\documentclass[a4paper,twoside]{article}

\usepackage{epsfig}
\usepackage{subfigure}
\usepackage{calc}
\usepackage{amssymb}
\usepackage{amstext}
\usepackage{amsmath}
\usepackage{amsthm}
\usepackage{multicol}
\usepackage{pslatex}
\usepackage{apalike}
\usepackage{SCITEPRESS}
\usepackage[small]{caption}

\usepackage[linesnumbered,ruled,vlined,commentsnumbered]{algorithm2e}
\usepackage{mathtools}  

\subfigtopskip=0pt
\subfigcapskip=0pt
\subfigbottomskip=0pt

\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 sensor
nodes drain their  energy from batteries. In fact,  strong constraints on energy
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. % TO BE CONTINUED
Sensor nodes runs on batteries with limited capacities~\cite{Sudip03}
and  it  is  impossible,  difficult  or expensive  to  recharge  and/or  replace
batteries  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.

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 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 periods, where a period starts with
a discovery phase  to exchange information between sensors  of the subregion, in
order to choose in a suitable manner a sensor node (the leader) to carry out the
coverage  strategy.  Our  DiLCO protocol  involves solving  an  integer program,
which  provides the  activation of  the  sensors for  the sensing  phase of  the
current period.

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 futher 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{ 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.
\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.

\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}
\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 periods fashion as shown in figure~\ref{fig2}.
\begin{figure}[ht!]
\centering
\includegraphics[width=75mm]{FirstModel.pdf} % 70mm
\caption{DiLCO protocol}
\label{fig2}
\end{figure} 

%Modifier la figure pour faire apparaitre des periodes et dans le schema en bleu, indiquer sensing round au lieu de sensing tout seul.

Each period  is divided  into 4 phases  : Information  (INFO) Exchange,
Leader  Election, Decision,  and  Sensing.  For  each  period 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 periods. On the  one hand,  if a node failure is detected before
making the decision, the node will not participate to this phase, and,
on the other hand, if the  node failure occurs after the decision, the
sensing task of the network  will be temporarily affected: only during
the period of sensing until a new period starts, since a new set cover
will take charge of the sensing task in the next period.  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
period.  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.
%\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 Active or Sleep during the sensing phase.
\end{itemize}
%\end{enumerate}

There are five status for each sensor node 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}
%Below, we describe each phase in more details.
Algorithm 1 gives a brief description of the protocol applied by each sensor node (denoted by $s_j$ for a sensor node indexed by $j$).
Initially, the sensor node checks its remaining energy in order to participate in the current period. 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. 
Then all the sensor nodes in the same subregion will select the leader based on the received informations. 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}) which provides a set of sensors planned to be active in the sensing round. 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. On the contrary, if the sensor is not the leader, it will wait for the Active-Sleep packet to know its state for the sensing round.



\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
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 neighbours,  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{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,  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 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:
\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 $p$ is equal
to $\sum_{j \in J} \alpha_{jp} * X_{j}$ 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 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
  $p$ 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}}  
\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}.

\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}

We  performed  simulations for five different densities varying from 50 to 250~nodes. Experimental results are the average obtained from 25 randomly generated networks (25 for each network density) 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.\\

We first concentrate on the required number of subregions making effective our protocol. Thus 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}. 

\begin{table}[ht]
\caption{The Energy Consumption Model}
% title of Table
\centering
% used for centering table
\begin{tabular}{|c|c|c|c|c|}
% centered columns (4 columns)
      \hline
%inserts double horizontal lines
Sensor mode & 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}

For the sake of simplicity we ignore the energy needed to turn on the
radio, to start up the sensor node, the transition from one status to another, etc. 
%We also do not consider the need of collecting sensing data. PAS COMPRIS
Thus, when a sensor becomes active (i.e., it already decides its 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 energy needed to send or receive a 1-bit is equal to $0.2575 mW$.

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 mW) 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: 

%\begin{enumerate}[i)]
\begin{itemize}
  
\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:
\begin{equation*}
\scriptsize
\mbox{CR}(\%) = \frac{\mbox{$n$}}{\mbox{$N$}} \times 100.
\end{equation*}
where  $n$ is the number of covered grid points by the active sensors of all subregions during 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.
%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 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 the $Lifetime95$ or $Lifetime50$ divided by the number of periods. The EC can be computed as follow: \\
 \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}+E^{s} \right)}{M_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 $M$ 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 round.

\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 differnet subregions}
\subsection{Performance Analysis}
\label{sub1}
In this subsection, we study the performance of our DiLCO protocol for  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 do not take into account the DiLC0-1 protocol in our simulation results because it requires  high execution time to solve the integer program and thus it is too costly in term of energy.

Our method is compared with other two approaches. The first approach, called DESK and proposed by ~\cite{ChinhVu}  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. 


\subsubsection{Coverage Ratio} 
Figure~\ref{fig3} shows the average coverage ratio for 150 deployed nodes.  
\parskip 0pt    
\begin{figure}[h!]
\centering
 \includegraphics[scale=0.45] {R/CR.pdf} 
\caption{The Coverage Ratio}
\label{fig3}
\end{figure} 

Figure~\ref{fig3} shows that DESK and GAF provide a
a little better coverage ratio compared to DiLCO in the first thirty periods. This is due to the fact that our DiLCO protocol versions  put in sleep mode some sensors through optimization process (which slightly decreases the coverage ratio) while there are more active nodes  with DESK or GAF. With DiLCO-2 (respectively DiLCO-4), the coverage ratio decreases rapidly to reach zero value in period ... (respectively in period ....) whereas other methods guarantee a coverage ratio greater than $50\%$ after this period. 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 paragraph. Concerning DiLCO-8, DiLCO-16 and DiLCO-32, these methods seem to be more efficient than DESK and GAF because they can provide the same level of coverage (except in the first periods, slightly lower) for a greater number of periods. Unlike other methods, their strategy enables to activate a restricted number of nodes, and thus extends the lifetime of the network.
%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{The Energy Consumption}
Based on previous results in figure~\ref{fig3}, we keep DiLCO-16 and  DiLCO-32  and we compare their performances in terms of energy consumption with the two other approaches. We measure the energy consumed by the sensors during the communication, listening, computation, active, and sleep modes for different network densities.  Figure~\ref{fig95} illustrates the energy consumption for different network sizes.
% for $Lifetime95$ and $Lifetime50$. 
We denote by $DiLCO-/50$ (respectively  $DiLCO-/95$) as the amount of energy consumed during which the network can satisfy an area coverage greater than $50\%$ (repectively $95\%$) and we refer to the same definition for the two other approaches.
\begin{figure}[h!]
\centering
\includegraphics[scale=0.45]{R/EC.pdf} 
\caption{The Energy Consumption}
\label{fig95}
\end{figure} 

The results show that 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. 


%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}
We observe the impact of the network size and of the number of subregions on the computation time. We report the average execution times in seconds needed to solve the optimization problem 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 $\left( \frac{35330}{2} \times \frac{1}{6}\right)$ and 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. Excessive subdivision of the area of interest prevents to ensure good coverage especially on the borders of the subregions.

%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{The Network Lifetime}
In figure~\ref{figLT95}, network lifetime is illustrated for different network sizes. The term $/50$ (respectively  $/95$) next to the name of the method refers to the amount of time during which the network can satisfy an area coverage greater than $50\%$ ($Lifetime50$)(repectively $95\%$ ($Lifetime95$)) 

\begin{figure}[h!]
\centering
\includegraphics[scale=0.45]{R/LT.pdf}  
\caption{The Network Lifetime}
\label{figLT95}
\end{figure} 


As highlighted by figure~\ref{figLT95}, the network lifetime obviously
increases when the size of the network increases. For the same level of coverage, DiLCO outperforms DESK and GAF for the lifetime of the network. If we focus on level of coverage greater than $95\%$, 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 Works}}
\label{sec:Conclusion and Future Works}
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 set of active nodes to ensure a high level of coverage.
We have compared this method with two other approaches using many metrics as coverage ratio, execution time, lifetime.
Some experiments have been performed to study the choice of the number of
subregions  which subdivide  the  sensing field,  considering different  network
sizes. They show that as the number of subregions increases, so does the network
lifetime. Moreover,  it makes  the DiLCO protocol  more robust  against random
network  disconnection due  to node  failures.  However,  too  much subdivisions
reduces the advantage  of the optimization. In fact, there  is a balance between
the  benefit  from the  optimization  and the  execution  time  needed to  solve
it. Therefore, the subdivision in $16$ subregions seems to be the most appropriate. 
\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.





%\vfill
\bibliographystyle{apalike}
{\small
\bibliography{Example}}


%\vfill
\end{document}
