Solving conflicts

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 \keywords{Wireless   Sensor   Networks,   Area   Coverage,   Network   lifetime,
 Optimization, Scheduling.}
 
 \keywords{Wireless   Sensor   Networks,   Area   Coverage,   Network   lifetime,
 Optimization, Scheduling.}
 

-\abstract{One  of the fundamental  challenges in  Wireless Sensor  Networks (WSNs)  is the
-coverage preservation and the extension of the network lifetime continuously and
-effectively when  monitoring a  certain area (or  region) of interest.   In this
-paper, a Distributed Lifetime Coverage Optimization protocol (DiLCO) to maintain
-the  coverage  and  to improve  the  lifetime  in  wireless sensor  networks  is
-proposed.   The  area of  interest  is first  divided  into  subregions using  a
-divide-and-conquer  method and  then the  DiLCO protocol  is distributed  on the
-sensor nodes  in each  subregion. The DiLCO  combines two  efficient techniques:
-leader election  for each subregion, followed by  an optimization-based planning
-of activity  scheduling decisions for  each subregion. The proposed  DiLCO works
-into rounds during which a small  number of nodes, remaining active for sensing,
-is selected to ensure coverage so as to maximize the lifetime of wireless sensor
-network.   Each  round  consists   of  four  phases:  (i)~Information  Exchange,
-(ii)~Leader Election, (iii)~Decision, and (iv)~Sensing.  The decision process is
-carried out  by a leader node,  which solves an integer  program.  Compared with
-some existing protocols, simulation results  show that the proposed protocol can
-prolong the network lifetime and improve the coverage performance effectively.}
+\abstract{ One of the main research challenges faced in Wireless Sensor Networks
+  (WSNs) is to preserve continuously and effectively the coverage of an area (or
+  region) of interest  to be monitored, while simultaneously  preventing as much
+  as possible a network failure due to battery-depleted nodes.  In this paper we
+  propose a protocol, called Distributed Lifetime Coverage Optimization protocol
+  (DiLCO), which maintains the coverage  and improves the lifetime of a wireless
+  sensor  network. As  a  first step  we  partition the  area  of interest  into
+  subregions using a classical  divide-and-conquer method. Our DiLCO protocol is
+  then distributed  on the sensor nodes in  each subregion in a  second step. To
+  fulfill  our   objective,  the   proposed  protocol  combines   two  effective
+  techniques:   a  leader   election   in  each   subregion,   followed  by   an
+  optimization-based node activity scheduling  performed by each elected leader.
+  This two-step process takes place periodically, in order to choose a small set
+  of nodes remaining  active for sensing during a time slot.   Each set is built
+  to ensure  coverage at  a low  energy cost, allowing  to optimize  the network
+  lifetime. More  precisely, a period  consists of four  phases: (i)~Information
+  Exchange,  (ii)~Leader   Election,  (iii)~Decision,  and   (iv)~Sensing.   The
+  decision process, which results in  an activity scheduling vector,  is carried
+  out by a leader node through  the solving of an integer program. In comparison
+  with  some other  protocols, the  simulations  done using  the discrete  event
+  simulator OMNeT++ show that our approach  is able to increase the WSN lifetime
+  and provides improved coverage performance. }

 
 \onecolumn \maketitle \normalsize \vfill
 
 \section{\uppercase{Introduction}}
 \label{sec:introduction}
 
 \onecolumn \maketitle \normalsize \vfill
 
 \section{\uppercase{Introduction}}
 \label{sec:introduction}

-\noindent 
-Energy efficiency is very important issue in WSNs since sensors are powered by  batteries. Therefore, reducing energy consumption and extending network lifetime are the main challenges in the design of WSNs. One of  the major scientific research challenges in WSNs,  which has been  addressed by a  large amount of literature  during the last few  years, is the design  of energy efficient approaches  for coverage and connectivity~\cite{conti2014mobile}.
-Coverage reflects how well a sensor field is monitored, is one of the most important performance metrics to measure WSNs. The most discussed coverage problems in literature can be classified
-into three types \cite{li2013survey}: area (blanket) coverage (where every
-point inside an area is to be monitored), target (sweep) coverage (where the main objective is to cover only a finite number of discrete
-points  called targets), and barrier coverage (The problem of preventing an intruder from entering a region of interest is referred to as the barrier coverage).
- It is required to monitor the area of interest efficiently~\cite{Nayak04}, but in the same time  the power consumption should be minimized. Since sensor nodes have a limited batteries life~\cite{Sudip03}  and since it is impossible, difficult or expensive to be recharged and /or replaced after they are deployed in  remote, hostile,  or  unpractical environments, Therefore, it is desired that the WSNs are deployed with high densities so as to exploit the overlapping sensing regions of some  sensor nodes to save energy by turning off some of them during the sensing phase to prolong the network lifetime by elaborate managing the duty cycle of nodes in WSN.
-
-In this paper we concentrate on the area coverage problem with the objective of
-maximizing the  network lifetime by using DiLCO protocol to maintain the coverage and to improve  the  lifetime  in  WSNs. The  area of interest is divided into subregions using divide-and-conquer method and an activity scheduling based optimization for sensor nodes is planned by the elected leader in each subregion. In fact,  the nodes in a subregion can be seen as a cluster  where each node sends  sensing data to  the cluster head or  the sink node.  Furthermore, the  activities in a subregion/cluster can  continue even if another  cluster stops due  to too  many node  failures.  Our  DiLCO protocol considers rounds, where  a round starts with a discovery phase to exchange information between sensors of the subregion, in order to choose in a suitable manner a sensor  node to carry out a coverage strategy.  Our DiLCO protocol involves solving an integer program, which provides the activation of the sensors for the sensing phase of the current round.

 
 

-The remainder of the paper is organized as follows. The next section reviews  the related  work  in  the field.  Section~\ref{sec:The DiLCO Protocol Description} is devoted to the DiLCO protocol Description. Section~\ref{cp}  gives the coverage model
-formulation which is used to schedule the activation of sensors.
-Section~\ref{sec:Simulation Results and Analysis} shows the simulation results.  Finally, we give concluding remarks and some suggestions for
-future works in Section~\ref{sec:Conclusion and Future Works}.
+\noindent 
+Energy efficiency is  a crucial issue in wireless  sensor networks since sensory
+consumption, in  order to  maximize the network  lifetime, represents  the major
+difficulty when designing WSNs. As a consequence, one of the scientific research
+challenges in  WSNs, which has  been addressed by  a large amount  of literature
+during the  last few  years, is  the design of  energy efficient  approaches for
+coverage and connectivity~\cite{conti2014mobile}.   Coverage reflects how well a
+sensor  field is  monitored. On  the one  hand we  want to  monitor the  area of
+interest in the most efficient way~\cite{Nayak04}.  On the other hand we want to
+use as less energy as possible.   Sensor nodes are battery-powered with no means
+of recharging or replacing, usually due to environmental (hostile or unpractical
+environments)  or cost  reasons.  Therefore,  it is  desired that  the  WSNs are
+deployed with high densities so as to exploit the overlapping sensing regions of
+some sensor nodes to save energy by  turning off some of them during the sensing
+phase to prolong the network lifetime.
+
+In this  paper we design  a protocol that  focuses on the area  coverage problem
+with  the objective  of maximizing  the network  lifetime. Our  proposition, the
+Distributed  Lifetime  Coverage  Optimization  (DILCO) protocol,  maintains  the
+coverage  and improves  the lifetime  in  WSNs. The  area of  interest is  first
+divided  into subregions using  a divide-and-conquer  algorithm and  an activity
+scheduling  for sensor  nodes is  then  planned by  the elected  leader in  each
+subregion. In fact, the nodes in a subregion can be seen as a cluster where each
+node sends sensing data to the  cluster head or the sink node.  Furthermore, the
+activities in a subregion/cluster can continue even if another cluster stops due
+to too many node failures.  Our DiLCO protocol considers periods, where a period
+starts with a discovery phase to  exchange information between sensors of a same
+subregion, in order to choose in a suitable manner a sensor node (the leader) to
+carry out the coverage strategy. In each subregion the activation of the sensors
+for the  sensing phase of the current  period is obtained by  solving an integer
+program. The  resulting activation  vector is broadcasted  by a leader  to every
+node of its subregion.
+
+The remainder  of the  paper continues with  Section~\ref{sec:Literature Review}
+where a  review of some related  works is presented. The  next section describes
+the  DiLCO  protocol,  followed   in  Section~\ref{cp}  by  the  coverage  model
+formulation    which    is    used     to    schedule    the    activation    of
+sensors. Section~\ref{sec:Simulation Results  and Analysis} shows the simulation
+results. The paper  ends with conclusions and some  suggestions for further work
+in Section~\ref{sec:Conclusion and Future Works}.

 
 \section{\uppercase{Literature Review}}
 \label{sec:Literature Review}
 
 \section{\uppercase{Literature Review}}
 \label{sec:Literature Review}

-\noindent In this section, we summarize some related works regarding coverage lifetime maximization and scheduling, and distinguish our DiLCO protocol from the works presented in the literature. 

 
 

-The work presented in~\cite{luo2014parameterized,tian2014distributed} try to solve the target coverage problem so as to extend the network lifetime since it is easy to verify the coverage status of discreet target.
-The work proposed in~\cite{kim2013maximum} considered the barrier-coverage problem in WSNs. The final goal is to maximize the network lifetime such that any penetration of the intruder is detected.
-In \cite{ChinhVu},  the authors are proposed a localized and distributed greedy algorithm named DESK for generating non-disjoint cover sets which provide the k-coverage for the whole network. 
-Our Work in~\cite{idrees2014coverage} is 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 are considered only distributing the coverage protocol over two subregions.  
-The work presented in ~\cite{Zhang} focuses on a distributed clustering method, which aims to extend the network lifetime, while the coverage is ensured.
+\noindent In  this section, we  summarize some related works  regarding coverage
+problem  and distinguish  our DiLCO  protocol from  the works  presented  in the
+literature.
+
+The most discussed coverage  problems in literature
+can  be classified into  three types  \cite{li2013survey}: area  coverage (where
+every point inside an area is  to be monitored), target coverage (where the main
+objective is to  cover only a finite number of  discrete points called targets),
+and  barrier coverage (to  prevent intruders  from entering  into the  region of
+interest). 
+{\it In DiLCO  protocol, the area coverage, i.e. the coverage  of every point in
+  the sensing  region, is transformed  to the coverage  of a fraction  of points
+  called primary points. }
+
+The major  approach to extend network  lifetime while preserving  coverage is to
+divide/organize the  sensors into a suitable  number of set  covers (disjoint or
+non-disjoint)  where each  set completely  covers a  region of  interest  and to
+activate these set  covers successively. The network activity  can be planned in
+advance and scheduled  for the entire network lifetime  or organized in periods,
+and the set of  active sensor nodes is decided at the  beginning of each period.
+Active node selection is determined based on the problem requirements (e.g. area
+monitoring,  connectivity,  power   efficiency).  Different  methods  have  been
+proposed in literature.
+{\it DiLCO protocol  works in periods, where each  period contains a preliminary
+  phase  for information  exchange and  decisions, followed  by a  sensing phase
+  where one cover set is in charge of the sensing task.}
+
+Various   approaches,   including   centralized,  distributed,   and   localized
+algorithms, have been proposed to extend the network lifetime.
+%For instance, in order to hide the occurrence of faults, or the sudden unavailability of
+%sensor nodes, some distributed algorithms have been developed in~\cite{Gallais06,Tian02,Ye03,Zhang05,HeinzelmanCB02}. 
+In       distributed      algorithms~\cite{yangnovel,ChinhVu,qu2013distributed},
+information  is   disseminated  throughout   the  network  and   sensors  decide
+cooperatively by communicating with their neighbors which of them will remain in
+sleep    mode   for    a   certain    period   of    time.     The   centralized
+algorithms~\cite{cardei2005improving,zorbas2010solving,pujari2011high}     always
+provide nearly or close to optimal  solution since the algorithm has global view
+of the whole  network, but such a method has the  disadvantage of requiring high
+communication costs,  since the  node (located at  the base station)  making the
+decision needs information from all the sensor nodes in the area.
+
+A large  variety of coverage scheduling  algorithms have been  proposed. Many of
+the existing  algorithms, dealing with the  maximization of the  number of cover
+sets, are heuristics.  These heuristics  involve the construction of a cover set
+by including in priority the sensor  nodes which cover critical targets, that is
+to  say targets  that  are covered  by  the smallest  number  of sensors.  Other
+approaches  are based  on  mathematical programming  formulations and  dedicated
+techniques (solving with a branch-and-bound algorithms available in optimization
+solver).  The problem is formulated  as an optimization problem (maximization of
+the  lifetime  or  number  of  cover  sets) under  target  coverage  and  energy
+constraints.   Column  generation techniques,  well-known  and widely  practiced
+techniques for solving  linear programs with too many  variables, have been also
+used~\cite{castano2013column,rossi2012exact,deschinkel2012column}.
+
+Diongue  and  Thiare~\cite{diongue2013alarm}  proposed  an  energy  aware  sleep
+scheduling  algorithm  for lifetime  maximization  in  wireless sensor  networks
+(ALARM).  The proposed approach permits to schedule redundant nodes according to
+the weibull distribution.  This work did not analyze the  ALARM scheme under the
+coverage problem.
+
+Shi et al.~\cite{shi2009} modeled the Area Coverage Problem (ACP), which will be
+changed  into a  set coverage  problem. By  using this  model, they  proposed an
+Energy-Efficient central-Scheduling  greedy algorithm, which  can reduces energy
+consumption and increases network lifetime, by selecting a appropriate subset of
+sensor nodes to support the networks periodically.
+
+In ~\cite{chenait2013distributed},  the authors presented  a coverage-guaranteed
+distributed  sleep/wake scheduling  scheme so  ass to  prolong  network lifetime
+while guaranteeing network coverage. This scheme mitigates scheduling process to
+be more stable by avoiding  useless transitions between states without affecting
+the coverage level required by the application.
+
+The work  in~\cite{cheng2014achieving} presented a  unified sensing architecture
+for duty  cycled sensor  networks, called uSense,  which comprises  three ideas:
+Asymmetric Architecture, Generic Switching  and Global Scheduling. The objective
+is to provide a flexible and efficient coverage in sensor networks.
+
+In~\cite{ling2009energy},  the  lifetime  of  a  sensor  node  is  divided  into
+epochs. At  each epoch,  the base station  deduces the current  sensing coverage
+requirement  from application  or user  request. It  then applies  the heuristic
+algorithm in order to produce the set  of active nodes which take the mission of
+sensing during the current epoch.  After  that, the produced schedule is sent to
+the sensor nodes in the network.
+
+{\it  In DiLCO  protocol,  the area  coverage  is divided  into several  smaller
+  subregions, and in  each of which, a  node called the leader is  on charge for
+  selecting the active sensors for the current period.}
+
+Yang et al.~\cite{yang2014energy} investigated  full area coverage problem under
+the probabilistic  sensing model in the  sensor networks. They  have studied the
+relationship between the coverage of two adjacent points mathematically and then
+convert  the problem of  full area  coverage into  point coverage  problem. They
+proposed $\varepsilon$-full area coverage optimization (FCO) algorithm to select
+a subset of sensors to provide  probabilistic area coverage dynamically so as to
+extend the network lifetime.
+
+The work proposed by  \cite{qu2013distributed} considers the coverage problem in
+WSNs where  each sensor has variable  sensing radius. The final  objective is to
+maximize the network coverage lifetime in WSNs.
+
+{\it  In DiLCO  protocol,  each leader,  in  each subregion,  solves an  integer
+  program with a double objective  consisting in minimizing the overcoverage and
+  limiting  the  undercoverage.  This  program  is inspired  from  the  work  of
+  \cite{pedraza2006}  where the  objective is  to maximize  the number  of cover
+  sets.}
+ 
+\iffalse
+
+Some algorithms have been developed in ~\cite{yang2014energy,ChinhVu,vashistha2007energy,deschinkel2012column,shi2009,qu2013distributed,ling2009energy,xin2009area,cheng2014achieving,ling2009energy} to solve the area coverage problem so as to preserve coverage and prolong the network lifetime.
+
+
+Yang et al.~\cite{yang2014energy} investigated full area coverage problem
+under the probabilistic sensing model in the sensor networks. They have studied the relationship between the
+coverage of two adjacent points mathematically and then convert the problem of full area coverage into point coverage problem. They proposed $\varepsilon$-full area coverage optimization (FCO) algorithm to select a subset
+of sensors to provide probabilistic area coverage dynamically so as to extend the network lifetime.
+
+
+Vu et al.~\cite{ChinhVu} proposed a localized and distributed greedy algorithm named DESK for generating non-disjoint cover sets which provide the k-area coverage for the whole network. 

 
 

-The work proposed by \cite{qu2013distributed} considered the coverage problem in WSNs where each sensor has variable sensing radius. The final objective is to maximize the network coverage lifetime in WSNs.
+ 
+Qu et al.~\cite{qu2013distributed} developed a distributed algorithm using  adjustable sensing sensors
+for maintaining the full coverage of such sensor networks. The
+algorithm contains two major parts: the first part aims at
+providing $100\%$ coverage and the second part aims at saving
+energy by decreasing the sensing radius.
+
+Shi et al.~\cite{shi2009} modeled the Area Coverage Problem (ACP), which will be changed into a set coverage
+problem. By using this model, they are proposed  an  Energy-Efficient central-Scheduling greedy algorithm, which can reduces energy consumption and increases network lifetime, by selecting a appropriate subset of sensor nodes to support the networks periodically. 
+
+The work in~\cite{cheng2014achieving} presented a unified sensing architecture for duty cycled sensor networks, called uSense, which comprises three ideas: Asymmetric Architecture, Generic Switching and Global Scheduling. The objective is to  provide a flexible and efficient coverage in sensor networks.

 
 

+ In~\cite{ling2009energy}, the lifetime of
+a sensor node is divided into epochs. At each epoch, the
+base station deduces the current sensing coverage requirement
+from application or user request. It then applies the heuristic algorithm in order to produce the set of active nodes which take the mission of sensing during the current epoch.  After that, the produced schedule is sent to the sensor nodes in the network. 
+\fi

 
 \iffalse
 
 \iffalse

+
+The work in ~\cite{vu2009delaunay} considered the area coverage problem for variable sensing radii in WSNs by improving the energy balancing heuristic proposed in ~\cite{wang2007energy} so that  the area of interest can be full covered using Delaunay triangulation structure.
+
+Diongue and Thiare~\cite{diongue2013alarm} proposed an energy aware sleep scheduling algorithm for lifetime maximization in wireless sensor networks (ALARM).  The proposed approach permits to schedule redundant nodes according to the weibull distribution. This work did not analyze the ALARM scheme under the coverage problem. 
+ 
+
+In~\cite{xin2009area}, the authors proposed a circle intersection localized coverage algorithm
+to maintain connectivity  based  on loose connectivity critical condition
+. By using the connected coverage node set, it can maintain network
+connection in the case which loose condition is not meet.
+The authors in ~\cite{vashistha2007energy} addressed the full area coverage problem using information
+coverage. They are proposed a low-complexity heuristic algorithm to obtain full area information covers (FAIC), which they refer to as Grid Based FAIC (GB-FAIC) algorithm. Using these FAICs, they are obtained the optimal schedule for applying the sensing activity of sensor nodes  in order to
+achieve increased sensing lifetime of the network. 
+
+
+
+  
+
+
+In \cite{xu2001geography}, Xu et al. proposed a Geographical Adaptive Fidelity (GAF) algorithm, 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.
+
+The main contributions of our DiLCO Protocol can be summarized as follows:
+(1) The distributed optimization over the subregions in the area of interest, 
+(2) The distributed dynamic leader election at each period by each sensor node in the subregion, 
+(3) The primary point coverage model to represent each sensor node in the network, 
+(4) 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  to take the mission of the coverage in each subregion, and (5) The improved energy consumption model.
+\fi
+\iffalse
+The work presented in~\cite{luo2014parameterized,tian2014distributed} tries to solve the target coverage problem so as to extend the network lifetime since it is easy to verify the coverage status of discreet target.
+%Je ne comprends pas la phrase ci-dessus
+The work proposed in~\cite{kim2013maximum} considers the barrier-coverage problem in WSNs. The final goal is to maximize the network lifetime such that any penetration of the intruder is detected.
+%inutile de parler de ce papier car il concerne barrier coverage
+In \cite{ChinhVu},  the authors propose a localized and distributed greedy algorithm named DESK for generating non-disjoint cover sets which provide the k-coverage for the whole network. 
+Our Work in~\cite{idrees2014coverage} proposes 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 are considered only distributing the coverage protocol over two subregions.  
+
+The work presented in ~\cite{Zhang} focuses on a distributed clustering method, which aims to extend the network lifetime, while the coverage is ensured.
+
+The work proposed by \cite{qu2013distributed} considers the coverage problem in WSNs where each sensor has variable sensing radius. The final objective is to maximize the network coverage lifetime in WSNs.
+
+
+

 Casta{\~n}o et al.~\cite{castano2013column} proposed a multilevel approach based on column generation (CG) to  extend the network lifetime with connectivity and coverage constraints. They are included  two heuristic methods  within the CG framework so as to accelerate the solution process. 
 In \cite{diongue2013alarm}, diongue is proposed an energy Aware sLeep scheduling AlgoRithm for lifetime maximization in WSNs (ALARM) algorithm for coverage lifetime maximization in wireless sensor networks. ALARM is sensor node scheduling approach for lifetime maximization in WSNs in which it schedule redundant nodes according to the weibull distribution  taking into consideration frequent nodes failure.
 Yu et al.~\cite{yu2013cwsc} presented a connected k-coverage working sets construction
 approach (CWSC) to maintain k-coverage and connectivity. This approach try to select the minimum number of connected sensor nodes that can provide k-coverage ($k \geq 1$).
 In~\cite{cheng2014achieving}, the authors are presented a unified sensing architecture for duty cycled sensor networks, called uSense, which comprises three ideas: Asymmetric Architecture, Generic Switching and Global Scheduling. The objective is to  provide a flexible and efficient coverage in sensor networks.
 Casta{\~n}o et al.~\cite{castano2013column} proposed a multilevel approach based on column generation (CG) to  extend the network lifetime with connectivity and coverage constraints. They are included  two heuristic methods  within the CG framework so as to accelerate the solution process. 
 In \cite{diongue2013alarm}, diongue is proposed an energy Aware sLeep scheduling AlgoRithm for lifetime maximization in WSNs (ALARM) algorithm for coverage lifetime maximization in wireless sensor networks. ALARM is sensor node scheduling approach for lifetime maximization in WSNs in which it schedule redundant nodes according to the weibull distribution  taking into consideration frequent nodes failure.
 Yu et al.~\cite{yu2013cwsc} presented a connected k-coverage working sets construction
 approach (CWSC) to maintain k-coverage and connectivity. This approach try to select the minimum number of connected sensor nodes that can provide k-coverage ($k \geq 1$).
 In~\cite{cheng2014achieving}, the authors are presented a unified sensing architecture for duty cycled sensor networks, called uSense, which comprises three ideas: Asymmetric Architecture, Generic Switching and Global Scheduling. The objective is to  provide a flexible and efficient coverage in sensor networks.

-\fi
+

 In~\cite{yang2013energy}, the authors are investigated full area coverage problem
 under the probabilistic sensing model in the sensor networks. %They are designed $\varepsilon-$full area coverage optimization (FCO) algorithm to select a subset of sensors to provide probabilistic area coverage dynamically so as to extend the network lifetime.
 In \cite{xu2001geography}, Xu et al. proposed a Geographical Adaptive Fidelity (GAF) algorithm, 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.
 In~\cite{yang2013energy}, the authors are investigated full area coverage problem
 under the probabilistic sensing model in the sensor networks. %They are designed $\varepsilon-$full area coverage optimization (FCO) algorithm to select a subset of sensors to provide probabilistic area coverage dynamically so as to extend the network lifetime.
 In \cite{xu2001geography}, Xu et al. proposed a Geographical Adaptive Fidelity (GAF) algorithm, 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.


@@ -105,36 +304,57 @@ The main contributions of our DiLCO Protocol can be summarized as follows:
 (4) 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  to take the mission of the coverage in each subregion,
 (5) The improved energy consumption model.
 
 (4) 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  to take the mission of the coverage in each subregion,
 (5) The improved energy consumption model.
 

+\fi

 
 

-
-\section{ The DiLCO Protocol Description}
+\section{\uppercase{Description of the DiLCO protocol}}

 \label{sec:The DiLCO Protocol Description}
 
 \label{sec:The DiLCO Protocol Description}
 

-\noindent In this section, we introduce a Distributed Lifetime Coverage Optimization protocol, which is called DiLCO. 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.  
-\iffalse The main features of our DiLCO 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 rounds, 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 set 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.
+\noindent In this section, we  introduce the DiLCO protocol which 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,  applied  periodically  to  efficiently
+maximize the lifetime in the network.
+\iffalse  The main  features of  our DiLCO  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 rounds, 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 set 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. 

 \fi
 \fi

-\subsection{ Assumptions and Models}
-\noindent We consider  a randomly and  uniformly deployed network  consisting of
-static  wireless sensors. The  wireless sensors  are deployed  in high
-density to ensure initially a high coverage ratio of the interested area. We
-assume that  all nodes are  homogeneous in terms of  communication and
-processing capabilities and heterogeneous in term of energy provision.
-The  location  information is  available  to  the  sensor node  either
-through hardware such as embedded GPS or through location discovery
-algorithms. We consider a boolean  disk coverage model which is the most
-widely used sensor coverage model in the literature. Each sensor has a
-constant sensing range $R_s$. All space points within a disk centered
-at the sensor with the radius of the sensing range is said to be
-covered by this sensor. We also assume that the communication range $R_c \geq 2R_s$.
-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.
-
-\indent Instead of working with the coverage area, we consider for each
-sensor a set of points called  primary points~\cite{idrees2014coverage}. We also assume that the
-sensing disk defined  by a sensor is covered if all the primary points of
-this sensor are covered.
+
+\subsection{Assumptions and models}
+
+\noindent  We consider  a sensor  network composed  of static  nodes distributed
+independently and uniformly at random.  A high density deployment ensures a high
+coverage ratio of the interested area at the starting. The nodes are supposed to
+have homogeneous characteristics from a  communication and a processing point of
+view, whereas they  have heterogeneous energy provisions.  Each  node has access
+to its location thanks,  either to a hardware component (like a  GPS unit), or a
+location discovery algorithm. 
+
+\indent We consider a boolean disk  coverage model which is the most widely used
+sensor coverage  model in the  literature. Thus, since  a sensor has  a constant
+sensing range $R_s$, every space points  within a disk centered at a sensor with
+the radius of  the sensing range is said  to be covered by this  sensor. We also
+assume  that  the communication  range  $R_c \geq  2R_s$.   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.
+
+\indent  For  each  sensor  we  also  define a  set  of  points  called  primary
+points~\cite{idrees2014coverage} to  approximate the area  coverage it provides,
+rather  than  working  with  a   continuous  coverage.   Thus,  a  sensing  disk
+corresponding to  a sensor node is covered  by its neighboring nodes  if all its
+primary points are covered. Obviously,  the approximation of coverage is more or
+less accurate according to the number of primary points.

 
 \iffalse
 By  knowing the  position (point  center: ($p_x,p_y$))  of  a wireless
 
 \iffalse
 By  knowing the  position (point  center: ($p_x,p_y$))  of  a wireless


@@ -180,11 +400,13 @@ $X_{13}=( p_x + R_s * (0), p_y + R_s * (\frac{-\sqrt{2}}{2})) $.
 
 \fi
 
 
 \fi
 

-\subsection{The Main Idea}
-\noindent The   area  of  interest   can  be  divided using the
-divide-and-conquer strategy into smaller areas  called subregions and
-then  our coverage  protocol  will be  implemented  in each  subregion
-simultaneously. Our DiLCO protocol works in rounds fashion as shown in figure~\ref{fig2}.
+\subsection{The main idea}
+\label{main_idea}
+
+\noindent We start  by applying a divide-and-conquer algorithm  to partition the
+area of interest  into smaller areas called subregions and  then our protocol is
+executed   simultaneously  in   each   subregion.
+

 \begin{figure}[ht!]
 \centering
 \includegraphics[width=75mm]{FirstModel.pdf} % 70mm
 \begin{figure}[ht!]
 \centering
 \includegraphics[width=75mm]{FirstModel.pdf} % 70mm


@@ -192,52 +414,64 @@ simultaneously. Our DiLCO protocol works in rounds fashion as shown in figure~\r
 \label{fig2}
 \end{figure} 
 
 \label{fig2}
 \end{figure} 
 

-Each round  is divided  into 4 phases  : Information  (INFO) Exchange,
-Leader  Election, Decision,  and  Sensing.  For  each  round there  is
-exactly one set cover responsible for the sensing task. This protocol is
-more reliable  against an unexpected node failure  because it works
-in rounds. 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 round starts, since a new set cover
-will take charge of the sensing task in the next round.  The energy
-consumption and some other constraints can easily be taken into
-account since the sensors can update and then exchange  their
-information (including their residual energy) at the beginning of each
-round.  However,   the  pre-sensing  phases   (INFO  Exchange,  Leader
-Election,  Decision) are energy  consuming for  some nodes,  even when
-they do not  join the network to monitor the  area. 
-We define two types of packets to be used by our DiLCO protocol.
+As  shown  in Figure~\ref{fig2},  the  proposed  DiLCO  protocol is  a  periodic
+protocol where  each period is  decomposed into 4~phases:  Information Exchange,
+Leader Election ,  Decision, and Sensing. For each period  there will be exactly
+one  cover  set  in charge  of  the  sensing  task.   A periodic  scheduling  is
+interesting  because it  enhances the  robustness  of the  network against  node
+failures. First,  a node  that has not  enough energy  to complete a  period, or
+which fails before  the decision is taken, will be  excluded from the scheduling
+process. Second,  if a node  fails later, whereas  it was supposed to  sense the
+region  of interest,  it will  only  affect the  quality of  coverage until  the
+definition of a new cover set  in the next period.  Constraints, like the energy
+consumption, can be easily taken into consideration since the sensors can update
+and exchange their  information during the first phase.  Let  us notice that the
+phases  before  the sensing  one  (Information  Exchange,  Leader Election,  and
+Decision) are  energy consuming for all the  nodes, even nodes that  will not be
+retained by the leader to keep watch over the corresponding area.
+
+During the execution of the DiLCO protocol, two kinds of packets will be used:

 %\begin{enumerate}[(a)]
 \begin{itemize} 
 %\begin{enumerate}[(a)]
 \begin{itemize} 

-\item INFO packet: sent by each sensor node to all the nodes of it's subregion for information exchange.
-\item ActiveSleep packet: sent by the leader to all the nodes in the same of it's subregion to inform them to be Active or Sleep during the sensing phase.
+\item INFO  packet: sent  by each  sensor node to  all the  nodes inside  a same
+  subregion for information exchange.
+\item ActiveSleep packet:  sent by the leader to all the  nodes in its subregion
+  to inform them to be stay Active or to go Sleep during the sensing phase.

 \end{itemize}
 %\end{enumerate}
 \end{itemize}
 %\end{enumerate}

-
-There are four status for each sensor node in the network
+and each sensor node will have five possible status in the network:

 %\begin{enumerate}[(a)] 
 \begin{itemize} 
 %\begin{enumerate}[(a)] 
 \begin{itemize} 

-\item LISTENING: Sensor is waiting for a decision (to be active or not)
-\item COMPUTATION: Sensor applies the optimization process as leader
-\item ACTIVE: Sensor is active
-\item SLEEP: Sensor is turned off
-\item COMMUNICATION: Sensor is transmitting or receiving packet
+\item LISTENING: sensor is waiting for a decision (to be active or not);
+\item COMPUTATION: sensor applies the optimization process as leader;
+\item ACTIVE: sensor is active;
+\item SLEEP: sensor is turned off;
+\item COMMUNICATION: sensor is transmitting or receiving packet.

 \end{itemize}
 %\end{enumerate}
 \end{itemize}
 %\end{enumerate}

-%Below, we describe each phase in more details.
-In Algorithm 1, Initially, the sensor node check it's remaining energy in order to participate in the current round. Each sensor node determines it's position and it's subregion based Embedded GPS  or Location Discovery Algorithm. After that, all the sensors collect position coordinates, remaining energy $RE_j$, sensor node id, and the number of its one-hop live neighbors during the information exchange. The sensor node enter in listening mode waiting to receive ActiveSleep packet from the leader to take the decision. The selection criteria for the leader in order  of priority  are: larger number  of neighbours,  larger remaining  energy, and  then in  case of
-equality, larger index. 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 select the set of sensor nodes to take the mission of coverage during the sensing phase. 
-
-

 
 

+An outline of the  protocol implementation is given by Algorithm~\ref{alg:DiLCO}
+which describes  the execution of  a period  by a node  (denoted by $s_j$  for a
+sensor  node indexed by  $j$). At  the beginning  a node  checks whether  it has
+enough energy to stay active during the next sensing phase. If yes, it exchanges
+information  with  all the  other  nodes belonging  to  the  same subregion:  it
+collects from each node its position coordinates, remaining energy ($RE_j$), ID,
+and  the number  of  one-hop neighbors  still  alive. Once  the  first phase  is
+completed, the nodes  of a subregion choose a leader to  take the decision based
+on  the  following  criteria   with  decreasing  importance:  larger  number  of
+neighbors, larger remaining energy, and  then in case of equality, larger index.
+After that,  if the sensor node is  leader, it will execute  the integer program
+algorithm (see Section~\ref{cp})  which provides a set of  sensors planned to be
+active in the next sensing phase. As leader, it will send an Active-Sleep packet
+to each sensor  in the same subregion to  indicate it if it has to  be active or
+not.  Alternately, if  the  sensor  is not  the  leader, it  will  wait for  the
+Active-Sleep packet to know its state for the coming sensing phase.

 
 \iffalse
 \subsubsection{Information Exchange Phase}
 
 Each sensor node $j$ sends its position, remaining energy $RE_j$, and
 
 \iffalse
 \subsubsection{Information Exchange Phase}
 
 Each sensor node $j$ sends its position, remaining energy $RE_j$, and

-the number of neighbours  $NBR_j$ to all wireless sensor nodes in
+the number of neighbors  $NBR_j$ to all wireless sensor nodes in

 its subregion by using an INFO packet and then listens to the packets
 sent from  other nodes.  After that, each  node will  have information
 about  all the  sensor  nodes in  the  subregion.  In  our model,  the
 its subregion by using an INFO packet and then listens to the packets
 sent from  other nodes.  After that, each  node will  have information
 about  all the  sensor  nodes in  the  subregion.  In  our model,  the


@@ -252,7 +486,7 @@ independently  for each  round.  All the  sensor  nodes cooperate  to
 select WSNL.  The nodes in the  same subregion will  select the leader
 based on  the received  information from all  other nodes in  the same
 subregion.  The selection criteria  in order  of priority  are: larger
 select WSNL.  The nodes in the  same subregion will  select the leader
 based on  the received  information from all  other nodes in  the same
 subregion.  The selection criteria  in order  of priority  are: larger

-number  of neighbours,  larger remaining  energy, and  then in  case of
+number  of neighbors,  larger remaining  energy, and  then in  case of

 equality, larger index. 
 
 \subsubsection{Decision phase}
 equality, larger index. 
 
 \subsubsection{Decision phase}


@@ -263,23 +497,23 @@ sensor in the subregion based on the algorithm's results.
 
 
 \subsubsection{Sensing phase}
 
 
 \subsubsection{Sensing phase}

-Active  sensors  in the  round  will  execute  their sensing  task  to
-preserve maximal  coverage in the  region of interest. We  will assume
-that the cost  of keeping a node awake (or asleep)  for sensing task is
-the same  for all wireless sensor  nodes in the  network.  Each sensor
-will receive  an Active-Sleep  packet from WSNL  informing it  to stay
-awake or to go to sleep  for a time  equal to  the period of  sensing until
-starting a new round. Algorithm 1, which
-will be executed by each node at the beginning of a round, explains how the
-Active-Sleep packet is obtained.
+
+Active sensors in the round will  execute their sensing task to preserve maximal
+coverage in the  region of interest. We  will assume that the cost  of keeping a
+node awake  (or asleep)  for sensing task  is the  same for all  wireless sensor
+nodes in the network.  Each sensor will receive an Active-Sleep packet from WSNL
+informing it to stay  awake or to go to sleep for a time  equal to the period of
+sensing until starting a new round.  Algorithm 1, which will be executed by each
+node  at the  beginning of  a  round, explains  how the  Active-Sleep packet  is
+obtained.

 
 \fi
 
 
 \iffalse
 \subsection{DiLCO protocol Algorithm}
 
 \fi
 
 
 \iffalse
 \subsection{DiLCO protocol Algorithm}

-we first show the pseudo-code of DiLCO protocol, which is executed by each sensor in the subregion and then describe it in more detail. 
-\fi
+we  first show  the pseudo-code  of DiLCO  protocol, which  is executed  by each
+sensor in the subregion and then describe it in more detail.  \fi

 
 \begin{algorithm}[h!]                
  % \KwIn{all the parameters related to information exchange}
 
 \begin{algorithm}[h!]                
  % \KwIn{all the parameters related to information exchange}


@@ -287,7 +521,7 @@ we first show the pseudo-code of DiLCO protocol, which is executed by each senso
   \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} \; 
   

-  \If{ $RE_j \geq E_{R}$ }{
+  \If{ $RE_j \geq E_{th}$ }{

       \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{$s_j.status$ = COMMUNICATION}\;
       \emph{Send $INFO()$ packet to other nodes in the subregion}\;
       \emph{Wait $INFO()$ packet from other nodes in the subregion}\; 


@@ -329,22 +563,20 @@ The sensor node enter in listening mode waiting to receive ActiveSleep packet fr
 \fi
 
 
 \fi
 
 

-\section{Coverage problem formulation}
+\section{\uppercase{Coverage problem formulation}}

 \label{cp}
 
 \label{cp}
 

-\indent   Our   model   is   based   on  the   model   proposed   by
-\cite{pedraza2006} where the objective is  to find a maximum number of
-disjoint  cover sets.   To accomplish  this goal,  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 $X_{j}$,  which  determine  the
-activation of  sensor $j$ in the  sensing phase of the  round. We also
-consider  primary points  as targets.   The set  of primary  points is
-denoted by $P$ and the set of sensors by $J$.
-
-\noindent  For  a primary  point  $p$,  let  $\alpha_{jp}$ denote  the
-indicator function of whether the point $p$ is covered, that is:
+\indent Our model is based on the model proposed by \cite{pedraza2006} where the
+objective is  to find a  maximum number of  disjoint cover sets.   To accomplish
+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  variable $X_{j}$ which  determine the  activation of
+sensor $j$  in the sensing  phase. We also  consider primary points  as targets.
+The set of primary points is denoted by $P$ and the set of sensors by $J$.
+
+\noindent Let $\alpha_{jp}$ denote the indicator function of whether the primary
+point $p$ is covered, that is:

 \begin{equation}
 \alpha_{jp} = \left \{ 
 \begin{array}{l l}
 \begin{equation}
 \alpha_{jp} = \left \{ 
 \begin{array}{l l}


@@ -354,8 +586,8 @@ indicator function of whether the point $p$ is covered, that is:
 \end{array} \right.
 %\label{eq12} 
 \end{equation}
 \end{array} \right.
 %\label{eq12} 
 \end{equation}

-The number of active sensors that cover the primary point $p$ is equal
-to $\sum_{j \in J} \alpha_{jp} * X_{j}$ where:
+The  number of  active sensors  that cover  the primary  point $p$  can  then be
+computed by $\sum_{j \in J} \alpha_{jp} * X_{j}$ where:

 \begin{equation}
 X_{j} = \left \{ 
 \begin{array}{l l}
 \begin{equation}
 X_{j} = \left \{ 
 \begin{array}{l l}


@@ -374,10 +606,9 @@ We define the Overcoverage variable $\Theta_{p}$ as:
 \end{array} \right.
 \label{eq13} 
 \end{equation}
 \end{array} \right.
 \label{eq13} 
 \end{equation}

-\noindent More precisely, $\Theta_{p}$ represents the number of active
-sensor  nodes  minus  one  that  cover the  primary  point  $p$.\\
-The Undercoverage variable $U_{p}$ of the primary point $p$ is defined
-by:
+\noindent More  precisely, $\Theta_{p}$ represents  the number of  active sensor
+nodes minus  one that  cover the primary  point~$p$. The  Undercoverage variable
+$U_{p}$ of the primary point $p$ is defined by:

 \begin{equation}
 U_{p} = \left \{ 
 \begin{array}{l l}
 \begin{equation}
 U_{p} = \left \{ 
 \begin{array}{l l}


@@ -387,7 +618,7 @@ U_{p} = \left \{
 \label{eq14} 
 \end{equation}
 
 \label{eq14} 
 \end{equation}
 

-\noindent Our coverage optimization problem can then be formulated as follows
+\noindent Our coverage optimization problem can then be formulated as follows:

 \begin{equation} \label{eq:ip2r}
 \left \{
 \begin{array}{ll}
 \begin{equation} \label{eq:ip2r}
 \left \{
 \begin{array}{ll}


@@ -404,38 +635,32 @@ X_{j} \in \{0,1\}, &\forall j \in J
 \right.
 \end{equation}
 
 \right.
 \end{equation}
 

-
-

 \begin{itemize}
 \begin{itemize}

-\item $X_{j}$  : indicates whether or  not the sensor  $j$ is actively
-  sensing in the round (1 if yes and 0 if not);
-\item $\Theta_{p}$  : {\it overcoverage}, the number  of sensors minus
-  one that are covering the primary point $p$;
-\item $U_{p}$  : {\it undercoverage},  indicates whether or  not the primary point
+\item $X_{j}$ :  indicates whether or not the sensor $j$  is actively sensing (1
+  if yes and 0 if not);
+\item $\Theta_{p}$  : {\it overcoverage}, the  number of sensors  minus one that
+  are covering the primary point $p$;
+\item $U_{p}$ : {\it undercoverage},  indicates whether or not the primary point

   $p$ is being covered (1 if not covered and 0 if covered).
 \end{itemize}
 
   $p$ is being covered (1 if not covered and 0 if covered).
 \end{itemize}
 

-The first group  of constraints indicates that some  primary point $p$
-should be covered by at least one  sensor and, if it is not always the
-case,  overcoverage  and  undercoverage  variables  help  balancing  the
-restriction  equations by taking  positive values.  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  to
-guarantee that  the maximum number  of points are covered  during each
-round.
-
-
-
-
-\section{\uppercase{Simulation Results and Analysis}}  
+The first group  of constraints indicates that some primary  point $p$ should be
+covered by at least  one sensor and, if it is not  always the case, overcoverage
+and undercoverage  variables help balancing the restriction  equations by taking
+positive values. Two objectives can be noticed in our model. First, we limit the
+overcoverage of primary  points to activate as few  sensors as possible. Second,
+to  avoid   a  lack  of  area   monitoring  in  a  subregion   we  minimize  the
+undercoverage. Both  weights $w_\theta$  and $w_U$ must  be carefully  chosen in
+order to  guarantee that the  maximum number of  points are covered  during each
+period.
+
+\section{\uppercase{Protocol evaluation}}  

 \label{sec:Simulation Results and Analysis}
 \label{sec:Simulation Results and Analysis}

-\noindent \subsection{Simulation Framework}
-In this subsection, we conducted a series of simulations to evaluate the
-efficiency and the relevance of our DiLCO protocol, using the discrete event
-simulator OMNeT++  \cite{varga}. The simulation parameters are summarized in
-Table~\ref{table3}
+\noindent \subsection{Simulation framework}
+
+To assess the performance of our DiLCO protocol, we have used the discrete
+event simulator OMNeT++ \cite{varga} to run different series of simulations.
+Table~\ref{table3} gives the chosen parameters setting.

 
 \begin{table}[ht]
 \caption{Relevant parameters for network initializing.}
 
 \begin{table}[ht]
 \caption{Relevant parameters for network initializing.}


@@ -461,43 +686,49 @@ Nodes Number &  50, 100, 150, 200 and 250~nodes   \\
 Initial Energy  & 500-700~joules  \\  
 %\hline
 Sensing Period & 60 Minutes \\
 Initial Energy  & 500-700~joules  \\  
 %\hline
 Sensing Period & 60 Minutes \\

-$E_{thr}$ & 36 Joules\\
+$E_{th}$ & 36 Joules\\

 $R_s$ & 5~m   \\     
 %\hline
 $w_{\Theta}$ & 1   \\
 % [1ex] adds vertical space
 %\hline
 $R_s$ & 5~m   \\     
 %\hline
 $w_{\Theta}$ & 1   \\
 % [1ex] adds vertical space
 %\hline

-$w_{U}$ & $|P^2|$
+$w_{U}$ & $|P|^2$

 %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}
 

-25 simulation runs are performed with different network topologies. The results presented hereafter are the average of these 25 runs. 
-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 precisely, the deployment is controlled at a coarse scale in order to ensure that the deployed nodes can cover the sensing field with a high coverage ratio.\\
-
-Our DiLCO protocol is declined into five versions: DiLCO-2, DiLCO-4, DiLCO-8, DiLCO-16, and DiLCO-32, corresponding to $2$, $4$, $8$, $16$ or $32$ subregions (leaders).  
-
-We use an energy consumption model proposed by~\cite{ChinhVu} and based on ~\cite{raghunathan2002energy} with slight modifications.
-The energy consumption for sending/receiving the packets is added whereas the part related to the sensing range is removed because we consider a fixed sensing range.
-% We are took into account the energy consumption needed for the high computation during executing the algorithm on the sensor node. 
-%The new energy consumption model will take into account the energy consumption for communication (packet transmission/reception), the radio of the sensor node, data sensing, computational energy of Micro-Controller Unit (MCU) and high computation energy of MCU. 
-%revoir la phrase
-
-For our energy consumption model, we refer to the sensor node (Medusa II) which uses 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 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 is equal to $0.2575 mW$.
+Simulations with five  different node densities going from  50 to 250~nodes were
+performed  considering  each  time  25~randomly generated  networks,  to  obtain
+experimental results  which are relevant. The  nodes are deployed on  a field of
+interest of $(50 \times 25)~m^2 $ in such a way that they cover the field with a
+high coverage ratio.
+
+We chose as energy consumption model the one proposed proposed by~\cite{ChinhVu}
+and based on ~\cite{raghunathan2002energy} with slight modifications. The energy
+consumed by  the communications  is added  and the part  relative to  a variable
+sensing range is removed. We also assume that the nodes have the characteristics
+of the  Medusa II sensor  node platform \cite{raghunathan2002energy}.   A sensor
+node typically  consists of  four units: a  MicroController Unit, an  Atmels AVR
+ATmega103L in  case of Medusa II,  to perform the  computations; a communication
+(radio) unit able to send and  receive messages; a sensing unit to collect data;
+a power supply  which provides the energy consumed by  node. Except the battery,
+all the other unit  can be be switched off to save  energy according to the node
+status.   Table~\ref{table4} summarizes  the energy  consumed (in  milliWatt per
+second) by a node for each of its possible status.

 
 \begin{table}[ht]
 
 \begin{table}[ht]

-\caption{The Energy Consumption Model}
+\caption{Energy consumption model}

 % title of Table
 \centering
 % used for centering table
 % title of Table
 \centering
 % used for centering table

+{\scriptsize

 \begin{tabular}{|c|c|c|c|c|}
 % centered columns (4 columns)
       \hline
 %inserts double horizontal lines
 \begin{tabular}{|c|c|c|c|c|}
 % centered columns (4 columns)
       \hline
 %inserts double horizontal lines

-Sensor mode & MCU   & Radio & Sensing & Power (mWs) \\ [0.5ex]
+Sensor status & MCU   & Radio & Sensing & Power (mW) \\ [0.5ex]

 \hline
 % inserts single horizontal line
 Listening & ON & ON & ON & 20.05 \\
 \hline
 % inserts single horizontal line
 Listening & ON & ON & ON & 20.05 \\


@@ -512,32 +743,63 @@ Computation & ON & ON & ON & 26.83 \\
 %\multicolumn{4}{|c|}{Energy needed to send/receive a 1-bit} & 0.2575\\
  \hline
 \end{tabular}
 %\multicolumn{4}{|c|}{Energy needed to send/receive a 1-bit} & 0.2575\\
  \hline
 \end{tabular}

+}

 
 \label{table4}
 % is used to refer this table in the text
 \end{table}
 
 
 \label{table4}
 % 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 start up the sensor node, the transition from mode 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. DiLCO protocol uses two types of packets for communication. The size of the INFO-Packet and Status-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.
-
-The initial energy of each node is randomly set in the interval $[500-700]$.  Each  sensor  node will  not participate in the next round if its remaining energy is less than $E_{th}=36 Joules$, the minimum energy needed for the node to stay alive during one round. This value has been computed by multiplying the energy consumed in active state (9.72 mWs) by the time in second for one round (3600 seconds). According to the interval of initial energy, a sensor may be alive during at most 20 rounds.\\ 
-
-
-In the simulations, we introduce the following performance metrics to evaluate the efficiency of our approach: 
+Less  influent  energy consumption  sources  like  when  turning on  the  radio,
+starting the sensor node, changing the status of a node, etc., will be neglected
+for the  sake of simplicity. Each node  saves energy by switching  off its radio
+once it has  received its decision status from the  corresponding leader (it can
+be itself).  As explained previously in subsection~\ref{main_idea}, two kinds of
+packets  for communication  are  considered  in our  protocol:  INFO packet  and
+ActiveSleep  packet. To  compute the  energy  needed by  a node  to transmit  or
+receive such  packets, we  use the equation  giving the  energy spent to  send a
+1-bit-content   message  defined   in~\cite{raghunathan2002energy}   (we  assume
+symmetric  communication costs), and  we set  their respective  size to  112 and
+24~bits. The energy required to send  or receive a 1-bit-content message is thus
+is equal to 0.2575 mW.
+
+Each node has an initial energy level, in Joules, which is randomly drawn in the
+interval  $[500-700]$.  If  it's  energy  provision reaches  a  value below  the
+threshold  $E_{th}=36$~Joules, the  minimum energy  needed  for a  node to  stay
+active during one period, it will no more participate in the coverage task. This
+value  corresponds  to the  energy  needed by  the  sensing  phase, obtained  by
+multiplying the energy consumed in active  state (9.72 mW) by the time in seconds
+for one period (3600 seconds), and  adding the energy for the pre-sensing phases.
+According to  the interval of initial energy,  a sensor may be  active during at
+most 20 rounds.
+
+In the simulations,  we introduce the follow80ing performance  metrics to evaluate
+the efficiency of our approach:

 
 %\begin{enumerate}[i)]
 \begin{itemize}
 
 %\begin{enumerate}[i)]
 \begin{itemize}

+\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 $Lifetime_{50}$) the amount of time during which
+  the  network can  satisfy an  area coverage  greater than  $95\%$ (respectively
+  $50\%$). We assume that the sensor  network can fulfill its task until all its
+  nodes have  been drained of their  energy or it  becomes disconnected. Network
+  connectivity  is crucial because  an active  sensor node  without connectivity
+  towards a base  station cannot transmit any information  regarding an observed
+  event in the area that it monitors.

   
   

-\item {{\bf Coverage Ratio (CR)}:} the coverage ratio measures how much the area of a sensor field is  covered. In our case, we treated the sensing fields as a grid, and used each grid point as a sample point
-for calculating the coverage. The coverage ratio can be calculated by:
+    
+\item {{\bf Coverage Ratio (CR)}:} it measures how well the WSN is able to 
+  observe the area of interest. In our case, we discretized the sensor field
+  as a regular grid, which yields the following equation to compute the
+  coverage ratio: 

 \begin{equation*}
 \scriptsize
 \begin{equation*}
 \scriptsize

-\mbox{CR}(\%) = \frac{\mbox{$n^t$}}{\mbox{$N$}} \times 100.
+\mbox{CR}(\%) = \frac{\mbox{$n$}}{\mbox{$N$}} \times 100.

 \end{equation*}
 \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 of grid points in the sensing field of the network. In our simulation $N = 51 \times 26 = 1326$ grid points.
+where  $n$ is  the number  of covered  grid points  by active  sensors  of every
+subregions during  the current  sensing phase  and $N$ is  total number  of grid
+points in  the sensing field. In  our simulations, we have  a layout of  $N = 51
+\times 26 = 1326$ grid points.

 %The accuracy of this method depends on the distance between grids. In our
 %simulations, the sensing field has been divided into 50 by 25 grid points, which means
 %there are $51 \times 26~ = ~ 1326$ points in total.
 %The accuracy of this method depends on the distance between grids. In our
 %simulations, the sensing field has been divided into 50 by 25 grid points, which means
 %there are $51 \times 26~ = ~ 1326$ points in total.


@@ -556,48 +818,38 @@ Where: $A_r^t$ is the number of active sensors in the subregion $r$ during round
 
 \fi
 
 
 \fi
 

-\item {{\bf Network Lifetime}:} we define the network lifetime as the time until the coverage ratio drops below a predefined threshold. We denoted by $Lifetime95$ (respectively  $Lifetime50$) as the amount of  time during which  the network  can  satisfy an area  coverage greater than $95\%$ (repectively $50\%$). We assume that the network
-is alive  until all  nodes have  been drained of  their energy  or the
-sensor network becomes disconnected . Network connectivity is important because an
-active sensor node without  connectivity towards a base station cannot
-transmit information on an event in the area that it monitors.
- 
+\item {{\bf  Energy Consumption}:}  energy consumption (EC)  can be seen  as the
+  total   energy   consumed   by   the   sensors   during   $Lifetime_{95}$   or
+  $Lifetime_{50}$, divided  by the number of periods.  Formally, the computation
+  of EC can be expressed as follows:
+  \begin{equation*}
+    \scriptsize
+    \mbox{EC} = \frac{\sum\limits_{m=1}^{M} \left( E^{\mbox{com}}_m+E^{\mbox{list}}_m+E^{\mbox{comp}}_m  
+      + E^{a}_m+E^{s}_m \right)}{M},
+  \end{equation*}
+
+where $M$  corresponds to the number  of periods.  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, $E^a_{m}$ and $E^s_{m}$ indicate  the energy consumed
+by the whole network in the sensing phase (active and sleeping nodes).

 
 

-\item {{\bf Energy Consumption}:}
-
- Energy Consumption (EC) can be seen as the total energy consumed by the sensors during the $Lifetime95$ or $Lifetime50$ divided by the number of rounds. The EC can be computed as follow: \\
- \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*}
-
-%\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 $t$.

 
 \iffalse 
 
 \iffalse 

-\item {{\bf Execution Time}:} a  sensor  node has  limited  energy  resources  and computing  power,
-therefore it is important that the proposed algorithm has the shortest
-possible execution  time. The energy of  a sensor node  must be mainly
-used   for  the  sensing   phase,  not   for  the   pre-sensing  ones.   
+\item {{\bf  Execution Time}:}  a sensor node  has limited energy  resources and
+  computing power, therefore it is important that the proposed algorithm has the
+  shortest possible execution  time. The energy of a sensor  node must be mainly
+  used for the sensing phase, not for the pre-sensing ones.

  
  

-\item {{\bf Stopped simulation runs}:} A simulation
-ends  when the  sensor network  becomes
-disconnected (some nodes are dead and are not able to send information to the base station). We report the number of simulations that are stopped due to network disconnections and for which round it occurs.
+\item {{\bf Stopped simulation runs}:} A simulation ends when the sensor network
+  becomes disconnected (some nodes are dead and are not able to send information
+  to the base station). We report the number of simulations that are stopped due
+  to network disconnections and for which round it occurs.

 
 \fi
 
 
 \fi
 


@@ -605,89 +857,180 @@ disconnected (some nodes are dead and are not able to send information to the ba
 %\end{enumerate}
 
 
 %\end{enumerate}
 
 

-%\subsection{Performance Analysis for differnet subregions}
-\subsection{Performance Analysis}
+%\subsection{Performance Analysis for different subregions}
+\subsection{Performance analysis}

 \label{sub1}
 \label{sub1}

-In this subsection, we are studied the performance of our DiLCO protocol for a different number of subregions (Leaders).
-The DiLCO-1 protocol is a centralized approach on all the area of the interest, while  DiLCO-2, DiLCO-4, DiLCO-8, DiLCO-16 and DiLCO-32 are distributed on two, four, eight, sixteen, and thirty-two subregions respectively. We did not take the DiLCO-1 protocol in our simulation results because it need high execution time to give the decision leading to consume all it's energy before producing the solution for optimization problem. our DiLCO protocol compared with other two approches. The first approach, called DESK that proposed by ~\cite{ChinhVu}, which is a full distributed coverage algorithm. The second approach, called GAF ~\cite{xu2001geography}, consists in dividing the region into fixed squares.   During the  decision phase,  in  each square,  one sensor  is chosen to remain on during the sensing phase time. 

 
 

+In this subsection, we first focus  on the performance of our DiLCO protocol for
+different numbers  of subregions.  We consider partitions  of the WSN  area into
+$2$, $4$, $8$, $16$, and $32$ subregions. Thus the DiLCO protocol is declined in
+five versions:  DiLCO-2, DiLCO-4,  DiLCO-8, DiLCO-16, and  DiLCO-32. Simulations
+without  partitioning  the  area  of  interest,  case  which  corresponds  to  a
+centralized  approach, are  not presented  because they  require  high execution
+times to solve the integer program and therefore consume too much energy.
+
+We compare our protocol to two  other approaches. The first one, called DESK and
+proposed  by ~\cite{ChinhVu}  is a  fully distributed  coverage  algorithm.  The
+second one, called GAF  ~\cite{xu2001geography}, consists in dividing the region
+into fixed  squares.  During the decision  phase, in each square,  one sensor is
+chosen to remain active during the sensing phase.
+
+\subsubsection{Coverage ratio} 
+
+Figure~\ref{fig3} shows  the average coverage  ratio for 150 deployed  nodes. It
+can  be seen  that both  DESK and  GAF provide  a little  better  coverage ratio
+compared to DiLCO  in the first thirty periods. This can  be easily explained by
+the number of  active nodes: the optimization process  of our protocol activates
+less nodes  than DESK  or GAF, resulting  in a  slight decrease of  the coverage
+ratio. In case of DiLCO-2  (respectively DiLCO-4), the coverage ratio exhibits a
+fast decrease  with the number  of periods and  reaches zero value  in period~18
+(respectively 46), whereas  the other versions of DiLCO, DESK,  and GAF ensure a
+coverage ratio above  50\% for subsequent periods.  We  believe that the results
+obtained with these two methods can be explained by a high consumption of energy
+and we will check this assumption in the next subsection.
+
+Concerning  DiLCO-8, DiLCO-16,  and  DiLCO-32,  these methods  seem  to be  more
+efficient than DESK  and GAF, since they can provide the  same level of coverage
+(except in the first periods where  DESK and GAF slightly outperform them) for a
+greater number  of periods. In fact, when  our protocol is applied  with a large
+number of subregions (from 8 to 32~regions), it activates a restricted number of
+nodes, and thus allow to extend the network lifetime.

 
 

-\subsubsection{Coverage Ratio} 
-In this experiment, Figure~\ref{fig3} shows the average coverage ratio for 150 deployed nodes.  

 \parskip 0pt    
 \parskip 0pt    

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

 \centering
  \includegraphics[scale=0.45] {R/CR.pdf} 
 \centering
  \includegraphics[scale=0.45] {R/CR.pdf} 

-\caption{The Coverage Ratio}
+\caption{Coverage ratio}

 \label{fig3}
 \end{figure} 
 
 \label{fig3}
 \end{figure} 
 

-It is shown that DESK and GAF provides a
-a little better coverage ratio with 99.99\% and 99.91\% against 98.9\%, 99.1\%, 99.2\%, 99.1\% and 99.4\% produced by DiLCO-2, DiLCO-4, DiLCO-8, DiLCO-16 and DiLCO-32 for the lowest number of rounds. This is due to the fact that our DiLCO protocol versions  put in sleep mode redundant sensors using optimization (which lightly decreases the coverage ratio) while there are more nodes are active in the case of DESK and GAF.
-
-As shown in the figure ~\ref{fig3}, as the number of subregions increases,  the coverage preservation for area of interest increases for a larger number of rounds. Coverage ratio decreases when the number of rounds increases due to dead nodes. Although  some nodes are dead,
-thanks to  DiLCO-8,  DiLCO-16 and  DiLCO-32 protocols,  other nodes are  preserved to  ensure the coverage. Moreover, when  we have a dense sensor network, it leads to maintain the  coverage for a larger number of rounds. DiLCO-8,  DiLCO-16 and  DiLCO-32 protocols are
-slightly more efficient than other protocols, because they subdivides
-the area of interest into 8, 16 and 32~subregions if one of the subregions becomes disconnected, the coverage may be still ensured in the remaining subregions.
+%As shown in the figure ~\ref{fig3}, as the number of subregions increases,  the coverage preservation for area of interest increases for a larger number of periods. Coverage ratio decreases when the number of periods increases due to dead nodes. Although  some nodes are dead,
+%thanks to  DiLCO-8,  DiLCO-16 and  DiLCO-32 protocols,  other nodes are  preserved to  ensure the coverage. Moreover, when  we have a dense sensor network, it leads to maintain the  coverage for a larger number of rounds. DiLCO-8,  DiLCO-16 and  DiLCO-32 protocols are
+%slightly more efficient than other protocols, because they subdivides
+%the area of interest into 8, 16 and 32~subregions if one of the subregions becomes disconnected, the coverage may be still ensured in the remaining subregions.%

 
 

+\subsubsection{Energy consumption}

 
 

+Based on  the results shown in  Figure~\ref{fig3}, we focus on  the DiLCO-16 and
+DiLCO-32 versions of our protocol,  and we compare their energy consumption with
+the DESK and GAF approaches. For each sensor node we measure the energy consumed
+according to its successive status,  for different network densities.  We denote
+by $\mbox{\it  Protocol}/50$ (respectively $\mbox{\it  Protocol}/95$) the amount
+of energy consumed  while the area coverage is  greater than $50\%$ (repectively
+$95\%$),  where  {\it  Protocol}  is  one  of the  four  protocols  we  compare.
+Figure~\ref{fig95} presents  the energy consumptions observed  for network sizes
+going from 50  to 250~nodes. Let us  notice that the same network  sizes will be
+used for the different performance metrics.

 
 

-\subsubsection{The Energy Consumption}
-Based on the result in figure~\ref{fig3}, we are chose DiLCO-16 and  DiLCO-32 protocols to be compared with other approaches. We measure the energy consumed by the sensors during the communication, listening, computation, active, and sleep modes for different network densities and compare it for different approaches.  Figure~\ref{fig95} illustrates the energy consumption for different network sizes.
-% for $Lifetime95$ and $Lifetime50$. 
-We denoted by $DiLCO-16/50$ (respectively  $DiLCO-16/95$) as the amount of energy consumed during which the network can satisfy an area coverage greater than $50\%$ (repectively $95\%$) and we refer the same definition for the other approches.

 \begin{figure}[h!]
 \centering
 \includegraphics[scale=0.45]{R/EC.pdf} 
 \begin{figure}[h!]
 \centering
 \includegraphics[scale=0.45]{R/EC.pdf} 

-\caption{The Energy Consumption}
+\caption{Energy consumption}

 \label{fig95}
 \end{figure} 
 
 \label{fig95}
 \end{figure} 
 

-The results show that our DiLCO-16/50, DiLCO-32/50, DiLCO-16/95 and DiLCO-32/95 protocols are 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 modes of sensor nodes. In fact,  a distributed  method on the subregions greatly reduces the number of communications and the time of listening so thanks to the partitioning of the initial network into several independent subnetworks. 
+The  results  depict the  good  performance of  the  different  versions of  our
+protocol.   Indeed,  the protocols  DiLCO-16/50,  DiLCO-32/50, DiLCO-16/95,  and
+DiLCO-32/95  consume less  energy than  their DESK  and GAF  counterparts  for a
+similar level of area coverage.   This observation reflects the larger number of
+nodes set active by DESK and GAF.
+
+
+%In fact,  a distributed  method on the subregions greatly reduces the number of communications and the time of listening so thanks to the partitioning of the initial network into several independent subnetworks. 

 %As shown in Figures~\ref{fig95} and ~\ref{fig50} , DiLCO-2 consumes more energy than the other versions of DiLCO, especially for large sizes of network. This is easy to understand since the bigger the number of sensors involved in the integer program, the larger the time computation to solve the optimization problem as well as the higher energy consumed during the communication.  
 
 %As shown in Figures~\ref{fig95} and ~\ref{fig50} , DiLCO-2 consumes more energy than the other versions of DiLCO, especially for large sizes of network. This is easy to understand since the bigger the number of sensors involved in the integer program, the larger the time computation to solve the optimization problem as well as the higher energy consumed during the communication.  
 

+\subsubsection{Execution time}

 
 

-\subsubsection{Execution Time}
-In this experiment, we study the the impact of the size of the network on the excution time of the our distributed optimization approach. Figure~\ref{fig8} gives the average execution times in seconds for the decision phase (solving of the optimization problem) during one round. They are given for the different approaches and various numbers of sensors. 
-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 AVR ATmega103L microcontroller (6 MHz) and a MIPS rate equal to 6 to run the optimization resolution, this time is multiplied by 2944.2 $\left( \frac{35330}{2} \times 6\right)$ and reported on Figure~\ref{fig8} for different network sizes.
+Another interesting point to investigate  is the evolution of the execution time
+with the size of the WSN and  the number of subregions. Therefore, we report for
+every version of  our protocol the average execution times  in seconds needed to
+solve the optimization problem for  different WSN sizes. The execution times are
+obtained on a laptop DELL  which has an Intel Core~i3~2370~M~(2.4~GHz) dual core
+processor and a MIPS rating equal to 35330. The corresponding execution times on
+a MEDUSA II sensor node are then  extrapolated according to the MIPS rate of the
+Atmels  AVR  ATmega103L  microcontroller  (6~MHz),  which  is  equal  to  6,  by
+multiplying    the    laptop     times    by    $\left(\frac{35330}{2}    \times
+\frac{1}{6}\right)$.  The  expected times  on  a  sensor  node are  reported  on
+Figure~\ref{fig8}.

 
 \begin{figure}[h!]
 \centering
 \includegraphics[scale=0.45]{R/T.pdf}  
 
 \begin{figure}[h!]
 \centering
 \includegraphics[scale=0.45]{R/T.pdf}  

-\caption{Execution Time (in seconds)}
+\caption{Execution time in seconds}

 \label{fig8}
 \end{figure} 
 
 \label{fig8}
 \end{figure} 
 

+Figure~\ref{fig8} shows that DiLCO-32 has very low execution times in comparison
+with  other DiLCO  versions, because  the activity  scheduling is  tackled  by a
+larger  number of  leaders and  each  leader solves  an integer  problem with  a
+limited number  of variables and  constraints.  Conversely, DiLCO-2  requires to
+solve an optimization problem with half of the network nodes and thus presents a
+high execution time.  Nevertheless if  we refer to Figure~\ref{fig3}, we observe
+that DiLCO-32  is slightly less efficient  than DilCO-16 to maintain  as long as
+possible high  coverage. In fact excessive  subdivision of the  area of interest
+prevents   to  ensure   good  coverage   especially  on   the  borders   of  the
+subregions. Thus,  the optimal number of  subregions can be seen  as a trade-off
+between execution time and coverage performance.

 
 

-We can see from figure~\ref{fig8}, that the DiLCO-32 has very low execution times in comparison with other DiLCO versions, because it distributed on larger number of small subregions.  Conversely, the DiLCO-2 which requires to solve an optimization problem considering half  the nodes  in each subregion presents  high execution times.
-
-The DiLCO-32 has more suitable times in the same time it turn on redundent nodes more.  We think that in distributed fashion the solving of the  optimization problem 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.
+%The DiLCO-32 has more suitable times in the same time it turn on redundent nodes more.  We think that in distributed fashion the solving of the  optimization problem 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.

 
 

+\subsubsection{Network lifetime}

 
 

-\subsubsection{The Network Lifetime}
-In figure~\ref{figLT95}, network lifetime is illustrated for different network sizes. We denoted by $DiLCO-16/50$ (respectively  $DiLCO-16/95$) as the amount of time during which the network can satisfy an area coverage greater than $50\%$ ($Lifetime50$)(repectively $95\%$ ($Lifetime95$)) and we refer the same definition for the other approches.
+In the next figure, the network lifetime is illustrated. Obviously, the lifetime
+increases with  the network  size, whatever the  considered protocol,  since the
+correlated node  density also  increases.  A high  network density means  a high
+node redundancy  which allows  to turn-off  many nodes and  thus to  prolong the
+network lifetime.

 
 \begin{figure}[h!]
 \centering
 \includegraphics[scale=0.45]{R/LT.pdf}  
 
 \begin{figure}[h!]
 \centering
 \includegraphics[scale=0.45]{R/LT.pdf}  

-\caption{The Network Lifetime}
+\caption{Network lifetime}

 \label{figLT95}
 \end{figure} 
 
 \label{figLT95}
 \end{figure} 
 

+As  highlighted by  Figure~\ref{figLT95},  when the  coverage  level is  relaxed
+($50\%$) the network lifetime also  improves. This observation reflects the fact
+that  the higher  the coverage  performance, the  more nodes  must be  active to
+ensure the  wider monitoring.  For a  same level of  coverage, DiLCO outperforms
+DESK and GAF for the lifetime of  the network. More specifically, if we focus on
+the larger level  of coverage ($95\%$) in case of  our protocol, the subdivision
+in $16$~subregions seems to be the most appropriate.
+
+% with  our DiLCO-16/50, DiLCO-32/50, DiLCO-16/95 and DiLCO-32/95 protocols
+% that leads to the larger lifetime improvement in comparison with other approaches. By choosing the best 
+% suited nodes, for each round, to cover the area of interest and by
+% letting the other ones sleep in order to be used later in next rounds. Comparison shows that our DiLCO-16/50, DiLCO-32/50, DiLCO-16/95 and DiLCO-32/95 protocols, which are used distributed optimization over the subregions, are 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 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.
+
+\section{\uppercase{Conclusion and future work}}
+\label{sec:Conclusion and Future Works} 
+
+A crucial problem in WSN is  to schedule the sensing activities of the different
+nodes  in order to  ensure both  coverage of  the area  of interest  and longest
+network lifetime. The inherent limitations of sensor nodes, in energy provision,
+communication and computing capacities,  require protocols that optimize the use
+of  the  available resources  to  fulfill the  sensing  task.   To address  this
+problem, this paper proposes a  two-step approach. Firstly, the field of sensing
+is  divided into  smaller  subregions using  the  concept of  divide-and-conquer
+method. Secondly,  a distributed  protocol called Distributed  Lifetime Coverage
+Optimization is applied in each  subregion to optimize the coverage and lifetime
+performances.   In a subregion,  our protocol  consists to  elect a  leader node
+which will then perform a sensor activity scheduling. The challenges include how
+to  select   the  most  efficient  leader   in  each  subregion   and  the  best
+representative set of active nodes to ensure a high level of coverage. To assess
+the performance of our approach, we  compared it with two other approaches using
+many performance metrics  like coverage ratio or network  lifetime. We have also
+study the  impact of the  number of subregions  chosen to subdivide the  area of
+interest,  considering  different  network  sizes.  The  experiments  show  that
+increasing the  number of subregions allows  to improves the  lifetime. The more
+there  are   subregions,  the  more   the  network  is  robust   against  random
+disconnection resulting from dead nodes.  However, for a given sensing field and
+network size  there is an optimal  number of subregions.  Therefore,  in case of
+our simulation  context a  subdivision in $16$~subregions  seems to be  the most
+relevant. The optimal number of subregions will be investigated in the future.

 
 

-As highlighted by figures~\ref{figLT95}, the network lifetime obviously
-increases when the size of the network increases, with  our DiLCO-16/50, DiLCO-32/50, DiLCO-16/95 and DiLCO-32/95 protocols
-that leads to the larger lifetime improvement in comparison with other approaches. By choosing the best 
-suited nodes, for each round, to cover the area of interest and by
-letting the other ones sleep in order to be used later in next rounds. Comparison shows that our DiLCO-16/50, DiLCO-32/50, DiLCO-16/95 and DiLCO-32/95 protocols, which are used distributed optimization over the subregions, are 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 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.
-
-
-
-
-\section{\uppercase{Conclusion and Future Works}}
-\label{sec:Conclusion and Future Works}
-
+\iffalse

 \noindent 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
 \noindent 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


@@ -716,20 +1059,18 @@ optimization  methods. \iffalse The round  will still consist of 4 phases, but t
   which, aggregated together, define a kind of meta-sensing phase.
 The computation of all cover sets in one time is far more
 difficult, but will reduce the communication overhead. \fi
   which, aggregated together, define a kind of meta-sensing phase.
 The computation of all cover sets in one time is far more
 difficult, but will reduce the communication overhead. \fi

+\fi

 
 \section*{\uppercase{Acknowledgements}}
 
 \section*{\uppercase{Acknowledgements}}

-\noindent As a Ph.D. student, Ali Kadhum IDREES would like to gratefully acknowledge the University of Babylon - IRAQ for the financial support and Campus France for the received support.
-
-
-

 
 

+\noindent  As  a Ph.D.  student,  Ali Kadhum  IDREES  would  like to  gratefully
+acknowledge  the University  of Babylon  - IRAQ  for the  financial  support and
+Campus France for the received support.

 
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