literature.
The most discussed coverage problems in literature
-can be classified into three types \cite{li2013survey}: area coverage (where
-every point inside an area is to be monitored), target coverage (where the main
-objective is to cover only a finite number of discrete points called targets),
-and barrier coverage (to prevent intruders from entering into the region of
-interest).
+can be classified into three types \cite{li2013survey}: area coverage \cite{Misra} where
+every point inside an area is to be monitored, target coverage \cite{yang2014novel} where the main
+objective is to cover only a finite number of discrete points called targets,
+and barrier coverage \cite{Kumar:2005}\cite{kim2013maximum} to prevent intruders from entering into the region of interest. In \cite{Deng2012} authors transform the area coverage problem to the target coverage problem taking into account the intersection points among disks of sensors nodes or between disk of sensor nodes and boundaries.
{\it In DiLCO protocol, the area coverage, i.e. the coverage of every point in
the sensing region, is transformed to the coverage of a fraction of points
called primary points. }
+
The major approach to extend network lifetime while preserving coverage is to
divide/organize the sensors into a suitable number of set covers (disjoint or
-non-disjoint) where each set completely covers a region of interest and to
+non-disjoint), where each set completely covers a region of interest, and to
activate these set covers successively. The network activity can be planned in
advance and scheduled for the entire network lifetime or organized in periods,
-and the set of active sensor nodes is decided at the beginning of each period.
+and the set of active sensor nodes is decided at the beginning of each period \cite{ling2009energy}.
Active node selection is determined based on the problem requirements (e.g. area
-monitoring, connectivity, power efficiency). Different methods have been
-proposed in literature.
-{\it DiLCO protocol works in periods, where each period contains a preliminary
+monitoring, connectivity, power efficiency). For instance, Jaggi et al. \cite{jaggi2006}
+address the problem of maximizing network lifetime by dividing sensors into the maximum number of disjoint subsets such that each subset can ensure both coverage and connectivity. A greedy algorithm is applied once to solve this problem and the computed sets are activated in succession to achieve the desired network lifetime.
+Vu \cite{chin2007}, Padmatvathy et al. \cite{pc10}, propose algorithms working in a periodic fashion where a cover set is computed at the beginning of each period.
+{\it Motivated by these works, DiLCO protocol works in periods, where each period contains a preliminary
phase for information exchange and decisions, followed by a sensing phase
where one cover set is in charge of the sensing task.}
-Various approaches, including centralized, distributed, and localized
+Various approaches, including centralized, or distributed
algorithms, have been proposed to extend the network lifetime.
%For instance, in order to hide the occurrence of faults, or the sudden unavailability of
%sensor nodes, some distributed algorithms have been developed in~\cite{Gallais06,Tian02,Ye03,Zhang05,HeinzelmanCB02}.
sleep mode for a certain period of time. The centralized
algorithms~\cite{cardei2005improving,zorbas2010solving,pujari2011high} always
provide nearly or close to optimal solution since the algorithm has global view
-of the whole network, but such a method has the disadvantage of requiring high
+of the whole network. But such a method has the disadvantage of requiring high
communication costs, since the node (located at the base station) making the
-decision needs information from all the sensor nodes in the area.
+decision needs information from all the sensor nodes in the area and the amount of information can be huge.
+{\it In order to be suitable for large-scale network, in the DiLCO protocol, the area coverage is divided into several smaller
+ subregions, and in each of one, a node called the leader is in charge for
+ selecting the active sensors for the current period.}
-A large variety of coverage scheduling algorithms have been proposed. Many of
+A large variety of coverage scheduling algorithms have been developed. Many of
the existing algorithms, dealing with the maximization of the number of cover
sets, are heuristics. These heuristics involve the construction of a cover set
by including in priority the sensor nodes which cover critical targets, that is
-to say targets that are covered by the smallest number of sensors. Other
-approaches are based on mathematical programming formulations and dedicated
+to say targets that are covered by the smallest number of sensors \cite{berman04,zorbas2010solving}. Other
+approaches are based on mathematical programming formulations~\cite{cardei2005energy,5714480,pujari2011high,Yang2014} and dedicated
techniques (solving with a branch-and-bound algorithms available in optimization
solver). The problem is formulated as an optimization problem (maximization of
the lifetime or number of cover sets) under target coverage and energy
constraints. Column generation techniques, well-known and widely practiced
techniques for solving linear programs with too many variables, have been also
-used~\cite{castano2013column,rossi2012exact,deschinkel2012column}.
+used~\cite{castano2013column,rossi2012exact,deschinkel2012column}. {\it In DiLCO protocol, each leader, in each subregion, solves an integer
+ program with a double objective consisting in minimizing the overcoverage and
+ limiting the undercoverage. This program is inspired from the work of
+ \cite{pedraza2006} where the objective is to maximize the number of cover
+ sets.}
% ***** Part which must be rewritten - Start
% Start of Ali's papers catalog => there's no link between them or with our work
% (use of subregions; optimization based method; etc.)
-
+\iffalse
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
% What is the link between the previous work and this paragraph about DiLCO ?
-{\it In DiLCO protocol, the area coverage is divided into several smaller
- subregions, and in each of which, a node called the leader is on charge for
- selecting the active sensors for the current period.}
+
Yang et al.~\cite{yang2014energy} investigated full area coverage problem under
the probabilistic sensing model in the sensor networks. They have studied the
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
% Same remark, no link with the two previous citations...
-{\it In DiLCO protocol, each leader, in each subregion, solves an integer
- program with a double objective consisting in minimizing the overcoverage and
- limiting the undercoverage. This program is inspired from the work of
- \cite{pedraza2006} where the objective is to maximize the number of cover
- sets.}
+
% ***** Part which must be rewritten - End
\fi
-\subsection{The main idea}
+\subsection{Main idea}
\label{main_idea}
\noindent We start by applying a divide-and-conquer algorithm to partition the
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
+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
\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
+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.
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
+model, we consider that the binary variable $X_{j}$ determines 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 $J$.
%\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\\
+\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}
is equal to 0.2575 mW.
Each node has an initial energy level, in Joules, which is randomly drawn in the
-interval $[500-700]$. If it's energy provision reaches a value below the
+interval $[500-700]$. If its energy provision reaches a value below the
threshold $E_{th}=36$~Joules, the minimum energy needed for a node to stay
active during one period, it will no more participate in the coverage task. This
value corresponds to the energy needed by the sensing phase, obtained by
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
+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
\section*{\uppercase{Acknowledgements}}
-\noindent As a Ph.D. student, Ali Kadhum IDREES would like to gratefully
+\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.
+Campus France for the received support. This paper is also partially funded by
+the Labex ACTION program (contract ANR-11-LABX-01-01).
%\vfill
\bibliographystyle{apalike}
