[Sensornets15.git] / Example.tex

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\begin{document}

%\title{Authors' Instructions  \subtitle{Preparation of Camera-Ready Contributions to SCITEPRESS Proceedings} }

\title{Distributed Lifetime Coverage Optimization Protocol \\in Wireless Sensor Networks}

\author{\authorname{Ali Kadhum Idrees, Karine Deschinkel, Michel Salomon, and Rapha\"el Couturier}
\affiliation{FEMTO-ST Institute, UMR 6174 CNRS, University of Franche-Comte, Belfort, France}
%\affiliation{\sup{2}Department of Computing, Main University, MySecondTown, MyCountry}
\email{ali.idness@edu.univ-fcomte.fr, $\lbrace$karine.deschinkel, michel.salomon, raphael.couturier$\rbrace$@univ-fcomte.fr}
%\email{\{f\_author, s\_author\}@ips.xyz.edu, t\_author@dc.mu.edu}
}

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

\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 result 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}
\noindent 
Energy efficiency is  a crucial issue in wireless  sensor networks since sensory
consumption,  in order  to maximize  the network  lifetime, represent  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.  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). 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
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 Distributed Lifetime
Coverage Optimization (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 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}
\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. 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. 

 
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. 


\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. 


\fi
  


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 round 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.

\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.
\fi

\iffalse
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.

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.

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 round 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,
(5) The improved energy consumption model.

\fi

\section{\uppercase{Description of the DiLCO protocol}}
\label{sec:The DiLCO Protocol Description}

\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

\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
sensor node  and its $R_s$,  we calculate the primary  points directly
based on the proposed model. We  use these primary points (that can be
increased or decreased if necessary)  as references to ensure that the
monitored  region  of interest  is  covered  by  the selected  set  of
sensors, instead of using all the points in the area.

\indent  We can  calculate  the positions of the selected primary
points in the circle disk of the sensing range of a wireless sensor
node (see figure~\ref{fig1}) as follows:\\
$(p_x,p_y)$ = point center of wireless sensor node\\  
$X_1=(p_x,p_y)$ \\ 
$X_2=( p_x + R_s * (1), p_y + R_s * (0) )$\\           
$X_3=( p_x + R_s * (-1), p_y + R_s * (0)) $\\
$X_4=( p_x + R_s * (0), p_y + R_s * (1) )$\\
$X_5=( p_x + R_s * (0), p_y + R_s * (-1 )) $\\
$X_6= ( p_x + R_s * (\frac{-\sqrt{2}}{2}), p_y + R_s * (0)) $\\
$X_7=( p_x + R_s *  (\frac{\sqrt{2}}{2}), p_y + R_s * (0))$\\
$X_8=( p_x + R_s * (\frac{-\sqrt{2}}{2}), p_y + R_s * (\frac{-\sqrt{2}}{2})) $\\
$X_9=( p_x + R_s * (\frac{\sqrt{2}}{2}), p_y + R_s * (\frac{-\sqrt{2}}{2})) $\\
$X_{10}=( p_x + R_s * (\frac{-\sqrt{2}}{2}), p_y + R_s * (\frac{\sqrt{2}}{2})) $\\
$X_{11}=( p_x + R_s * (\frac{\sqrt{2}}{2}), p_y + R_s * (\frac{\sqrt{2}}{2})) $\\
$X_{12}=( p_x + R_s * (0), p_y + R_s * (\frac{\sqrt{2}}{2})) $\\
$X_{13}=( p_x + R_s * (0), p_y + R_s * (\frac{-\sqrt{2}}{2})) $.

 \begin{figure}[h!]
\centering
 \begin{multicols}{3}
\centering
%\includegraphics[scale=0.20]{fig21.pdf}\\~ ~ ~ ~ ~(a)
%\includegraphics[scale=0.20]{fig22.pdf}\\~ ~ ~ ~ ~(b)
\includegraphics[scale=0.25]{principles13.pdf}%\\~ ~ ~ ~ ~(c)
%\includegraphics[scale=0.10]{fig25.pdf}\\~ ~ ~(d)
%\includegraphics[scale=0.10]{fig26.pdf}\\~ ~ ~(e)
%\includegraphics[scale=0.10]{fig27.pdf}\\~ ~ ~(f)
\end{multicols} 
\caption{Wireless Sensor Node represented by 13 primary points}
%\caption{Wireless Sensor Node represented by (a)5, (b)9 and (c)13 primary points respectively}
\label{fig1}
\end{figure}

\fi

\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
\caption{DiLCO protocol}
\label{fig2}
\end{figure} 

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} 
\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}
and each sensor node will have five possible status in the network:
%\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.
\end{itemize}
%\end{enumerate}

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
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
remaining energy corresponds to the time that a sensor can live in the
active mode.

\subsubsection{Leader Election Phase}
This  step includes 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  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
number  of neighbors,  larger remaining  energy, and  then in  case of
equality, larger index. 

\subsubsection{Decision phase}
The  WSNL will  solve an  integer  program (see  section~\ref{cp})  to
select which sensors will be  activated in the following sensing phase
to cover  the subregion.  WSNL will send  Active-Sleep packet  to each
sensor in the subregion based on the algorithm's results.


\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.

\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

\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{ $RE_j \geq E_{th}$ }{
      \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{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{$\left\{\left(X_{1},\dots,X_{k},\dots,X_{J}\right)\right\}$ =
          Execute Integer Program Algorithm($J$)}\;
        \emph{$s_j.status$ = COMMUNICATION}\;
        \emph{Send $ActiveSleep()$ to each node $k$ in subregion} \;
        \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{DiLCO($s_j$)}
\label{alg:DiLCO}

\end{algorithm}

\iffalse
The DiLCO protocol work in rounds and executed at each sensor node in the network , each sensor node can still sense data while being in
LISTENING mode. Thus, by entering the LISTENING mode at the beginning of each round,
sensor nodes still executing sensing task while participating in the leader election and decision phases. More specifically, The DiLCO protocol algorithm works as follow: 
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, current remaining energy, sensor node id, and the number of its one-hop live neighbors during the information exchange. It stores this information into a list L.
The sensor node enter in listening mode waiting to receive ActiveSleep packet from the leader to take the decision. 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 select the set of sensor nodes to take the mission of coverage during the sensing phase. The leader will send ActiveSleep packet to each sensor node in the subregion to inform him to it's status during the period of sensing, either Active or sleep until the starting of next round. Based on the decision, the leader as other nodes in subregion, either go to be active or go to be sleep 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, all the sensor nodes in the same subregion will start new round by executing the DiLCO protocol and the lifetime in the subregion will continue until all the sensor nodes are died or the network becomes disconnected in the subregion.
\fi


\section{\uppercase{Coverage problem formulation}}
\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,  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}
  1 & \mbox{if the primary point $p$ is covered} \\
 & \mbox{by sensor node $j$}, \\
  0 & \mbox{otherwise.}\\
\end{array} \right.
%\label{eq12} 
\end{equation}
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}
  1& \mbox{if sensor $j$  is active,} \\
  0 &  \mbox{otherwise.}\\
\end{array} \right.
%\label{eq11} 
\end{equation}
We define the Overcoverage variable $\Theta_{p}$ as:
\begin{equation}
 \Theta_{p} = \left \{ 
\begin{array}{l l}
  0 & \mbox{if the primary point}\\
    & \mbox{$p$ is not covered,}\\
  \left( \sum_{j \in J} \alpha_{jp} * X_{j} \right)- 1 & \mbox{otherwise.}\\
\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:
\begin{equation}
U_{p} = \left \{ 
\begin{array}{l l}
  1 &\mbox{if the primary point $p$ is not covered,} \\
  0 & \mbox{otherwise.}\\
\end{array} \right.
\label{eq14} 
\end{equation}

\noindent Our coverage optimization problem can then be formulated as follows:
\begin{equation} \label{eq:ip2r}
\left \{
\begin{array}{ll}
\min \sum_{p \in P} (w_{\theta} \Theta_{p} + w_{U} U_{p})&\\
\textrm{subject to :}&\\
\sum_{j \in J}  \alpha_{jp} X_{j} - \Theta_{p}+ U_{p} =1, &\forall p \in P\\
%\label{c1} 
%\sum_{t \in T} X_{j,t} \leq \frac{RE_j}{e_t} &\forall j \in J \\
%\label{c2}
\Theta_{p}\in \mathbb{N} , &\forall p \in P\\
U_{p} \in \{0,1\}, &\forall p \in P \\
X_{j} \in \{0,1\}, &\forall j \in J
\end{array}
\right.
\end{equation}

\begin{itemize}
\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}

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}
\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.}
% title of Table
\centering
% used for centering table
\begin{tabular}{c|c}
% centered columns (4 columns)
      \hline
%inserts double horizontal lines
Parameter & Value  \\ [0.5ex]
   
%Case & Strategy (with Two Leaders) & Strategy (with One Leader) & Simple Heuristic \\ [0.5ex]
% inserts table
%heading
\hline
% inserts single horizontal line
Sensing  Field  & $(50 \times 25)~m^2 $   \\
% inserting body of the table
%\hline
Nodes Number &  50, 100, 150, 200 and 250~nodes   \\
%\hline
Initial Energy  & 500-700~joules  \\  
%\hline
Sensing Period & 60 Minutes \\
$E_{th}$ & 36 Joules\\
$R_s$ & 5~m   \\     
%\hline
$w_{\Theta}$ & 1   \\
% [1ex] adds vertical space
%\hline
$w_{U}$ & $|P|^2$
%inserts single line
\end{tabular}
\label{table3}
% is used to refer this table in the text
\end{table}

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]
\caption{Energy consumption model}
% 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
Sensor status & MCU   & Radio & Sensing & Power (mW) \\ [0.5ex]
\hline
% inserts single horizontal line
Listening & ON & ON & ON & 20.05 \\
% inserting body of the table
\hline
Active & ON & OFF & ON & 9.72 \\
\hline
Sleep & OFF & OFF & OFF & 0.02 \\
\hline
Computation & ON & ON & ON & 26.83 \\
%\hline
%\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}

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 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
$E_{th}=36$~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 has
been computed  by multiplying the energy  consumed in active state  (9.72 mW) by
the time in  second for one round (3600 seconds).  According  to the interval of
initial energy, a sensor may be active during at most 20 rounds.

In the simulations,  we introduce the following performance  metrics to evaluate
the efficiency of our approach:

%\begin{enumerate}[i)]
\begin{itemize}
  
\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
\mbox{CR}(\%) = \frac{\mbox{$n$}}{\mbox{$N$}} \times 100.
\end{equation*}
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.
% Therefore, for our simulations, the error in the coverage calculation is less than ~ 1 $\% $.

\iffalse

\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 communication  overhead  and maximize  the
network lifetime. The Active Sensors Ratio is defined as follows:
\begin{equation*}
\scriptsize
\mbox{ASR}(\%) =  \frac{\sum\limits_{r=1}^R \mbox{$A_r^t$}}{\mbox{$S$}} \times 100 .
\end{equation*}
Where: $A_r^t$ is the number of active sensors in the subregion $r$ during round $t$ in the current sensing phase, $S$ is the total number of sensors in the network, and $R$ is the total number of the subregions in the network.

\fi

\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 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.

\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 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

\end{itemize}
%\end{enumerate}


%\subsection{Performance Analysis for different subregions}
\subsection{Performance analysis}
\label{sub1}

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 {\bf
  X} (respectively {\bf Y}), 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.

\parskip 0pt    
\begin{figure}[t!]
\centering
 \includegraphics[scale=0.45] {R/CR.pdf} 
\caption{Coverage ratio}
\label{fig3}
\end{figure} 

%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.

\begin{figure}[h!]
\centering
\includegraphics[scale=0.45]{R/EC.pdf} 
\caption{Energy consumption}
\label{fig95}
\end{figure} 

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.  

\subsubsection{Execution time}

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}  
\caption{Execution time in seconds}
\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.

%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}

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}  
\caption{Network lifetime}
\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.

\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
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 a DiLCO protocol for optimizing the coverage and lifetime performances in each subregion.
The proposed protocol 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 representative active nodes that will optimize the network lifetime
while  taking the responsibility of covering the corresponding
subregion. The network lifetime in each subregion is divided into
rounds, each round consists  of four phases: (i) Information Exchange,
(ii) Leader Election, (iii) an optimization-based Decision in order to
select the  nodes remaining  active for  the  last phase,  and  (iv)
Sensing.  The  simulations show the relevance  of the proposed DiLCO
protocol in terms of lifetime, coverage ratio, active sensors ratio, energy consumption, execution time, and the number of stopped simulation runs due to network disconnection. Indeed, when
dealing with large and dense wireless sensor networks, a distributed
approach like the one we are proposed 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.

In future work, we plan to study  and propose a coverage optimization protocol, which
computes  all active sensor schedules in one time, using
optimization  methods. \iffalse The round  will still consist of 4 phases, but the
  decision phase will compute the schedules for several sensing phases
  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}}

\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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