed
-an  algorithm, which  allocates sensor  nodes  in mutually  independent sets  to
-monitor an area divided into several fields.  Their algorithm builds a cover set
-by including in  priority the sensor nodes which cover  critical fields, that is
-to say  fields that  are covered by  the smallest  number of sensors.   The time
+instance,  Slijepcevic  and  Potkonjak  \cite{Slijepcevic01powerefficient}  have
+proposed an algorithm, which allocates sensor nodes in mutually independent sets
+to monitor an area divided into  several fields.  Their algorithm builds a cover
+set by including in priority the  sensor nodes which cover critical fields, that
+is to say fields  that are covered by the smallest number  of sensors.  The time

 complexity of  their heuristic is $O(n^2)$  where $n$ is the  number of sensors.
 complexity of  their heuristic is $O(n^2)$  where $n$ is the  number of sensors.

-Abrams et al.~\cite{abrams2004set} designed three approximation algorithms for a
-variation of  the set k-cover problem,  where the objective is  to partition the
-sensors into covers such that the  number of covers that include an area, summed
-over  all   areas,  is  maximized.    Their  work  builds  upon   previous  work
+Abrams et al.~\cite{abrams2004set}  have designed three approximation algorithms
+for a variation of the set  k-cover problem, where the objective is to partition
+the sensors  into covers such  that the number  of covers that include  an area,
+summed  over all  areas, is  maximized.  Their  work builds  upon  previous work

 in~\cite{Slijepcevic01powerefficient}  and  the  generated  cover  sets  do  not
 provide complete coverage of the monitoring zone.
 
 in~\cite{Slijepcevic01powerefficient}  and  the  generated  cover  sets  do  not
 provide complete coverage of the monitoring zone.
 

-\cite{cardei2005improving} proposed a method  to efficiently compute the maximum
-number of disjoint  set covers such that each set can  monitor all targets. They
-first transform the problem into a  maximum flow problem, which is formulated as
-a mixed integer  programming (MIP). Then their heuristic uses  the output of the
-MIP to compute disjoint set covers.  Results show that this heuristic provides a
-number      of     set      covers     slightly      larger      compared     to
+In \cite{cardei2005improving}, the authors have proposed a method to efficiently
+compute the maximum number of disjoint set covers such that each set can monitor
+all targets. They first transform the problem into a maximum flow problem, which
+is formulated  as a mixed integer  programming (MIP). Then  their heuristic uses
+the output  of the MIP to compute  disjoint set covers.  Results  show that this
+heuristic  provides  a  number  of   set  covers  slightly  larger  compared  to

 \cite{Slijepcevic01powerefficient}, but with a  larger execution time due to the
 complexity of the mixed integer programming resolution.
 
 \cite{Slijepcevic01powerefficient}, but with a  larger execution time due to the
 complexity of the mixed integer programming resolution.
 


@@ -229,7 +346,7 @@ sets with a  slight growth rate in execution  time.  When producing non-disjoint
 cover sets,  both Static-CCF  and Dynamic-CCF algorithms,  where CCF  means that
 they  use a cost  function called  Critical Control  Factor, provide  cover sets
 offering longer network lifetime than those produced by \cite{cardei2005energy}.
 cover sets,  both Static-CCF  and Dynamic-CCF algorithms,  where CCF  means that
 they  use a cost  function called  Critical Control  Factor, provide  cover sets
 offering longer network lifetime than those produced by \cite{cardei2005energy}.

-Also, they require  a smaller number of node participations  in order to achieve
+Also, they require  a smaller number of participating nodes  in order to achieve

 these results.
 
 In  the  case  of  non-disjoint algorithms  \cite{pujari2011high},  sensors  may
 these results.
 
 In  the  case  of  non-disjoint algorithms  \cite{pujari2011high},  sensors  may


@@ -270,71 +387,73 @@ processing by the cooperating sensor nodes, but they are more scalable for large
 WSNs.  Localized and distributed algorithms generally result in non-disjoint set
 covers.
 
 WSNs.  Localized and distributed algorithms generally result in non-disjoint set
 covers.
 

-Some        distributed       algorithms        have        been       developed
-in~\cite{Gallais06,Tian02,Ye03,Zhang05,HeinzelmanCB02,    yardibi2010distributed}
-to perform  the scheduling so  as to preserve coverage.   Distributed algorithms
-typically operate  in rounds for a  predetermined duration. At  the beginning of
-each  round, a  sensor  exchanges information  with  its neighbors  and makes  a
-decision  to either  remain turned  on or  to go  to sleep  for the  round. This
-decision is basically made on  simple greedy criteria like the largest uncovered
-area    \cite{Berman05efficientenergy}     or    maximum    uncovered    targets
-\cite{lu2003coverage}.  In \cite{Tian02}, the  scheduling scheme is divided into
-rounds,  where each  round has  a self-scheduling  phase followed  by  a sensing
-phase.  Each  sensor broadcasts  a message containing  the node~ID and  the node
-location to its  neighbors at the beginning of each  round.  A sensor determines
-its status by a  rule named off-duty eligible rule, which tells  him to turn off
-if its sensing area is covered by its neighbors. A back-off scheme is introduced
-to let each sensor  delay the decision process with a random  period of time, in
-order  to avoid  simultaneous conflicting  decisions between  nodes and  lack of
-coverage  on  any  area.    \cite{prasad2007distributed}  defines  a  model  for
-capturing the  dependencies between different cover sets  and proposes localized
-heuristic based  on this  dependency. The algorithm  consists of two  phases, an
-initial setup phase during which each sensor computes and prioritizes the covers
-and a  sensing phase during which  each sensor first decides  its on/off status,
-and then remains on or off for the rest of the duration.
-
-The  authors in \cite{yardibi2010distributed}  developed a  Distributed Adaptive
-Sleep Scheduling Algorithm  (DASSA) for WSNs with partial  coverage.  DASSA does
-not require  location information of sensors while  maintaining connectivity and
-satisfying a  user defined  coverage target.  In  DASSA, nodes use  the residual
-energy levels  and feedback from the  sink for scheduling the  activity of their
-neighbors.  This  feedback mechanism reduces  the randomness in  scheduling that
-would  otherwise  occur  due  to   the  absence  of  location  information.   In
-\cite{ChinhVu},  the  author  proposed  a novel  distributed  heuristic,  called
-Distributed  Energy-efficient Scheduling  for k-coverage  (DESK),  which ensures
-that  the energy  consumption among  the sensors  is balanced  and  the lifetime
-maximized while the coverage requirement is maintained.  This heuristic works in
-rounds, requires only one-hop neighbor  information, and each sensor decides its
-status  (active or  sleep) based  on the  perimeter coverage  model  proposed in
-\cite{Huang:2003:CPW:941350.941367}.
+Many distributed algorithms have been  developed to perform the scheduling so as
+to          preserve         coverage,          see          for         example
+\cite{Gallais06,Tian02,Ye03,Zhang05,HeinzelmanCB02,yardibi2010distributed}.
+Distributed  algorithms   typically  operate  in  rounds   for  a  predetermined
+duration. At  the beginning of each  round, a sensor  exchanges information with
+its neighbors and makes a decision to  either remain turned on or to go to sleep
+for the  round. This decision is  basically made on simple  greedy criteria like
+the largest  uncovered area \cite{Berman05efficientenergy}  or maximum uncovered
+targets  \cite{lu2003coverage}.   In  \cite{Tian02},  the scheduling  scheme  is
+divided into rounds, where each round  has a self-scheduling phase followed by a
+sensing phase.  Each sensor broadcasts  a message containing the node~ID and the
+node  location to  its  neighbors at  the  beginning of  each  round.  A  sensor
+determines its status by a rule named off-duty eligible rule, which tells him to
+turn off if its  sensing area is covered by its neighbors.  A back-off scheme is
+introduced to let each sensor delay the decision process with a random period of
+time, in  order to  avoid simultaneous conflicting  decisions between  nodes and
+lack  of coverage  on any  area.   In \cite{prasad2007distributed}  a model  for
+capturing  the dependencies  between  different  cover sets  is  defined and  it
+proposes localized heuristic based on this dependency. The algorithm consists of
+two  phases,  an initial  setup  phase during  which  each  sensor computes  and
+prioritizes  the covers  and  a sensing  phase  during which  each sensor  first
+decides  its on/off  status, and  then remains  on or  off for  the rest  of the
+duration. 
+
+The  authors  in  \cite{yardibi2010distributed}  have  developed  a  Distributed
+Adaptive  Sleep Scheduling  Algorithm (DASSA)  for WSNs  with  partial coverage.
+DASSA  does  not  require  location  information of  sensors  while  maintaining
+connectivity and satisfying a user defined coverage target.  In DASSA, nodes use
+the  residual  energy levels  and  feedback from  the  sink  for scheduling  the
+activity of their neighbors.  This  feedback mechanism reduces the randomness in
+scheduling  that  would   otherwise  occur  due  to  the   absence  of  location
+information.  In  \cite{ChinhVu}, the author  have proposed a  novel distributed
+heuristic, called Distributed Energy-efficient Scheduling for k-coverage (DESK),
+which ensures that the energy consumption  among the sensors is balanced and the
+lifetime maximized while the coverage requirement is maintained.  This heuristic
+works in  rounds, requires  only one-hop neighbor  information, and  each sensor
+decides  its status  (active or  sleep) based  on the  perimeter  coverage model
+proposed in \cite{Huang:2003:CPW:941350.941367}.

 
 %Our Work, which is presented in~\cite{idrees2014coverage} proposed a coverage optimization protocol to improve the lifetime in
 %heterogeneous energy wireless sensor networks. 
 %In this work, the coverage protocol distributed in each sensor node in the subregion but the optimization take place over the the whole subregion. We consider only distributing the coverage protocol over two subregions. 
 
 
 %Our Work, which is presented in~\cite{idrees2014coverage} proposed a coverage optimization protocol to improve the lifetime in
 %heterogeneous energy wireless sensor networks. 
 %In this work, the coverage protocol distributed in each sensor node in the subregion but the optimization take place over the the whole subregion. We consider only distributing the coverage protocol over two subregions. 
 

-The  works presented in  \cite{Bang, Zhixin,  Zhang} focuses  on coverage-aware,
+The  works presented in  \cite{Bang, Zhixin,  Zhang} focus  on coverage-aware,

 distributed energy-efficient,  and distributed clustering  methods respectively,
 distributed energy-efficient,  and distributed clustering  methods respectively,

-which aims  to extend the network  lifetime, while the coverage  is ensured.  S.
-Misra et al.  \cite{Misra} proposed a localized algorithm for coverage in sensor
-networks. The algorithm conserve the  energy while ensuring the network coverage
-by activating the subset of sensors  with the minimum overlap area. The proposed
-method preserves the network connectivity  by formation of the network backbone.
-More recently,  Shibo et  al. \cite{Shibo} expressed  the coverage problem  as a
-minimum weight submodular set cover problem and proposed a Distributed Truncated
-Greedy Algorithm (DTGA) to solve it.  They take advantage from both temporal and
-spatial  correlations between  data sensed  by different  sensors,  and leverage
-prediction,  to   improve  the  lifetime.   In   \cite{xu2001geography},  Xu  et
-al. proposed  an algorithm, called  Geographical Adaptive Fidelity  (GAF), which
-uses geographic location  information to divide the area  of interest into fixed
-square grids. Within each grid, it keeps only one node staying awake to take the
-responsibility of sensing and communication.
+which aim  to extend the network  lifetime, while the coverage  is ensured.  S.
+Misra et al.   \cite{Misra} have proposed a localized  algorithm for coverage in
+sensor networks.  The  algorithm conserve the energy while  ensuring the network
+coverage by activating the subset of  sensors with the minimum overlap area. The
+proposed method preserves  the network connectivity by formation  of the network
+backbone.  More recently, Shibo et  al. \cite{Shibo} have expressed the coverage
+problem  as  a  minimum weight  submodular  set  cover  problem and  proposed  a
+Distributed Truncated Greedy Algorithm (DTGA)  to solve it.  They take advantage
+from both  temporal and  spatial correlations between  data sensed  by different
+sensors,   and    leverage   prediction,   to   improve    the   lifetime.    In
+\cite{xu2001geography},   Xu  et   al.  have   proposed  an   algorithm,  called
+Geographical Adaptive Fidelity (GAF), which uses geographic location information
+to divide  the area of  interest into fixed  square grids. Within each  grid, it
+keeps only  one node  staying awake  to take the  responsibility of  sensing and
+communication.

 
 Some  other  approaches (outside  the  scope  of our  work)  do  not consider  a
 synchronized and  predetermined period of time  where the sensors  are active or
 not.   Indeed, each  sensor maintains  its  own timer  and its  wake-up time  is
 randomized \cite{Ye03} or regulated \cite{cardei2005maximum} over time.
 
 
 Some  other  approaches (outside  the  scope  of our  work)  do  not consider  a
 synchronized and  predetermined period of time  where the sensors  are active or
 not.   Indeed, each  sensor maintains  its  own timer  and its  wake-up time  is
 randomized \cite{Ye03} or regulated \cite{cardei2005maximum} over time.
 

-The MuDiLCO protocol (for Multiperiod Distributed Lifetime Coverage Optimization
+The MuDiLCO protocol (for Multiround Distributed Lifetime Coverage Optimization

 protocol) presented  in this  paper is an  extension of the  approach introduced
 in~\cite{idrees2014coverage}.   In~\cite{idrees2014coverage},  the  protocol  is
 deployed over  only two  subregions. Simulation results  have shown that  it was
 protocol) presented  in this  paper is an  extension of the  approach introduced
 in~\cite{idrees2014coverage}.   In~\cite{idrees2014coverage},  the  protocol  is
 deployed over  only two  subregions. Simulation results  have shown that  it was


@@ -344,6 +463,10 @@ possibility of dividing  the sensing phase into multiple rounds  and we also add
 an  improved  model  of energy  consumption  to  assess  the efficiency  of  our
 approach.
 
 an  improved  model  of energy  consumption  to  assess  the efficiency  of  our
 approach.
 

+
+
+
+\fi

 %The main contributions of our MuDiLCO Protocol can be summarized as follows:
 %(1) The high coverage ratio, (2) The reduced number of active nodes, (3) The distributed optimization over the subregions in the area of interest, (4) The distributed dynamic leader election at each round based on some priority factors that led to energy consumption balancing among the nodes in the same subregion, (5) The primary point coverage model to represent each sensor node in the network, (6) The activity scheduling based optimization on the subregion, which are based on the primary point coverage model to activate as less number as possible of sensor nodes for a multirounds to take the mission of the coverage in each subregion, (7) The very low energy consumption, (8) The higher network lifetime.
 %\section{Preliminaries}
 %The main contributions of our MuDiLCO Protocol can be summarized as follows:
 %(1) The high coverage ratio, (2) The reduced number of active nodes, (3) The distributed optimization over the subregions in the area of interest, (4) The distributed dynamic leader election at each round based on some priority factors that led to energy consumption balancing among the nodes in the same subregion, (5) The primary point coverage model to represent each sensor node in the network, (6) The activity scheduling based optimization on the subregion, which are based on the primary point coverage model to activate as less number as possible of sensor nodes for a multirounds to take the mission of the coverage in each subregion, (7) The very low energy consumption, (8) The higher network lifetime.
 %\section{Preliminaries}


@@ -380,7 +503,7 @@ approach.
 %minimizing  overcoverage (points  covered by  multiple  active sensors
 %simultaneously).
 
 %minimizing  overcoverage (points  covered by  multiple  active sensors
 %simultaneously).
 

-%In this section, we introduce a Multiperiod Distributed Lifetime Coverage Optimization protocol, which is called MuDiLCO. It is  distributed on each subregion in the area of interest. It is based on two efficient techniques: network
+%In this section, we introduce a Multiround Distributed Lifetime Coverage Optimization protocol, which is called MuDiLCO. It is  distributed on each subregion in the area of interest. It is based on two efficient techniques: network

 %leader election and sensor activity scheduling for coverage preservation and energy conservation continuously and efficiently to maximize the lifetime in the network.  
 %The main features of our MuDiLCO protocol:
 %i)It divides the area of interest into subregions by using divide-and-conquer concept, ii)It requires only the information of the nodes within the subregion, iii) it divides the network lifetime into periods, which consists in round(s), iv)It based on the autonomous distributed decision by the nodes in the subregion to elect the Leader, v)It apply the activity scheduling based optimization on the subregion, vi)  it achieves an energy consumption balancing among the nodes in the subregion by selecting different nodes as a leader during the network lifetime, vii) It uses the optimization to select the best representative non-disjoint sets of sensors in the subregion by optimize the coverage and the lifetime over the area of interest, viii)It uses our proposed primary point coverage model, which represent the sensing range of the sensor as a set of points, which are used by the our optimization algorithm, ix) It uses a simple energy model that takes communication, sensing and computation energy consumptions into account to evaluate the performance of our Protocol.
 %leader election and sensor activity scheduling for coverage preservation and energy conservation continuously and efficiently to maximize the lifetime in the network.  
 %The main features of our MuDiLCO protocol:
 %i)It divides the area of interest into subregions by using divide-and-conquer concept, ii)It requires only the information of the nodes within the subregion, iii) it divides the network lifetime into periods, which consists in round(s), iv)It based on the autonomous distributed decision by the nodes in the subregion to elect the Leader, v)It apply the activity scheduling based optimization on the subregion, vi)  it achieves an energy consumption balancing among the nodes in the subregion by selecting different nodes as a leader during the network lifetime, vii) It uses the optimization to select the best representative non-disjoint sets of sensors in the subregion by optimize the coverage and the lifetime over the area of interest, viii)It uses our proposed primary point coverage model, which represent the sensing range of the sensor as a set of points, which are used by the our optimization algorithm, ix) It uses a simple energy model that takes communication, sensing and computation energy consumptions into account to evaluate the performance of our Protocol.


@@ -403,13 +526,12 @@ range  is  said  to  be  covered  by  this sensor.   We  also  assume  that  the
 communication   range  satisfies   $R_c  \geq   2R_s$.   In   fact,   Zhang  and
 Zhou~\cite{Zhang05} proved that if  the transmission range fulfills the previous
 hypothesis, a complete coverage of  a convex area implies connectivity among the
 communication   range  satisfies   $R_c  \geq   2R_s$.   In   fact,   Zhang  and
 Zhou~\cite{Zhang05} proved that if  the transmission range fulfills the previous
 hypothesis, a complete coverage of  a convex area implies connectivity among the

-working nodes in the active mode.
+active nodes.

 
 Instead  of working  with a  continuous coverage  area, we  make it  discrete by
 considering for each sensor a set of points called primary points. Consequently,
 we assume  that the sensing disk  defined by a sensor  is covered if  all of its
 
 Instead  of working  with a  continuous coverage  area, we  make it  discrete by
 considering for each sensor a set of points called primary points. Consequently,
 we assume  that the sensing disk  defined by a sensor  is covered if  all of its

-primary points are covered. The choice of number and locations of primary points
-is the subject of another study not presented here.
+primary points are covered. The choice of number and locations of primary points is the subject of another study not presented here.

 
 %By  knowing the  position (point  center: ($p_x,p_y$))  of  a wireless
 %sensor node  and its $R_s$,  we calculate the primary  points directly
 
 %By  knowing the  position (point  center: ($p_x,p_y$))  of  a wireless
 %sensor node  and its $R_s$,  we calculate the primary  points directly


@@ -425,16 +547,18 @@ is the subject of another study not presented here.
 %The sensor node enter in listening mode waiting to receive ActiveSleep packet from the leader after the decision to apply multi-round activity scheduling during the sensing phase. Each sensor node will execute the Algorithm~1 to know who is the leader. After that, if the sensor node is leader, It will execute the integer program algorithm ( see section~\ref{cp}) to optimize the coverage and the lifetime in it's subregion. After the decision, the optimization approach will produce the cover sets of sensor nodes to take the mission of coverage during the sensing phase for $T$ rounds. The leader will send ActiveSleep packet to each sensor node in the subregion to inform him to it's schedule for $T$ rounds during the period of sensing, either Active or sleep until the starting of next period. Based on the decision, the leader as other nodes in subregion, either go to be active or go to be sleep based on it's schedule for $T$ rounds during current sensing phase. the other nodes in the same subregion will stay in listening mode waiting the ActiveSleep packet from the leader. After finishing the time period for sensing, which are includes $T$ rounds, all the sensor nodes in the same subregion will start new period by executing the MuDiLCO protocol and the lifetime in the subregion will continue until all the sensor nodes are died or the network becomes disconnected in the subregion.
 
 \subsection{Background idea}
 %The sensor node enter in listening mode waiting to receive ActiveSleep packet from the leader after the decision to apply multi-round activity scheduling during the sensing phase. Each sensor node will execute the Algorithm~1 to know who is the leader. After that, if the sensor node is leader, It will execute the integer program algorithm ( see section~\ref{cp}) to optimize the coverage and the lifetime in it's subregion. After the decision, the optimization approach will produce the cover sets of sensor nodes to take the mission of coverage during the sensing phase for $T$ rounds. The leader will send ActiveSleep packet to each sensor node in the subregion to inform him to it's schedule for $T$ rounds during the period of sensing, either Active or sleep until the starting of next period. Based on the decision, the leader as other nodes in subregion, either go to be active or go to be sleep based on it's schedule for $T$ rounds during current sensing phase. the other nodes in the same subregion will stay in listening mode waiting the ActiveSleep packet from the leader. After finishing the time period for sensing, which are includes $T$ rounds, all the sensor nodes in the same subregion will start new period by executing the MuDiLCO protocol and the lifetime in the subregion will continue until all the sensor nodes are died or the network becomes disconnected in the subregion.
 
 \subsection{Background idea}

-
+%%RC : we need to clarify the difference between round and period. Currently it seems to be the same (for me at least).

 The area of  interest can be divided using  the divide-and-conquer strategy into
 The area of  interest can be divided using  the divide-and-conquer strategy into

-smaller  areas,  called  subregions,  and  then our  MuDiLCO  protocol  will  be
+smaller  areas,  called  subregions,  and  then our MuDiLCO  protocol will be

 implemented in each subregion in a distributed way.
 
 As  can be seen  in Figure~\ref{fig2},  our protocol  works in  periods fashion,
 where  each is  divided  into 4  phases: Information~Exchange,  Leader~Election,
 Decision, and Sensing.  Each sensing phase may be itself divided into $T$ rounds
 implemented in each subregion in a distributed way.
 
 As  can be seen  in Figure~\ref{fig2},  our protocol  works in  periods fashion,
 where  each is  divided  into 4  phases: Information~Exchange,  Leader~Election,
 Decision, and Sensing.  Each sensing phase may be itself divided into $T$ rounds

-and for each  round a set of sensors  (said a cover set) is  responsible for the
-sensing task.
+and for each round a set of sensors (a cover set) is responsible for the sensing
+task. In  this way  a multiround optimization  process is performed  during each
+period  after  Information~Exchange  and  Leader~Election phases,  in  order  to
+produce $T$ cover sets that will take the mission of sensing for $T$ rounds.

 \begin{figure}[ht!]
 \centering \includegraphics[width=100mm]{Modelgeneral.pdf} % 70mm
 \caption{The MuDiLCO protocol scheme executed on each node}
 \begin{figure}[ht!]
 \centering \includegraphics[width=100mm]{Modelgeneral.pdf} % 70mm
 \caption{The MuDiLCO protocol scheme executed on each node}


@@ -446,12 +570,18 @@ sensing task.
 % set cover responsible for the sensing task.  
 %For each round a set of sensors (said a cover set) is responsible for the sensing task.
 
 % set cover responsible for the sensing task.  
 %For each round a set of sensors (said a cover set) is responsible for the sensing task.
 

-This protocol is  reliable against an unexpected node  failure, because it works
-in periods.  On the one hand,  if a node  failure is detected before  making the
-decision, the node  will not participate to this phase, and,  on the other hand,
-if the node  failure occurs after the decision, the sensing  task of the network
-will be  temporarily affected:  only during  the period of  sensing until  a new
+This protocol minimizes the impact of unexpected node failure (not due to batteries
+running out of energy), because it works in periods. 
+%This protocol is reliable against an unexpected node failure, because it works in periods. 
+%%RC : why? I am not convinced
+ On the one hand, if a node failure is detected before  making the
+decision, the node will not participate to this phase, and, on the other hand,
+if the node failure occurs after the decision, the sensing  task of the network
+will be temporarily affected:  only during  the period of sensing until a new

 period starts.
 period starts.

+%%RC so if there are at least one failure per period, the coverage is bad...
+%%MS if we want to be reliable against many node failures we need to have an
+%% overcoverage...  

 
 The  energy consumption  and some  other constraints  can easily  be  taken into
 account,  since the  sensors  can  update and  then  exchange their  information
 
 The  energy consumption  and some  other constraints  can easily  be  taken into
 account,  since the  sensors  can  update and  then  exchange their  information


@@ -464,7 +594,7 @@ monitor the area.
 
 We define two types of packets that will be used by the proposed protocol:
 \begin{enumerate}[(a)] 
 
 We define two types of packets that will be used by the proposed protocol:
 \begin{enumerate}[(a)] 

-\item INFO  packet: a such packet  will be sent by  each sensor node  to all the
+\item INFO  packet: such a  packet  will be sent by  each sensor node  to all the

   nodes inside a subregion for information exchange.
 \item  Active-Sleep  packet: sent  by  the  leader to  all  the  nodes inside  a
   subregion to  inform them to remain Active  or to go Sleep  during the sensing
   nodes inside a subregion for information exchange.
 \item  Active-Sleep  packet: sent  by  the  leader to  all  the  nodes inside  a
   subregion to  inform them to remain Active  or to go Sleep  during the sensing


@@ -476,7 +606,7 @@ There are five status for each sensor node in the network:
 \item LISTENING: sensor node is waiting for a decision (to be active or not);
 \item  COMPUTATION: sensor  node  has been  elected  as leader  and applies  the
   optimization process;
 \item LISTENING: sensor node is waiting for a decision (to be active or not);
 \item  COMPUTATION: sensor  node  has been  elected  as leader  and applies  the
   optimization process;

-\item ACTIVE: sensor node participate to the monitoring of the area;
+\item ACTIVE: sensor node is taking part in the monitoring of the area;

 \item SLEEP: sensor node is turned off to save energy;
 \item COMMUNICATION: sensor node is transmitting or receiving packet.
 \end{enumerate}
 \item SLEEP: sensor node is turned off to save energy;
 \item COMMUNICATION: sensor node is transmitting or receiving packet.
 \end{enumerate}


@@ -503,7 +633,7 @@ This step  consists in  choosing the Wireless  Sensor Node Leader  (WSNL), which
 will be responsible for executing the coverage algorithm.  Each subregion in the
 area of  interest will select its  own WSNL independently for  each period.  All
 the sensor  nodes cooperate to  elect a WSNL.   The nodes in the  same subregion
 will be responsible for executing the coverage algorithm.  Each subregion in the
 area of  interest will select its  own WSNL independently for  each period.  All
 the sensor  nodes cooperate to  elect a WSNL.   The nodes in the  same subregion

-will select the  leader based on the received informations  from all other nodes
+will select the  leader based on the received information  from all other nodes

 in  the same subregion.   The selection  criteria are,  in order  of importance:
 larger  number  of neighbors,  larger  remaining energy,  and  then  in case  of
 equality, larger index. Observations on  previous simulations suggest to use the
 in  the same subregion.   The selection  criteria are,  in order  of importance:
 larger  number  of neighbors,  larger  remaining energy,  and  then  in case  of
 equality, larger index. Observations on  previous simulations suggest to use the


@@ -517,19 +647,78 @@ consumption due to the communications.
 
 \subsection{Decision phase}
 
 
 \subsection{Decision phase}
 

-Each  WSNL will solve  an integer  program to  select which  cover sets  will be
+Each  WSNL will \textcolor{red}{ execute an optimization algorithm (see section \ref{oa})} to  select which  cover sets  will be

 activated in  the following  sensing phase  to cover the  subregion to  which it
 activated in  the following  sensing phase  to cover the  subregion to  which it

-belongs.  The integer  program will produce $T$ cover sets,  one for each round.
-The WSNL will send an Active-Sleep  packet to each sensor in the subregion based
-on the algorithm's results, indicating if  the sensor should be active or not in
-each  round of the  sensing phase.  The integer  program is  based on  the model
-proposed by \cite{pedraza2006} with some modification, where the objective is to
-find a maximum number of disjoint cover sets.  To fulfill this goal, the authors
-proposed  an integer  program  which forces  undercoverage  and overcoverage  of
-targets to become minimal at the  same time.  They use binary variables $x_{jl}$
-to indicate if sensor  $j$ belongs to cover set $l$.  In  our model, we consider
-binary variables $X_{t,j}$ to determine  the possibility of activation of sensor
-$j$ during  the round $t$  of a given  sensing phase.  We also  consider primary
+belongs.  The \textcolor{red}{optimization algorithm} will produce $T$ cover sets,  one for each round. The WSNL will send an Active-Sleep  packet to each sensor in the subregion based on the algorithm's results, indicating if  the sensor should be active or not in
+each round  of the  sensing phase.  
+
+%solve  an integer  program
+
+\subsection{Sensing phase}
+
+The sensing phase consists of $T$ rounds. Each sensor node in the subregion will
+receive an Active-Sleep packet from WSNL, informing it to stay awake or to go to
+sleep for each round of the sensing  phase.  Algorithm~\ref{alg:MuDiLCO}, which
+will be  executed by each node  at the beginning  of a period, explains  how the
+Active-Sleep packet is obtained.
+
+% In each round during the sensing phase, there is a cover set of sensor nodes,  in which  the active  sensors will  execute  their sensing  task  to preserve maximal  coverage and lifetime in the subregion and this will continue until finishing the round $T$ and starting new period. 
+
+\begin{algorithm}[h!]                
+ % \KwIn{all the parameters related to information exchange}
+%  \KwOut{$winer-node$ (: the id of the winner sensor node, which is the leader of current round)}
+  \BlankLine
+  %\emph{Initialize the sensor node and determine it's position and subregion} \; 
+  
+  \If{ $RE_j \geq E_{R}$ }{
+      \emph{$s_j.status$ = COMMUNICATION}\;
+      \emph{Send $INFO()$ packet to other nodes in the subregion}\;
+      \emph{Wait $INFO()$ packet from other nodes in the subregion}\; 
+      %\emph{UPDATE $RE_j$ for every sent or received INFO Packet}\;
+      %\emph{ Collect information and construct the list L for all nodes in the subregion}\;
+      
+      %\If{ the received INFO Packet = No. of nodes in it's subregion -1  }{
+      \emph{LeaderID = Leader election}\;
+      \If{$ s_j.ID = LeaderID $}{
+        \emph{$s_j.status$ = COMPUTATION}\;
+        \emph{$\left\{\left(X_{1,k},\dots,X_{T,k}\right)\right\}_{k \in J}$ =
+          Execute \textcolor{red}{Optimization Algorithm}($T,J$)}\;
+        \emph{$s_j.status$ = COMMUNICATION}\;
+        \emph{Send $ActiveSleep()$ to each node $k$ in subregion a packet \\
+          with vector of activity scheduling $(X_{1,k},\dots,X_{T,k})$}\;
+        \emph{Update $RE_j $}\;
+      }          
+      \Else{
+        \emph{$s_j.status$ = LISTENING}\;
+        \emph{Wait $ActiveSleep()$ packet from the Leader}\;
+        % \emph{After receiving Packet, Retrieve the schedule and the $T$ rounds}\;
+        \emph{Update $RE_j $}\;
+      }  
+      %  }
+  }
+  \Else { Exclude $s_j$ from entering in the current sensing phase}
+  
+ %   \emph{return X} \;
+\caption{MuDiLCO($s_j$)}
+\label{alg:MuDiLCO}
+
+\end{algorithm}
+
+
+
+
+
+
+\section{\textcolor{red}{ Optimization Algorithm for Multiround Lifetime Coverage Optimization}}
+\label{oa}
+As shown in Algorithm~\ref{alg:MuDiLCO}, the leader will execute an optimization algorithm based on an integer program. The  integer program  is based on  the model
+proposed by  \cite{pedraza2006} with some modifications, where  the objective is
+to find  a maximum  number of disjoint  cover sets.   To fulfill this  goal, the
+authors proposed an integer  program which forces undercoverage and overcoverage
+of  targets to  become minimal  at  the same  time.  They  use binary  variables
+$x_{jl}$ to indicate if  sensor $j$ belongs to cover set $l$.   In our model, we
+consider binary  variables $X_{t,j}$ to determine the  possibility of activating
+sensor $j$ during round $t$ of  a given sensing phase.  We also consider primary

 points as targets.  The  set of primary points is denoted by  $P$ and the set of
 sensors by  $J$. Only sensors  able to  be alive during  at least one  round are
 involved in the integer program.
 points as targets.  The  set of primary points is denoted by  $P$ and the set of
 sensors by  $J$. Only sensors  able to  be alive during  at least one  round are
 involved in the integer program.


@@ -568,7 +757,7 @@ We define the Overcoverage variable $\Theta_{t,p}$ as:
 \label{eq13} 
 \end{equation}
 More  precisely, $\Theta_{t,p}$  represents the  number of  active  sensor nodes
 \label{eq13} 
 \end{equation}
 More  precisely, $\Theta_{t,p}$  represents the  number of  active  sensor nodes

-minus  one  that  cover  the  primary  point $p$  during  the  round  $t$.   The
+minus  one  that  cover  the  primary  point $p$  during  round  $t$.   The

 Undercoverage variable  $U_{t,p}$ of the primary  point $p$ during  round $t$ is
 defined by:
 \begin{equation}
 Undercoverage variable  $U_{t,p}$ of the primary  point $p$ during  round $t$ is
 defined by:
 \begin{equation}


@@ -611,13 +800,15 @@ U_{t,p} \in \lbrace0,1\rbrace, \hspace{10 mm}\forall p \in P, t = 1,\dots,T  \la
 %(W_{\theta}+W_{\psi} = P)    \label{eq19} 
 %\end{equation}
 
 %(W_{\theta}+W_{\psi} = P)    \label{eq19} 
 %\end{equation}
 

+%%RC why W_{\theta} is not defined (only one sentence)? How to define in practice Wtheta and Wu?
+

 \begin{itemize}
 \item $X_{t,j}$:  indicates whether  or not the  sensor $j$ is  actively sensing
 \begin{itemize}
 \item $X_{t,j}$:  indicates whether  or not the  sensor $j$ is  actively sensing

-  during the round $t$ (1 if yes and 0 if not);
+  during round $t$ (1 if yes and 0 if not);

 \item $\Theta_{t,p}$ - {\it overcoverage}:  the number of sensors minus one that
 \item $\Theta_{t,p}$ - {\it overcoverage}:  the number of sensors minus one that

-  are covering the primary point $p$ during the round $t$;
+  are covering the primary point $p$ during round $t$;

 \item  $U_{t,p}$ -  {\it undercoverage}:  indicates whether  or not  the primary
 \item  $U_{t,p}$ -  {\it undercoverage}:  indicates whether  or not  the primary

-  point $p$  is being covered during  the round $t$ (1  if not covered  and 0 if
+  point $p$  is being covered during round $t$ (1  if not covered  and 0 if

   covered).
 \end{itemize}
 
   covered).
 \end{itemize}
 


@@ -633,61 +824,178 @@ There  are two main  objectives.  First,  we limit  the overcoverage  of primary
 points in order to activate a  minimum number of sensors.  Second we prevent the
 absence  of  monitoring  on  some  parts  of the  subregion  by  minimizing  the
 undercoverage.  The weights  $W_\theta$ and $W_U$ must be  properly chosen so as
 points in order to activate a  minimum number of sensors.  Second we prevent the
 absence  of  monitoring  on  some  parts  of the  subregion  by  minimizing  the
 undercoverage.  The weights  $W_\theta$ and $W_U$ must be  properly chosen so as

-to guarantee that the maximum number of points are covered during each round. In
-our simulations priority is given  to the coverage by choosing $W_{\theta}$ very
-large compared to $W_U$.
+to guarantee that the maximum number of points are covered during each round. 
+%% MS W_theta is smaller than W_u => problem with the following sentence
+In our simulations priority is given  to the coverage by choosing $W_{U}$ very
+large compared to $W_{\theta}$.

 %The Active-Sleep packet includes the schedule vector with the number of rounds that should be applied by the receiving sensor node during the sensing phase.
 
 %The Active-Sleep packet includes the schedule vector with the number of rounds that should be applied by the receiving sensor node during the sensing phase.
 

-\subsection{Sensing phase}
+This integer program can be solved using two approaches:

 
 

-The sensing phase consists of $T$ rounds. Each sensor node in the subregion will
-receive an Active-Sleep packet from WSNL, informing it to stay awake or to go to
-sleep for  each round of the sensing  phase.  Algorithm~\ref{alg:MuDiLCO}, which
-will be  executed by each node  at the beginning  of a period, explains  how the
-Active-Sleep packet is obtained.
+\subsection{Optimization solver for Multiround Lifetime Coverage Optimization}
+\label{glpk}
+The modeling language for Mathematical Programming (AMPL)~\cite{AMPL} is  employed to generate the integer program instance  in a  standard format, which  is then read  and solved  by the optimization solver  GLPK (GNU  linear Programming Kit  available in  the public domain) \cite{glpk} through a Branch-and-Bound method. We named the protocol which is based on GLPK solver in the decision phase as MuDiLCO.

 
 

-% In each round during the sensing phase, there is a cover set of sensor nodes,  in which  the active  sensors will  execute  their sensing  task  to preserve maximal  coverage and lifetime in the subregion and this will continue until finishing the round $T$ and starting new period. 
+
+%\textcolor{red}{\textbf{\textsc{Answer:}   ali   }}
+
+
+\subsection{Genetic Algorithm (GA) for Multiround Lifetime Coverage Optimization}
+\label{GA}
+Metaheuristics  are a generic search strategies for exploring search spaces for solving the complex problems. These strategies have to dynamically balance between the exploitation of the accumulated search experience and the exploration of the search space. On one hand, this balance can find regions in the search space with high-quality solutions. On the other hand, it prevents waste too much time in regions of the search space which are either already explored or don’t provide high-quality solutions. Therefore,  metaheuristic provides an enough good solution to an optimization problem, especially with incomplete  information or limited computation capacity \cite{bianchi2009survey}. Genetic Algorithm (GA) is one of the population-based metaheuristic methods that simulates the process of natural selection \cite{hassanien2015applications}.  GA starts with a population of random candidate solutions (called individuals or phenotypes) . GA uses genetic operators inspired by natural evolution, such as selection, mutation, evaluation, crossover, and replacement so as to improve the initial population of candidate solutions. This process repeated until a stopping criterion is satisfied. Compared to GLPK optimization solver, GA provides a near optimal solution with acceptible execution time, while GLPK provides optimal solution but it requires high execution time for large problem.
+
+In this section, we present a metaheuristic based GA to solve our multiround lifetime coverage optimization problem. The proposed GA provides a near optimal sechedule for multiround sensing per period. The proposed GA is based on the mathematical model which is presented in Section \ref{oa}. Algorithm \ref{alg:GA} shows the proposed GA to solve the coverage lifetime optimization problem. We named the new protocol which is based on GA in the decision phase as GA-MuDiLCO. The proposed GA can be explained in more details as follow:

 
 \begin{algorithm}[h!]                
 
 \begin{algorithm}[h!]                

- % \KwIn{all the parameters related to information exchange}
-%  \KwOut{$winer-node$ (: the id of the winner sensor node, which is the leader of current round)}
+ \small
+ \SetKwInput{Input}{Input}
+ \SetKwInput{Output}{Output}
+ \Input{ $ P, J, T, S_{pop}, \alpha_{j,p}^{ind}, X_{t,j}^{ind}, \Theta_{t,p}^{ind}, U_{t,p}^{ind}, Child_{t,j}^{ind}, Ch.\Theta_{t,p}^{ind}, Ch.U_{t,p}^{ind_1}$}
+ \Output{$\left\{\left(X_{1,1},\dots, X_{t,j}, \dots, X_{T,J}\right)\right\}_{t \in T, j \in J}$}
+

   \BlankLine
   %\emph{Initialize the sensor node and determine it's position and subregion} \; 
   \BlankLine
   %\emph{Initialize the sensor node and determine it's position and subregion} \; 

+  \ForEach {Individual $ind$ $\in$ $S_{pop}$} {
+     \emph{Generate Randomly Chromosome $\left\{\left(X_{1,1},\dots, X_{t,j}, \dots, X_{T,J}\right)\right\}_{t \in T, j \in J}$}\;
+     
+     \emph{Update O-U-Coverage $\left\{(P, J, \alpha_{j,p}^{ind}, X_{t,j}^{ind}, \Theta_{t,p}^{ind}, U_{t,p}^{ind})\right\}_{p \in P}$}\;
+     
+  
+     \emph{Evaluate Individual $(P, J, X_{t,j}^{ind}, \Theta_{t,p}^{ind}, U_{t,p}^{ind})$}\;  
+  }
+  
+  \While{ Stopping criteria is not satisfied }{
+  
+  \emph{Selection $(ind_1, ind_2)$}\;
+    \emph{Crossover $(P_c, X_{t,j}^{ind_1}, X_{t,j}^{ind_2}, Child_{t,j}^{ind_1}, Child_{t,j}^{ind_2})$}\;
+    \emph{Mutation $(P_m, Child_{t,j}^{ind_1}, Child_{t,j}^{ind_2})$}\;
+   
+   
+   \emph{Update O-U-Coverage $(P, J, \alpha_{j,p}^{ind}, Child_{t,j}^{ind_1}, Ch.\Theta_{t,p}^{ind_1}, Ch.U_{t,p}^{ind_1})$}\;
+  \emph{Update O-U-Coverage $(P, J, \alpha_{j,p}^{ind}, Child_{t,j}^{ind_2}, Ch.\Theta_{t,p}^{ind_2}, Ch.U_{t,p}^{ind_2})$}\;  
+ 
+\emph{Evaluate New Individual$(P, J, Child_{t,j}^{ind_1}, Ch.\Theta_{t,p}^{ind_1}, Ch.U_{t,p}^{ind_1})$}\;  
+ \emph{Replacement $(P, J, T, Child_{t,j}^{ind_1}, Ch.\Theta_{t,p}^{ind_1}, Ch.U_{t,p}^{ind_1}, X_{t,j}^{ind}, \Theta_{t,p}^{ind}, U_{t,p}^{ind}  )$ }\;
+ 
+ \emph{Evaluate New Individual$(P, J, Child_{t,j}^{ind_2}, Ch.\Theta_{t,p}^{ind_2}, Ch.U_{t,p}^{ind_2})$}\;  
+  
+ \emph{Replacement $(P, J, T, Child_{t,j}^{ind_2}, Ch.\Theta_{t,p}^{ind_2}, Ch.U_{t,p}^{ind_2}, X_{t,j}^{ind}, \Theta_{t,p}^{ind}, U_{t,p}^{ind}  )$ }\;

   
   

-  \If{ $RE_j \geq E_{R}$ }{
-      \emph{$s_j.status$ = COMMUNICATION}\;
-      \emph{Send $INFO()$ packet to other nodes in the subregion}\;
-      \emph{Wait $INFO()$ packet from other nodes in the subregion}\; 
-      %\emph{UPDATE $RE_j$ for every sent or received INFO Packet}\;
-      %\emph{ Collect information and construct the list L for all nodes in the subregion}\;

       
       

-      %\If{ the received INFO Packet = No. of nodes in it's subregion -1  }{
-      \emph{LeaderID = Leader election}\;
-      \If{$ s_j.ID = LeaderID $}{
-        \emph{$s_j.status$ = COMPUTATION}\;
-        \emph{$\left\{\left(X_{1,k},\dots,X_{T,k}\right)\right\}_{k \in J}$ =
-          Execute Integer Program Algorithm($T,J$)}\;
-        \emph{$s_j.status$ = COMMUNICATION}\;
-        \emph{Send $ActiveSleep()$ to each node $k$ in subregion a packet \\
-          with vector of activity scheduling $(X_{1,k},\dots,X_{T,k})$}\;
-        \emph{Update $RE_j $}\;
-      }          
-      \Else{
-        \emph{$s_j.status$ = LISTENING}\;
-        \emph{Wait $ActiveSleep()$ packet from the Leader}\;
-        % \emph{After receiving Packet, Retrieve the schedule and the $T$ rounds}\;
-        \emph{Update $RE_j $}\;
-      }  
-      %  }

   }
   }

-  \Else { Exclude $s_j$ from entering in the current sensing phase}
+  \emph{$\left\{\left(X_{1,1},\dots,X_{t,j},\dots,X_{T,J}\right)\right\}$ =
+            Select Best Solution ($S_{pop}$)}\;
+ \emph{return X} \;
+\caption{GA($T, J$)}
+\label{alg:GA}
+
+\end{algorithm}
+
+
+\begin{enumerate} [I)]
+\item \textbf{Representation:} Since the proposed GA's goal is to find the optimal schedule of the sensor nodes which take the responsibility of monitoring the subregion for $T$ rounds in the next phase, the chromosome is defined as a schedule for alive  sensors and each chromosome contains $T$ rounds. Each round in the schedule includes J genes, the total alive sensors in the subregion. Therefore, the gene of such a chromosome is a schedule of a sensor. In other words, The genes corresponding to active nodes have the value of one, the others are zero. Figure \ref{chromo} shows solution representation in the proposed GA.
+%[scale=0.3]
+\begin{figure}[h!]
+\centering
+ \includegraphics [scale=0.35] {rep.pdf} 
+\caption{Candidate Solution representation by the proposed GA. }
+\label{chromo}
+\end{figure} 
+
+
+
+\item \textbf{Initialize Population:} The initial population is randomly generated and each chromosome  in the GA population represents a possible sensors schedule solution to cover the entire subregion for $T$ rounds during current period. Each sensor in the chromosome is given a random value (0 or  1) for all rounds. If the random value is 1, the remaining  energy of this sensor should be adequate to activate this sensor during current round. Otherwise, the value is set to 0. The energy constraint is applied for each sensor during all rounds. 
+
+
+\item \textbf{Update O-U-Coverage:} 
+After creating the initial population, The overcoverage $\Theta_{t,p}$ and undercoverage $U_{t,p}$ for each candidate solution are computed (see Algorithm \ref{OU}) so as to use them in the next step.
+
+\begin{algorithm}[h!]                

   
   

- %   \emph{return X} \;
-\caption{MuDiLCO($s_j$)}
-\label{alg:MuDiLCO}
+ \SetKwInput{Input}{Input}
+ \SetKwInput{Output}{Output}
+ \Input{ parameters $P, J, ind, \alpha_{j,p}^{ind}, X_{t,j}^{ind}$}
+ \Output{$U^{ind} = \left\lbrace U_{1,1}^{ind}, \dots, U_{t,p}^{ind}, \dots, U_{T,P}^{ind} \right\rbrace$ and $\Theta^{ind} = \left\lbrace \Theta_{1,1}^{ind}, \dots, \Theta_{t,p}^{ind}, \dots, \Theta_{T,P}^{ind} \right\rbrace$}
+
+  \BlankLine
+
+  \For{$t\leftarrow 1$ \KwTo $T$}{
+  \For{$p\leftarrow 1$ \KwTo $P$}{
+     
+ %    \For{$i\leftarrow 0$ \KwTo $I_j$}{
+       \emph{$SUM\leftarrow 0$}\;
+         \For{$j\leftarrow 1$ \KwTo $J$}{
+              \emph{$SUM \leftarrow SUM + (\alpha_{j,p}^{ind} \times X_{t,j}^{ind})$ }\;
+         }
+         
+         \If { SUM = 0} {
+         \emph{$U_{t,p}^{ind} \leftarrow 0$}\;
+         \emph{$\Theta_{t,p}^{ind} \leftarrow 1$}\;
+         }
+         \Else{
+         \emph{$U_{t,p}^{ind} \leftarrow SUM -1$}\;
+         \emph{$\Theta_{t,p}^{ind} \leftarrow 0$}\;
+         }
+     
+     }
+     
+  }
+\emph{return $U^{ind}, \Theta^{ind}$ } \;
+\caption{O-U-Coverage}
+\label{OU}

 
 \end{algorithm}
 
 
 \end{algorithm}
 

+
+
+\item \textbf{Evaluate Population:}
+After creating the initial population, each individual is evaluated and assigned a fitness value according to the fitness function is illustrated in Eq. \eqref{eqf}. In the proposed GA, the optimal (or near optimal) candidate solution, is the one with the minimum value for the fitness function. The lower the fitness values been assigned to an individual, the better opportunity it get survived.  In our works, the function rewards  the decrease in the sensor nodes which cover the same primary point and penalizes the decrease to zero in the sensor nodes which cover the primary point. 
+
+\begin{equation}
+ F^{ind} \leftarrow  \sum_{t=1}^{T} \sum_{p=1}^{P} \left(W_{\theta}* \Theta_{t,p} + W_{U} * U_{t,p}  \right)    \label{eqf} 
+\end{equation}
+
+
+\item \textbf{Selection:} In order to generate a new generation, a portion of the existing population is elected based on a fitness function that ranks the fitness of each candidate solution and preferentially select the best solutions. Two parents should be selected to the mating pool.  In the proposed GA-MuDiLCO algorithm, the first parent is selected by using binary tournament selection to select one of the parents \cite{goldberg1991comparative}. In this method,  two individuals are chosen at random from population and the better of the two
+individuals is selected. If they have similar fitness values, one of them will be selected randomly. The best individual in the population is selected as a second parent.
+
+
+
+\item \textbf{Crossover:} Crossover is a genetic operator used to take more than one parent solutions and produce a child solution from them. If crossover probability $P_c$ is 100$\%$, then the crossover operation takes place between two individuals. If it is 0$\%$, the  two selected individuals in the mating pool will be the new chromosomes without crossover. In the proposed GA, a two-point crossover is used. Figure \ref{cross} gives an example for a two-point crossover for 8 sensors in the subregion and the schedule for 3 rounds.
+
+
+\begin{figure}[h!]
+\centering
+ \includegraphics [scale = 0.3] {crossover.pdf} 
+\caption{Two-point crossover. }
+\label{cross}
+\end{figure} 
+
+
+\item \textbf{Mutation:}
+Mutation is a divergence operation which introduces random modifications.  The purpose of the mutation is to maintain diversity within the population and prevent premature convergence. Mutation is used to add new genetic information (divergence) in order to achieve a global search over the solution search space and avoid to fall in local optima. The mutation oprator in the proposed GA-MuDiLCO works as follow: If mutation probability $P_m$ is 100$\%$, then the mutation operation takes place on the the new individual. The round number is selected randomly within (1..T) in the schedule solution. After that one sensor within this round is selected randomly within (1..J). If the sensor is scheduled as active "1", it should be rescheduled to sleep "0". If the sensor is scheduled as sleep, it rescheduled to active only if it has adequate remaining energy.
+
+
+\item \textbf{Update O-U-Coverage for children:}
+Before evalute each new individual, Algorithm \ref{OU} is called for each new individual to compute the new undercoverage $Ch.U$ and overcoverage $Ch.\Theta$ parameters. 
+ 
+\item \textbf{Evaluate New Individuals:}
+Each new individual is evaluated using Eq. \ref{eqf} but with using the new undercoverage $Ch.U$ and overcoverage $Ch.\Theta$ parameters of the new children.
+
+\item \textbf{Replacement:}
+After evaluatation of new children, Triple Tournament Replacement (TTR) will be applied for each new individual. In TTR strategy, three individuals are selected
+randomly from the population. Find the worst from them and then check its fitness with the new individual fitness. If the fitness of the new individual is better than the fitness of  the worst individual, replace the new individual with the worst individual. Otherwise, the replacement is not done. 
+
+ 
+\item \textbf{Stopping criteria:}
+The proposed GA-MuDiLCO stops when the stopping criteria is met. It stops after running for an amount of time in seconds equal to \textbf{Time limit}. The \textbf{Time limit} is the execution time obtained by the optimization solver GLPK for solving the same size of problem divided by two. The best solution will be selected as a schedule of sensors for $T$ rounds during the sensing phase in the current period.
+
+
+
+\end{enumerate} 
+
+
+

 \section{Experimental study}
 \label{exp}
 \subsection{Simulation setup}
 \section{Experimental study}
 \label{exp}
 \subsection{Simulation setup}


@@ -700,12 +1008,14 @@ random topologies and  the results presented hereafter are  the average of these
 25 runs.
 %Based on the results of our proposed work in~\cite{idrees2014coverage}, we found as the region of interest are divided into larger subregions as the network lifetime increased. In this simulation, the network are divided into 16 subregions. 
 We  performed  simulations for  five  different  densities  varying from  50  to
 25 runs.
 %Based on the results of our proposed work in~\cite{idrees2014coverage}, we found as the region of interest are divided into larger subregions as the network lifetime increased. In this simulation, the network are divided into 16 subregions. 
 We  performed  simulations for  five  different  densities  varying from  50  to

-250~nodes. Experimental results are obtained from randomly generated networks in
-which  nodes  are deployed  over  a  $50 \times  25~m^2  $  sensing field.  More
+250~nodes deployed  over  a  $50 \times  25~m^2  $  sensing field.  More

 precisely, the  deployment is controlled  at a coarse  scale in order  to ensure
 that  the deployed  nodes can  cover the  sensing field  with the  given sensing
 range.
 
 precisely, the  deployment is controlled  at a coarse  scale in order  to ensure
 that  the deployed  nodes can  cover the  sensing field  with the  given sensing
 range.
 

+%%RC these parameters are realistic?
+%% maybe we can increase the field and sensing range. 5mfor Rs it seems very small... what do the other good papers consider ?
+

 \begin{table}[ht]
 \caption{Relevant parameters for network initializing.}
 % title of Table
 \begin{table}[ht]
 \caption{Relevant parameters for network initializing.}
 % title of Table


@@ -733,36 +1043,39 @@ Sensing time for one round & 60 Minutes \\
 $E_{R}$ & 36 Joules\\
 $R_s$ & 5~m   \\     
 %\hline
 $E_{R}$ & 36 Joules\\
 $R_s$ & 5~m   \\     
 %\hline

-$w_{\Theta}$ & 1   \\
+$W_{\theta}$ & 1   \\

 % [1ex] adds vertical space
 %\hline
 % [1ex] adds vertical space
 %\hline

-$w_{U}$ & $|P^2|$
+$W_{U}$ & $|P|^2$ \\
+$P_c$ & 0.95   \\ 
+$P_m$ & 0.6 \\
+$S_{pop}$ & 50

 %inserts single line
 \end{tabular}
 \label{table3}
 % is used to refer this table in the text
 \end{table}
   
 %inserts single line
 \end{tabular}
 \label{table3}
 % is used to refer this table in the text
 \end{table}
   

-Our protocol  is declined into  four versions: MuDiLCO-1,  MuDiLCO-3, MuDiLCO-5,
+\textcolor{red}{Our first protocol based GLPK optimization solver is declined into  four versions: MuDiLCO-1,  MuDiLCO-3, MuDiLCO-5,

 and  MuDiLCO-7, corresponding  respectively to  $T=1,3,5,7$ ($T$  the  number of
 and  MuDiLCO-7, corresponding  respectively to  $T=1,3,5,7$ ($T$  the  number of

-rounds  in one  sensing period).   In the  following, the  general case  will be
-denoted by  MuDiLCO-T and we will  make comparisons with two  other methods. The
-first method, called DESK and  proposed by \cite{ChinhVu}, is a full distributed
-coverage  algorithm.   The  second  method,  called  GAF~\cite{xu2001geography},
-consists in dividing the region  into fixed squares.  During the decision phase,
-in each  square, one sensor is then  chosen to remain active  during the sensing
-phase time.
+rounds in one sensing period). The second protocol based GA is declined into  four versions: GA-MuDiLCO-1,  GA-MuDiLCO-3, GA-MuDiLCO-5,
+and  GA-MuDiLCO-7 for the same reason of the first protocol. After extensive experiments, we chose the dedicated values for the parameters $P_c$, $P_m$, and $S_{pop}$ because they gave the best results}.  In  the following, we will make comparisons with
+two other methods. The first method, called DESK and proposed by \cite{ChinhVu},
+is  a   full  distributed  coverage   algorithm.   The  second   method,  called
+GAF~\cite{xu2001geography}, consists in dividing  the region into fixed squares.
+During the decision  phase, in each square, one sensor is  then chosen to remain
+active during the sensing phase time.

 
 Some preliminary experiments were performed to study the choice of the number of
 
 Some preliminary experiments were performed to study the choice of the number of

-subregions  which subdivide  the  sensing field,  considering different  network
+subregions  which subdivides  the  sensing field,  considering different  network

 sizes. They show that as the number of subregions increases, so does the network
 sizes. They show that as the number of subregions increases, so does the network

-lifetime. Moreover, it  makes the MuDiLCO-T protocol more  robust against random
-network  disconnection due  to  node failures.  However,  too much  subdivisions
-reduces the advantage  of the optimization. In fact, there  is a balance between
+lifetime. Moreover,  it makes  the MuDiLCO protocol  more robust  against random
+network  disconnection due  to node  failures.  However,  too  many subdivisions
+reduce the advantage  of the optimization. In fact, there  is a balance between

 the  benefit  from the  optimization  and the  execution  time  needed to  solve
 the  benefit  from the  optimization  and the  execution  time  needed to  solve

-it. Therefore, we  have set the number  of subregions to 16 rather  than 32. 
+it. Therefore, we have set the number of subregions to 16 rather than 32.

 
 

-\subsection{Energy Model}
+\subsection{Energy model}

 
 We  use an  energy consumption  model  proposed by~\cite{ChinhVu}  and based  on
 \cite{raghunathan2002energy} with slight  modifications.  The energy consumption
 
 We  use an  energy consumption  model  proposed by~\cite{ChinhVu}  and based  on
 \cite{raghunathan2002energy} with slight  modifications.  The energy consumption


@@ -777,13 +1090,12 @@ For our  energy consumption model, we  refer to the sensor  node Medusa~II which
 uses an Atmels  AVR ATmega103L microcontroller~\cite{raghunathan2002energy}. The
 typical  architecture  of a  sensor  is composed  of  four  subsystems: the  MCU
 subsystem which is capable of computation, communication subsystem (radio) which
 uses an Atmels  AVR ATmega103L microcontroller~\cite{raghunathan2002energy}. The
 typical  architecture  of a  sensor  is composed  of  four  subsystems: the  MCU
 subsystem which is capable of computation, communication subsystem (radio) which

-is  responsible  for  transmitting/receiving  messages, sensing  subsystem  that
+is responsible  for transmitting/receiving messages, the  sensing subsystem that

 collects  data, and  the  power supply  which  powers the  complete sensor  node
 \cite{raghunathan2002energy}. Each  of the first three subsystems  can be turned
 on or  off depending on  the current status  of the sensor.   Energy consumption
 (expressed in  milliWatt per second) for  the different status of  the sensor is
 collects  data, and  the  power supply  which  powers the  complete sensor  node
 \cite{raghunathan2002energy}. Each  of the first three subsystems  can be turned
 on or  off depending on  the current status  of the sensor.   Energy consumption
 (expressed in  milliWatt per second) for  the different status of  the sensor is

-summarized in Table~\ref{table4}.  The energy  needed to send or receive a 1-bit
-packet is equal to $0.2575~mW$.
+summarized in Table~\ref{table4}.

 
 \begin{table}[ht]
 \caption{The Energy Consumption Model}
 
 \begin{table}[ht]
 \caption{The Energy Consumption Model}


@@ -814,16 +1126,17 @@ COMPUTATION & on & on & on & 26.83 \\
 % is used to refer this table in the text
 \end{table}
 
 % is used to refer this table in the text
 \end{table}
 

-For sake  of simplicity we  ignore the  energy needed to  turn on the  radio, to
+For the sake of simplicity we ignore  the energy needed to turn on the radio, to

 start up the sensor node, to move from one status to another, etc.
 %We also do not consider the need of collecting sensing data. PAS COMPRIS
 start up the sensor node, to move from one status to another, etc.
 %We also do not consider the need of collecting sensing data. PAS COMPRIS

-Thus, when  a sensor becomes active  (i.e., it already decides  it's status), it
-can turn its  radio off to save  battery. MuDiLCO uses two types  of packets for
+Thus, when a sensor becomes active (i.e., it has already chosen its status), it can
+turn  its radio  off to  save battery.  MuDiLCO uses  two types  of  packets for

 communication. The size of the  INFO packet and Active-Sleep packet are 112~bits
 and 24~bits  respectively.  The  value of energy  spent to send  a 1-bit-content
 message is  obtained by using  the equation in  ~\cite{raghunathan2002energy} to
 calculate  the energy cost  for transmitting  messages and  we propose  the same
 communication. The size of the  INFO packet and Active-Sleep packet are 112~bits
 and 24~bits  respectively.  The  value of energy  spent to send  a 1-bit-content
 message is  obtained by using  the equation in  ~\cite{raghunathan2002energy} to
 calculate  the energy cost  for transmitting  messages and  we propose  the same

-value for receiving the packets.
+value for receiving the packets. The energy  needed to send or receive a 1-bit
+packet is equal to 0.2575~mW.

 
 The initial energy of each node  is randomly set in the interval $[500;700]$.  A
 sensor node  will not participate in the  next round if its  remaining energy is
 
 The initial energy of each node  is randomly set in the interval $[500;700]$.  A
 sensor node  will not participate in the  next round if its  remaining energy is


@@ -839,16 +1152,16 @@ To evaluate our approach we consider the following performance metrics:
 
 \begin{enumerate}[i]
   
 
 \begin{enumerate}[i]
   

-\item {{\bf Coverage Ratio (CR)}:} the coverage ratio measures how much the area
+\item {{\bf Coverage Ratio (CR)}:} the coverage ratio measures how much of the area

   of a sensor field is covered. In our case, the sensing field is represented as
   of a sensor field is covered. In our case, the sensing field is represented as

-  a connected grid  of points and we use  each grid point as a  sample point for
-  calculating the coverage. The coverage ratio can be calculated by:
+  a connected grid  of points and we use  each grid point as a  sample point to
+  compute the coverage. The coverage ratio can be calculated by:

 \begin{equation*}
 \scriptsize
 \mbox{CR}(\%) = \frac{\mbox{$n^t$}}{\mbox{$N$}} \times 100,
 \end{equation*}
 where $n^t$ is  the number of covered  grid points by the active  sensors of all
 \begin{equation*}
 \scriptsize
 \mbox{CR}(\%) = \frac{\mbox{$n^t$}}{\mbox{$N$}} \times 100,
 \end{equation*}
 where $n^t$ is  the number of covered  grid points by the active  sensors of all

-subregions during round $t$ in the current sensing phase and $N$ is total number
+subregions during round $t$ in the current sensing phase and $N$ is the total number

 of grid points  in the sensing field of  the network. In our simulations $N = 51
 \times 26 = 1326$ grid points.
 %The accuracy of this method depends on the distance between grids. In our
 of grid points  in the sensing field of  the network. In our simulations $N = 51
 \times 26 = 1326$ grid points.
 %The accuracy of this method depends on the distance between grids. In our


@@ -857,7 +1170,7 @@ of grid points  in the sensing field of  the network. In our simulations $N = 51
 % Therefore, for our simulations, the error in the coverage calculation is less than ~ 1 $\% $.
 
 \item{{\bf Number  of Active Sensors Ratio  (ASR)}:} it is important  to have as
 % Therefore, for our simulations, the error in the coverage calculation is less than ~ 1 $\% $.
 
 \item{{\bf Number  of Active Sensors Ratio  (ASR)}:} it is important  to have as

-  few  active  nodes  as  possible  in  each  round,in  order  to  minimize  the
+  few  active  nodes  as  possible  in  each  round, in  order  to  minimize  the

   communication overhead  and maximize the network lifetime.  The Active Sensors
   Ratio is defined as follows:
 \begin{equation*}
   communication overhead  and maximize the network lifetime.  The Active Sensors
   Ratio is defined as follows:
 \begin{equation*}


@@ -866,11 +1179,11 @@ of grid points  in the sensing field of  the network. In our simulations $N = 51
 \end{equation*}
 where $A_r^t$ is the number of  active sensors in the subregion $r$ during round
 $t$ in the  current sensing phase, $|J|$  is the total number of  sensors in the
 \end{equation*}
 where $A_r^t$ is the number of  active sensors in the subregion $r$ during round
 $t$ in the  current sensing phase, $|J|$  is the total number of  sensors in the

-network, and $R$ is the total number of the subregions in the network.
+network, and $R$ is the total number of subregions in the network.

 
 \item {{\bf Network Lifetime}:} we define the network lifetime as the time until
   the  coverage  ratio  drops  below   a  predefined  threshold.  We  denote  by
 
 \item {{\bf Network Lifetime}:} we define the network lifetime as the time until
   the  coverage  ratio  drops  below   a  predefined  threshold.  We  denote  by

-  $Lifetime_{95}$ (respectively  $Lifetime_{50}$) as  the amount of  time during
+  $Lifetime_{95}$ (respectively  $Lifetime_{50}$) the amount of  time during

   which  the  network   can  satisfy  an  area  coverage   greater  than  $95\%$
   (respectively $50\%$). We assume that the network is alive until all nodes have
   been   drained    of   their   energy   or   the    sensor   network   becomes
   which  the  network   can  satisfy  an  area  coverage   greater  than  $95\%$
   (respectively $50\%$). We assume that the network is alive until all nodes have
   been   drained    of   their   energy   or   the    sensor   network   becomes


@@ -882,28 +1195,40 @@ network, and $R$ is the total number of the subregions in the network.
   seen as the total energy consumed by the sensors during the $Lifetime_{95}$ or
   $Lifetime_{50}$  divided  by the  number  of rounds.  EC  can  be computed  as
   follows:
   seen as the total energy consumed by the sensors during the $Lifetime_{95}$ or
   $Lifetime_{50}$  divided  by the  number  of rounds.  EC  can  be computed  as
   follows:

- \begin{equation*}
-\scriptsize
-\mbox{EC} = \frac{\sum\limits_{m=1}^{M_L} \left( E^{\mbox{com}}_m+E^{\mbox{list}}_m+E^{\mbox{comp}}_m \right) +
-  \sum\limits_{t=1}^{T_L} \left( E^{a}_t+E^{s}_t \right)}{T_L},
-\end{equation*}

 
 

+  % New version with global loops on period
+  \begin{equation*}
+    \scriptsize
+    \mbox{EC} = \frac{\sum\limits_{m=1}^{M} \left[ \left( E^{\mbox{com}}_m+E^{\mbox{list}}_m+E^{\mbox{comp}}_m \right) +\sum\limits_{t=1}^{T_m} \left( E^{a}_t+E^{s}_t \right) \right]}{\sum\limits_{m=1}^{M} T_m},
+  \end{equation*}
+
+
+% Old version with loop on round outside the loop on period
+%  \begin{equation*}
+%    \scriptsize
+%    \mbox{EC} = \frac{\sum\limits_{m=1}^{M_L} \left( E^{\mbox{com}}_m+E^{\mbox{list}}_m+E^{\mbox{comp}}_m \right) +\sum\limits_{t=1}^{T_L} \left( E^{a}_t+E^{s}_t \right)}{T_L},
+%  \end{equation*}
+
+% Ali version 

 %\begin{equation*}
 %\scriptsize
 %\mbox{EC} =  \frac{\mbox{$\sum\limits_{d=1}^D E^c_d$}}{\mbox{$D$}} + \frac{\mbox{$\sum\limits_{d=1}^D %E^l_d$}}{\mbox{$D$}} + \frac{\mbox{$\sum\limits_{d=1}^D E^a_d$}}{\mbox{$D$}} + %\frac{\mbox{$\sum\limits_{d=1}^D E^s_d$}}{\mbox{$D$}}.
 %\end{equation*}
 
 %\begin{equation*}
 %\scriptsize
 %\mbox{EC} =  \frac{\mbox{$\sum\limits_{d=1}^D E^c_d$}}{\mbox{$D$}} + \frac{\mbox{$\sum\limits_{d=1}^D %E^l_d$}}{\mbox{$D$}} + \frac{\mbox{$\sum\limits_{d=1}^D E^a_d$}}{\mbox{$D$}} + %\frac{\mbox{$\sum\limits_{d=1}^D E^s_d$}}{\mbox{$D$}}.
 %\end{equation*}
 

-where $M_L$ and  $T_L$ are respectively the number of  periods and rounds during
-$Lifetime_{95}$ or  $Lifetime_{50}$.  The total  energy consumed by  the sensors
-(EC) comes through taking into consideration four main energy factors. The first
-one ,  denoted $E^{\scriptsize \mbox{com}}_m$, represent  the energy consumption
-spent  by  all  the  nodes   for  wireless  communications  during  period  $m$.
-$E^{\scriptsize  \mbox{list}}_m$, the  next  factor, corresponds  to the  energy
-consumed by the sensors in LISTENING  status before receiving the decision to go
-active or  sleep in  period $m$. $E^{\scriptsize  \mbox{comp}}_m$ refers  to the
-energy needed  by all  the leader nodes  to solve  the integer program  during a
-period. Finally, $E^a_t$ and $E^s_t$  indicate the energy consummed by the whole
-network in round $t$.
+% Old version -> where $M_L$ and  $T_L$ are respectively the number of  periods and rounds during
+%$Lifetime_{95}$ or  $Lifetime_{50}$. 
+% New version
+where  $M$ is  the number  of periods  and  $T_m$ the  number of  rounds in  a
+period~$m$, both  during $Lifetime_{95}$  or $Lifetime_{50}$.  The  total energy
+consumed by the  sensors (EC) comes through taking  into consideration four main
+energy  factors.   The  first  one  ,  denoted  $E^{\scriptsize  \mbox{com}}_m$,
+represents  the  energy   consumption  spent  by  all  the   nodes  for  wireless
+communications  during period  $m$.  $E^{\scriptsize  \mbox{list}}_m$,  the next
+factor, corresponds  to the energy consumed  by the sensors  in LISTENING status
+before  receiving   the  decision  to  go   active  or  sleep   in  period  $m$.
+$E^{\scriptsize \mbox{comp}}_m$  refers to the  energy needed by all  the leader
+nodes to solve the integer program during a period. Finally, $E^a_t$ and $E^s_t$
+indicate the energy consumed by the whole network in round $t$.

 
 %\item {Network Lifetime:} we  have defined the network  lifetime as the  time until all
 %nodes  have  been drained  of  their  energy  or each  sensor  network monitoring  an area has become  disconnected.
 
 %\item {Network Lifetime:} we  have defined the network  lifetime as the  time until all
 %nodes  have  been drained  of  their  energy  or each  sensor  network monitoring  an area has become  disconnected.


@@ -920,78 +1245,80 @@ network in round $t$.
 
 \end{enumerate}
 
 
 \end{enumerate}
 

-%%%%%%%%%%%%%%%%%%%%%%%%VU JUSQU ICI**************************************************
+\subsection{Results and analysis}

 
 

-\section{Results and analysis}
-
-\subsection{Coverage ratio} 
+\subsubsection{Coverage ratio} 

 
 Figure~\ref{fig3} shows  the average coverage  ratio for 150 deployed  nodes. We
 can notice that for the first thirty rounds both DESK and GAF provide a coverage
 
 Figure~\ref{fig3} shows  the average coverage  ratio for 150 deployed  nodes. We
 can notice that for the first thirty rounds both DESK and GAF provide a coverage

-which is a little bit better than the  one of MuDiLCO-T. This is due to the fact
-that in  comparison with MuDiLCO that  uses optimization to put  in SLEEP status
-redundant sensors,  more sensor  nodes remain  active with DESK  and GAF.   As a
-consequence,  when the  number  of rounds  increases,  a larger  number of  node
-failures can be observed in DESK and  GAF, resulting in a faster decrease of the
-coverage ratio.  Furthermore,  our protocol allows to maintain  a coverage ratio
-greater than  50\% for far more  rounds.  Overall, the  proposed sensor activity
-scheduling based on optimization in  MuDiLCO maintains higher coverage ratios of
-the area of interest for a larger number of rounds. It also means that MuDiLCO-T
-saves more  energy, with less dead nodes,  at most for several  rounds, and thus
-should extend the network lifetime.
+which is a little bit better than the one of MuDiLCO.  
+%%RC : need to uniformize MuDiLCO or MuDiLCO-T? 
+%%MS : MuDiLCO everywhere
+%%RC maybe increase the size of the figure for the reviewers, no?
+This is due  to the fact that, in comparison with  MuDiLCO which uses optimization
+to put in  SLEEP status redundant sensors, more sensor  nodes remain active with
+DESK and GAF.   As a consequence, when the number of  rounds increases, a larger
+number of node failures  can be observed in DESK and GAF,  resulting in a faster
+decrease of the coverage ratio.   Furthermore, our protocol allows to maintain a
+coverage ratio  greater than  50\% for far  more rounds.  Overall,  the proposed
+sensor  activity scheduling based  on optimization  in MuDiLCO  maintains higher
+coverage ratios of the  area of interest for a larger number  of rounds. It also
+means that MuDiLCO saves more energy,  with less dead nodes, at most for several
+rounds, and thus should extend the network lifetime.

 
 

-\begin{figure}[t!]
+\begin{figure}[ht!]

 \centering
 \centering

- \includegraphics[scale=0.5] {R1/CR.pdf} 
+ \includegraphics[scale=0.5] {R/CR.pdf} 

 \caption{Average coverage ratio for 150 deployed nodes}
 \label{fig3}
 \end{figure} 
 
 \caption{Average coverage ratio for 150 deployed nodes}
 \label{fig3}
 \end{figure} 
 

-\subsection{Active sensors ratio} 
+\textcolor{red}{ We
+can see that for the first thirty nine rounds GA-MuDiLCO provides a little bit better coverage ratio  than MuDiLCO. Both DESK and GAF provide a coverage
+which is a little bit better than the one of MuDiLCO and GA-MuDiLCO for the first thirty rounds because they activate a larger number of nodes during sensing phase. After that GA-MuDiLCO provides a coverage ratio near to the  MuDiLCO and better than DESK and GAF. GA-MuDiLCO gives approximate solution with activation a larger number of nodes than MuDiLCO during sensing phase while it activates a less number of nodes in comparison with both DESK and GAF. The results of GA-MuDiLCO seems to be comparable and can maintain the lifetime coverage as long as possible.}
+
+
+
+\subsubsection{Active sensors ratio} 

 
 It is crucial to have as few active nodes as possible in each round, in order to
 
 It is crucial to have as few active nodes as possible in each round, in order to

-minimize    the    communication    overhead    and   maximize    the    network
-lifetime. Figure~\ref{fig4}  presents the active  sensor ratio for  150 deployed
+minimize the communication overhead and maximize    the network lifetime. Figure~\ref{fig4}  presents the active  sensor ratio for  150 deployed

 nodes all along the network lifetime. It appears that up to round thirteen, DESK
 and GAF have  respectively 37.6\% and 44.8\% of nodes  in ACTIVE status, whereas
 nodes all along the network lifetime. It appears that up to round thirteen, DESK
 and GAF have  respectively 37.6\% and 44.8\% of nodes  in ACTIVE status, whereas

-MuDiLCO-T clearly outperforms  them with only 24.8\% of  active nodes. After the
-thirty  fifth round,  MuDiLCO-T exhibits  larger number  of active  nodes, which
-agrees with  the dual observation of  higher level of  coverage made previously.
-Obviously, in  that case DESK  and GAF have  less active nodes, since  they have
-activated many nodes at the beginning. Anyway, MuDiLCO-T activates the available
-nodes in a more efficient manner.
+MuDiLCO clearly outperforms them  with only 24.8\%  of active nodes. \textcolor{red}{GA-MuDiLCO activates a number of sensor nodes larger than MuDiLCO but lower than both DESK and GAF. GA-MuDiLCO-1, GA-MuDiLCO-3, and GA-MuDiLCO-5 continue in providing a larger number of active sensors until the forty-sixth round after that it provides less number of active nodes due to the died nodes. GA-MuDiLCO-7 provides a larger number of sensor nodes and maintains a better coverage ratio compared to MuDiLCO-7 until the fifty-seventh round.  After the thirty-fifth round, MuDiLCO exhibits larger numbers of active nodes compared with DESK  and GAF, which agrees with  the  dual  observation  of  higher  level  of  coverage  made  previously}.
+Obviously, in that case DESK  and GAF have less active nodes, since  they have activated many nodes  at the beginning. Anyway, MuDiLCO  activates the available nodes in a more efficient manner. \textcolor{red}{GA-MuDiLCO activates near optimal number of sensor nodes also in efficient manner compared with both DESK  and GAF}.

 
 

-\begin{figure}[t!]
+\begin{figure}[ht!]

 \centering
 \centering

-\includegraphics[scale=0.5]{R1/ASR.pdf}  
+\includegraphics[scale=0.5]{R/ASR.pdf}  

 \caption{Active sensors ratio for 150 deployed nodes}
 \label{fig4}
 \end{figure} 
 
 \caption{Active sensors ratio for 150 deployed nodes}
 \label{fig4}
 \end{figure} 
 

-\subsection{Stopped simulation runs}
+%\textcolor{red}{GA-MuDiLCO activates a sensor nodes larger than MuDiLCO but lower than both DESK and GAF }
+
+
+\subsubsection{Stopped simulation runs}

 %The results presented in this experiment, is to show the comparison of our MuDiLCO protocol with other two approaches from the point of view the stopped simulation runs per round. Figure~\ref{fig6} illustrates the percentage of stopped simulation
 %runs per round for 150 deployed nodes. 
 
 Figure~\ref{fig6} reports the cumulative  percentage of stopped simulations runs
 %The results presented in this experiment, is to show the comparison of our MuDiLCO protocol with other two approaches from the point of view the stopped simulation runs per round. Figure~\ref{fig6} illustrates the percentage of stopped simulation
 %runs per round for 150 deployed nodes. 
 
 Figure~\ref{fig6} reports the cumulative  percentage of stopped simulations runs

-per round for  150 deployed nodes. This figure gives the  breakpoint for each of
-the methods.  DESK stops first,  after around 45~rounds, because it consumes the
+per round for  150 deployed nodes. This figure gives the  breakpoint for each method.  DESK stops first,  after approximately 45~rounds, because it consumes the

 more energy by  turning on a large number of redundant  nodes during the sensing
 more energy by  turning on a large number of redundant  nodes during the sensing

-phase. GAF  stops secondly for the  same reason than  DESK.  MuDiLCO-T overcomes
-DESK and GAF because the  optimization process distributed on several subregions
-leads  to coverage  preservation and  so extends  the network  lifetime.  Let us
-emphasize that the  simulation continues as long as a network  in a subregion is
-still connected.
+phase. GAF  stops secondly for the  same reason than  DESK. \textcolor{red}{GA-MuDiLCO  stops thirdly for the  same reason than  DESK and GAF.} \textcolor{red}{MuDiLCO and GA-MuDiLCO overcome}
+DESK and GAF because \textcolor{red}{they activate less number of sensor nodes, as well as }the optimization process distributed on several subregions leads to coverage  preservation and  so extends  the network  lifetime.  
+Let us emphasize that the  simulation continues as long as a network  in a subregion is still connected. 

 
 %%% The optimization effectively continues as long as a network in a subregion is still connected. A VOIR %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
 
 %%% The optimization effectively continues as long as a network in a subregion is still connected. A VOIR %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 

-\begin{figure}[t!]
+\begin{figure}[ht!]

 \centering
 \centering

-\includegraphics[scale=0.5]{R1/SR.pdf} 
+\includegraphics[scale=0.5]{R/SR.pdf} 

 \caption{Cumulative percentage of stopped simulation runs for 150 deployed nodes }
 \label{fig6}
 \end{figure} 
 
 \caption{Cumulative percentage of stopped simulation runs for 150 deployed nodes }
 \label{fig6}
 \end{figure} 
 

-\subsection{Energy Consumption} \label{subsec:EC}
+\subsubsection{Energy consumption} \label{subsec:EC}

 
 We  measure  the  energy  consumed  by the  sensors  during  the  communication,
 listening, computation, active, and sleep status for different network densities
 
 We  measure  the  energy  consumed  by the  sensors  during  the  communication,
 listening, computation, active, and sleep status for different network densities


@@ -1002,34 +1329,34 @@ network sizes, for $Lifetime_{95}$ and $Lifetime_{50}$.
 \begin{figure}[h!]
   \centering
   \begin{tabular}{cl}
 \begin{figure}[h!]
   \centering
   \begin{tabular}{cl}

-    \parbox{9.5cm}{\includegraphics[scale=0.5]{R1/EC95.pdf}} & (a) \\
+    \parbox{9.5cm}{\includegraphics[scale=0.5]{R/EC95.pdf}} & (a) \\

     \verb+ + \\
     \verb+ + \\

-    \parbox{9.5cm}{\includegraphics[scale=0.5]{R1/EC50.pdf}} & (b)
+    \parbox{9.5cm}{\includegraphics[scale=0.5]{R/EC50.pdf}} & (b)

   \end{tabular}
   \caption{Energy consumption for (a) $Lifetime_{95}$ and 
     (b) $Lifetime_{50}$}
   \label{fig7}
 \end{figure} 
 
   \end{tabular}
   \caption{Energy consumption for (a) $Lifetime_{95}$ and 
     (b) $Lifetime_{50}$}
   \label{fig7}
 \end{figure} 
 

-The  results  show  that MuDiLCO-T  is  the  most  competitive from  the  energy
+The  results  show  that  MuDiLCO  is  the  most  competitive  from  the  energy

 consumption point of view.  The  other approaches have a high energy consumption
 due  to activating a  larger number  of redundant  nodes as  well as  the energy
 consumed during  the different  status of the  sensor node. Among  the different
 versions of our protocol, the MuDiLCO-7  one consumes more energy than the other
 versions. This is  easy to understand since the bigger the  number of rounds and
 consumption point of view.  The  other approaches have a high energy consumption
 due  to activating a  larger number  of redundant  nodes as  well as  the energy
 consumed during  the different  status of the  sensor node. Among  the different
 versions of our protocol, the MuDiLCO-7  one consumes more energy than the other
 versions. This is  easy to understand since the bigger the  number of rounds and

-the  number of  sensors involved  in the  integer program,  the larger  the time
-computation to  solve the optimization  problem. To improve the  performances of
+the number of  sensors involved in the integer program are,  the larger the time
+computation to solve the optimization problem is. To improve the performances of

 MuDiLCO-7, we  should increase the  number of subregions  in order to  have less
 sensors to consider in the integer program.
 
 %In fact,  a distributed optimization decision, which produces T rounds, on the subregions is  greatly reduced the cost of communications and the time of listening as well as the energy needed for sensing phase and computation so thanks to the partitioning of the initial network into several independent subnetworks and producing T rounds for each subregion periodically. 
 
 
 MuDiLCO-7, we  should increase the  number of subregions  in order to  have less
 sensors to consider in the integer program.
 
 %In fact,  a distributed optimization decision, which produces T rounds, on the subregions is  greatly reduced the cost of communications and the time of listening as well as the energy needed for sensing phase and computation so thanks to the partitioning of the initial network into several independent subnetworks and producing T rounds for each subregion periodically. 
 
 

-\subsection{Execution time}
+\subsubsection{Execution time}

 
 We observe  the impact of the  network size and of  the number of  rounds on the
 computation  time.   Figure~\ref{fig77} gives  the  average  execution times  in
 
 We observe  the impact of the  network size and of  the number of  rounds on the
 computation  time.   Figure~\ref{fig77} gives  the  average  execution times  in

-seconds (needed to solve optimization problem) for different values of $T$.  The
+seconds (needed to solve optimization problem) for different values of $T$. The modeling language for Mathematical Programming (AMPL)~\cite{AMPL} is  employed to generate the Mixed Integer Linear Program instance  in a  standard format, which  is then read  and solved  by the optimization solver  GLPK (GNU  linear Programming Kit  available in  the public domain) \cite{glpk} through a Branch-and-Bound method. The

 original execution time  is computed on a laptop  DELL with Intel Core~i3~2370~M
 (2.4 GHz)  processor (2  cores) and the  MIPS (Million Instructions  Per Second)
 rate equal to 35330. To be consistent  with the use of a sensor node with Atmels
 original execution time  is computed on a laptop  DELL with Intel Core~i3~2370~M
 (2.4 GHz)  processor (2  cores) and the  MIPS (Million Instructions  Per Second)
 rate equal to 35330. To be consistent  with the use of a sensor node with Atmels


@@ -1038,19 +1365,19 @@ optimization   resolution,   this  time   is   multiplied   by  2944.2   $\left(
 \frac{35330}{2} \times  \frac{1}{6} \right)$ and  reported on Figure~\ref{fig77}
 for different network sizes.
 
 \frac{35330}{2} \times  \frac{1}{6} \right)$ and  reported on Figure~\ref{fig77}
 for different network sizes.
 

-\begin{figure}[t!]
+\begin{figure}[ht!]

 \centering
 \centering

-\includegraphics[scale=0.5]{R1/T.pdf}  
+\includegraphics[scale=0.5]{R/T.pdf}  

 \caption{Execution Time (in seconds)}
 \label{fig77}
 \end{figure} 
 
 As expected,  the execution time increases  with the number of  rounds $T$ taken
 \caption{Execution Time (in seconds)}
 \label{fig77}
 \end{figure} 
 
 As expected,  the execution time increases  with the number of  rounds $T$ taken

-into account for scheduling of the sensing phase. The times obtained for $T=1,3$
-or $5$ seems bearable, but for $T=7$ they become quickly unsuitable for a sensor
+into account to schedule the sensing phase. The times obtained for $T=1,3$
+or $5$ seem bearable, but for $T=7$ they become quickly unsuitable for a sensor

 node, especially when  the sensor network size increases.   Again, we can notice
 that if we want  to schedule the nodes activities for a  large number of rounds,
 node, especially when  the sensor network size increases.   Again, we can notice
 that if we want  to schedule the nodes activities for a  large number of rounds,

-we need to choose a relevant number of subregion in order to avoid a complicated
+we need to choose a relevant number of subregions in order to avoid a complicated

 and cumbersome optimization.  On the one hand, a large value  for $T$ permits to
 reduce the  energy-overhead due  to the three  pre-sensing phases, on  the other
 hand  a leader  node may  waste a  considerable amount  of energy  to  solve the
 and cumbersome optimization.  On the one hand, a large value  for $T$ permits to
 reduce the  energy-overhead due  to the three  pre-sensing phases, on  the other
 hand  a leader  node may  waste a  considerable amount  of energy  to  solve the


@@ -1058,18 +1385,18 @@ optimization problem.
 
 %While MuDiLCO-1, 3, and 5 solves the optimization process with suitable execution times to be used on wireless sensor network because it distributed on larger number of small subregions as well as it is used acceptable number of round(s) T.  We think that in distributed fashion the solving of the optimization problem to produce T rounds in a subregion can be tackled by sensor nodes. Overall, to be able to deal with very large networks, a distributed method is clearly required.
 
 
 %While MuDiLCO-1, 3, and 5 solves the optimization process with suitable execution times to be used on wireless sensor network because it distributed on larger number of small subregions as well as it is used acceptable number of round(s) T.  We think that in distributed fashion the solving of the optimization problem to produce T rounds in a subregion can be tackled by sensor nodes. Overall, to be able to deal with very large networks, a distributed method is clearly required.
 

-\subsection{Network Lifetime}
+\subsubsection{Network lifetime}

 
 The next  two figures,  Figures~\ref{fig8}(a) and \ref{fig8}(b),  illustrate the
 network lifetime  for different network sizes,  respectively for $Lifetime_{95}$
 and  $Lifetime_{50}$.  Both  figures show  that the  network  lifetime increases
 together with the  number of sensor nodes, whatever the  protocol, thanks to the
 
 The next  two figures,  Figures~\ref{fig8}(a) and \ref{fig8}(b),  illustrate the
 network lifetime  for different network sizes,  respectively for $Lifetime_{95}$
 and  $Lifetime_{50}$.  Both  figures show  that the  network  lifetime increases
 together with the  number of sensor nodes, whatever the  protocol, thanks to the

-node  density  which  result in  more  and  more  redundant  nodes that  can  be
-deactivated  and  thus save  energy.   Compared  to  the other  approaches,  our
-MuDiLCO-T protocol  maximizes the  lifetime of the  network.  In  particular the
-gain in  lifetime for a coverage over  95\% is greater than  38\% when switching
-from GAF to MuDiLCO-3.  The slight  decrease that can bee observed for MuDiLCO-7
-in case of  $Lifetime_{95}$ with large wireless sensor  networks result from the
+node  density  which  results in  more  and  more  redundant  nodes that  can  be
+deactivated and thus save energy.  Compared to the other approaches, our MuDiLCO
+protocol  maximizes the  lifetime of  the network.   In particular  the  gain in
+lifetime for a  coverage over 95\% is greater than 38\%  when switching from GAF
+to MuDiLCO-3.  The  slight decrease that can be observed  for MuDiLCO-7 in case
+of  $Lifetime_{95}$  with  large  wireless  sensor  networks  results  from  the

 difficulty  of the optimization  problem to  be solved  by the  integer program.
 This  point was  already noticed  in subsection  \ref{subsec:EC} devoted  to the
 energy consumption,  since network lifetime and energy  consumption are directly
 difficulty  of the optimization  problem to  be solved  by the  integer program.
 This  point was  already noticed  in subsection  \ref{subsec:EC} devoted  to the
 energy consumption,  since network lifetime and energy  consumption are directly


@@ -1078,35 +1405,35 @@ linked.
 \begin{figure}[t!]
   \centering
   \begin{tabular}{cl}
 \begin{figure}[t!]
   \centering
   \begin{tabular}{cl}

-    \parbox{9.5cm}{\includegraphics[scale=0.5]{R1/LT95.pdf}} & (a) \\
+    \parbox{9.5cm}{\includegraphics[scale=0.5]{R/LT95.pdf}} & (a) \\

     \verb+ + \\
     \verb+ + \\

-    \parbox{9.5cm}{\includegraphics[scale=0.5]{R1/LT50.pdf}} & (b)
+    \parbox{9.5cm}{\includegraphics[scale=0.5]{R/LT50.pdf}} & (b)

   \end{tabular}
   \caption{Network lifetime for (a) $Lifetime_{95}$ and 
     (b) $Lifetime_{50}$}
   \label{fig8}
 \end{figure} 
 
   \end{tabular}
   \caption{Network lifetime for (a) $Lifetime_{95}$ and 
     (b) $Lifetime_{50}$}
   \label{fig8}
 \end{figure} 
 

-% By choosing the best suited nodes, for each round, by optimizing the coverage and lifetime of the network to cover the area of interest with a maximum number rounds and by letting the other nodes sleep in order to be used later in next rounds, our MuDiLCO-T protocol efficiently prolonges the network lifetime. 
+% By choosing the best suited nodes, for each round, by optimizing the coverage and lifetime of the network to cover the area of interest with a maximum number rounds and by letting the other nodes sleep in order to be used later in next rounds, our MuDiLCO protocol efficiently prolonges the network lifetime. 

 
 

-%In Figure~\ref{fig8}, Comparison shows that our MuDiLCO-T protocol, which are used distributed optimization on the subregions with the ability of producing T rounds, is the best one because it is robust to network disconnection during the network lifetime as well as it consume less energy in comparison with other approaches. It also means that distributing the protocol in each sensor node and subdividing the sensing field into many subregions, which are managed independently and simultaneously, is the most relevant way to maximize the lifetime of a network.
+%In Figure~\ref{fig8}, Comparison shows that our MuDiLCO protocol, which are used distributed optimization on the subregions with the ability of producing T rounds, is the best one because it is robust to network disconnection during the network lifetime as well as it consume less energy in comparison with other approaches. It also means that distributing the protocol in each sensor node and subdividing the sensing field into many subregions, which are managed independently and simultaneously, is the most relevant way to maximize the lifetime of a network.

 
 
 %We see that our MuDiLCO-7 protocol results in execution times that quickly become unsuitable for a sensor network as well as the energy consumption seems to be huge because it used a larger number of rounds T during performing the optimization decision in the subregions, which is led to decrease the network lifetime. On the other side, our MuDiLCO-1, 3, and 5 protocol seems to be more efficient in comparison with other approaches because they are prolonged the lifetime of the network more than DESK and GAF.
 
 
 
 
 %We see that our MuDiLCO-7 protocol results in execution times that quickly become unsuitable for a sensor network as well as the energy consumption seems to be huge because it used a larger number of rounds T during performing the optimization decision in the subregions, which is led to decrease the network lifetime. On the other side, our MuDiLCO-1, 3, and 5 protocol seems to be more efficient in comparison with other approaches because they are prolonged the lifetime of the network more than DESK and GAF.
 
 

-\section{Conclusion and Future Works}
+\section{Conclusion and future works}

 \label{sec:conclusion}
 
 \label{sec:conclusion}
 

-In this  paper, we have addressed the  problem of the coverage  and the lifetime
-optimization in  wireless sensor networks. This  is a key issue  as sensor nodes
-have limited resources  in terms of memory, energy,  and computational power. To
-cope with this problem, the field  of sensing is divided into smaller subregions
-using the concept  of divide-and-conquer method, and then  we propose a protocol
-which  optimizes  coverage and  lifetime  performances  in  each subregion.  Our
-protocol,   called   MuDiLCO    (Multiperiod   Distributed   Lifetime   Coverage
-Optimization)  combines two  efficient techniques:  network leader  election and
-sensor activity scheduling.
+We have addressed  the problem of the coverage and of the lifetime optimization in
+wireless  sensor networks.  This is  a key  issue as  sensor nodes  have limited
+resources in terms of memory, energy, and computational power. To cope with this
+problem,  the field  of sensing  is divided  into smaller  subregions  using the
+concept  of divide-and-conquer  method, and  then  we propose  a protocol  which
+optimizes coverage  and lifetime performances in each  subregion.  Our protocol,
+called MuDiLCO (Multiround  Distributed Lifetime Coverage Optimization) combines
+two  efficient   techniques:  network   leader  election  and   sensor  activity
+scheduling.

 %,  where the challenges
 %include how to select the  most efficient leader in each subregion and
 %the best cover sets %of active nodes that will optimize the network lifetime
 %,  where the challenges
 %include how to select the  most efficient leader in each subregion and
 %the best cover sets %of active nodes that will optimize the network lifetime


@@ -1114,17 +1441,17 @@ sensor activity scheduling.
 %subregion using more than one cover set during the sensing phase. 
 The activity  scheduling in each subregion  works in periods,  where each period
 consists of four  phases: (i) Information Exchange, (ii)  Leader Election, (iii)
 %subregion using more than one cover set during the sensing phase. 
 The activity  scheduling in each subregion  works in periods,  where each period
 consists of four  phases: (i) Information Exchange, (ii)  Leader Election, (iii)

-Decision Phase to plan the activity  of the sensors over $T$ rounds (iv) Sensing
-Phase itself divided into T rounds.
+Decision Phase to plan the activity  of the sensors over $T$ rounds, (iv) Sensing
+Phase itself divided into $T$ rounds.

 
 Simulations  results show the  relevance of  the proposed  protocol in  terms of
 lifetime, coverage  ratio, active  sensors ratio, energy  consumption, execution
 time. Indeed,  when dealing with  large wireless sensor networks,  a distributed
 
 Simulations  results show the  relevance of  the proposed  protocol in  terms of
 lifetime, coverage  ratio, active  sensors ratio, energy  consumption, execution
 time. Indeed,  when dealing with  large wireless sensor networks,  a distributed

-approach like  the one we  propose allows to  reduce the difficulty of  a single
+approach, like  the one we  propose, allows to  reduce the difficulty of  a single

 global optimization problem by partitioning it in many smaller problems, one per
 subregion, that can be solved  more easily. Nevertheless, results also show that
 it is not possible to plan the activity of sensors over too many rounds, because
 global optimization problem by partitioning it in many smaller problems, one per
 subregion, that can be solved  more easily. Nevertheless, results also show that
 it is not possible to plan the activity of sensors over too many rounds, because

-the resulting optimization problem leads to too high resolution time and thus to
+the resulting optimization problem leads to too high resolution times and thus to

 an excessive energy consumption.
 
 %In  future work, we plan  to study and propose adjustable sensing range coverage optimization protocol, which computes  all active sensor schedules in one time, by using
 an excessive energy consumption.
 
 %In  future work, we plan  to study and propose adjustable sensing range coverage optimization protocol, which computes  all active sensor schedules in one time, by using


@@ -1132,11 +1459,14 @@ an excessive energy consumption.
 % use section* for acknowledgement
 
 \section*{Acknowledgment}
 % use section* for acknowledgement
 
 \section*{Acknowledgment}

-As a Ph.D.  student, Ali Kadhum IDREES would like  to gratefully acknowledge the
+This work is  partially funded by the Labex ACTION program (contract ANR-11-LABX-01-01).
+As a Ph.D.  student, Ali Kadhum IDREES would like to gratefully acknowledge the

 University  of Babylon  - Iraq  for the  financial support,  Campus  France (The
 French  national agency  for the  promotion of  higher  education, international
 University  of Babylon  - Iraq  for the  financial support,  Campus  France (The
 French  national agency  for the  promotion of  higher  education, international

-student   services,  and   international  mobility),   and  the   University  of
-Franche-Comt\'e - France for all the support in France.
+student   services,  and   international  mobility).%,   and  the   University  ofFranche-Comt\'e - France for all the support in France. 
+
+
+

 
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@@ -1160,7 +1490,7 @@ Franche-Comt\'e - France for all the support in France.
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+\bibliography{article}

   
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