Various approaches, including centralised, distributed and localized algorithms, have been proposed to extend the network lifetime.
%For instance, in order to hide the occurrence of faults, or the sudden unavailability of
%sensor nodes, some distributed algorithms have been developed in~\cite{Gallais06,Tian02,Ye03,Zhang05,HeinzelmanCB02}.
-In distributed algorithms, information is disseminated throughout the network and sensors decide cooperatively by communicating with their neighbours which of them will remain in sleep mode for a certain period of time.
-The centralized algorithms always provide nearly
+
+In distributed algorithms~\cite{yangnovel,ChinhVu,qu2013distributed}, information is disseminated throughout the network and sensors decide cooperatively by communicating with their neighbours which of them will remain in sleep mode for a certain period of time.
+The centralized algorithms~\cite{cardei2005improving,zorbas2010solving,pujari2011high} always provide nearly
or close to optimal solution since the algorithm has global view of the whole
network, but such a method has the disadvantage of requiring
high communication costs, since the node (located at the base station) making the decision needs information from all the sensor nodes in the area.
+A large variety of coverage scheduling algorithms have been proposed in the literature. Many of the existing algorithms, dealing with the maximisation of the number of cover sets, are heuristics. These heuristics involve the construction of a cover set by including in priority the sensor nodes which cover critical targets, that is to say targets that are covered by the smallest number of sensors. Other approaches are based on mathematical programming formulations and dedicated techniques (solving with a branch-and-bound algorithms available in optimization solver). The problem is formulated as an optimization problem (maximization of the lifetime, of the number of cover sets) under target coverage and energy constraints. Column generation techniques, well-known and widely practiced techniques for solving linear programs with too many variables, have been also used~\cite{castano2013column,rossi2012exact,deschinkel2012column}.
+
+Diongue and Thiare~\cite{diongue2013alarm} proposed an energy aware sleep scheduling algorithm for lifetime maximization in wireless sensor networks (ALARM). The proposed approach permits to schedule redundant nodes according to the weibull distribution. This work did not analyze the ALARM scheme under the coverage problem.
+
+Shi et al.~\cite{shi2009} modeled the Area Coverage Problem (ACP), which will be changed into a set coverage
+problem. By using this model, they 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.
+
+In ~\cite{chenait2013distributed}, the authors presented a coverage-guaranteed distributed sleep/wake scheduling scheme so as to prolong network lifetime while guaranteeing network coverage. This scheme mitigates scheduling process to be more stable by avoiding useless transitions between states without affecting the coverage level required by the application.
+
+The work in~\cite{cheng2014achieving} presented a unified sensing architecture for duty cycled sensor networks, called uSense, which comprises three ideas: Asymmetric Architecture, Generic Switching and Global Scheduling. The objective is to provide a flexible and efficient coverage in sensor networks.
+
+In~\cite{ling2009energy}, the lifetime of
+a sensor node is divided into epochs. At each epoch, the
+base station deduces the current sensing coverage requirement
+from application or user request. It then applies the heuristic algorithm in order to produce the set of active nodes which take the mission of sensing during the current epoch. After that, the produced schedule is sent to the sensor nodes in the network.
+
{\it In DiLCO protocol, the area coverage is divided into several smaller subregions, and in each of which, a node called the leader is on charge for selecting the active sensors for the current period.}
-A large variety of coverage scheduling algorithms have been proposed in the literature. Many of the existing algorithms, dealing with the maximisation of the number of cover sets, are heuristics. These heuristics involve the construction of a cover set by including in priority the sensor nodes which cover critical targets, that is to say targets that are covered by the smallest number of sensors. Other approaches are based on mathematical programming formulations and dedicated techniques (solving with a branch-and-bound algorithms available in optimization solver). The problem is formulated as an optimization problem (maximization of the lifetime, of the 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}.
+Yang et al.~\cite{yang2014energy} investigated full area coverage problem
+under the probabilistic sensing model in the sensor networks. They have studied the relationship between the
+coverage of two adjacent points mathematically and then convert the problem of full area coverage into point coverage problem. They proposed $\varepsilon$-full area coverage optimization (FCO) algorithm to select a subset
+of sensors to provide probabilistic area coverage dynamically so as to extend the network lifetime.
+
+The work 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.
+The work proposed by \cite{qu2013distributed} considers the coverage problem in WSNs where each sensor has variable sensing radius. The final objective is to maximize the network coverage lifetime in WSNs.
-{\it In DiLCO protocol, each leader, in each subregion, solves an integer program with a double objective consisting in minimizing the overcoverage and limiting the undercoverage. This program is inspired from the work of \cite{} where the objective is to maximize the number of cover sets.}
+{\it In DiLCO protocol, each leader, in each subregion, solves an integer program with a double objective consisting in minimizing the overcoverage and limiting the undercoverage. This program is inspired from the work of \cite{pedraza2006} where the objective is to maximize the number of cover sets.}
\iffalse
%\begin{enumerate}[i)]
\begin{itemize}
+\item {{\bf Network Lifetime}:} we define the network lifetime as the time until
+ the coverage ratio drops below a predefined threshold. We denote by
+ $Lifetime_{95}$ (respectively $Lifetime_{50}$) the amount of time during which
+ the network can satisfy an area coverage greater than $95\%$ (respectively
+ $50\%$). We assume that the sensor network can fulfill its task until all its
+ nodes have been drained of their energy or it becomes disconnected. Network
+ connectivity is crucial because an active sensor node without connectivity
+ towards a base station cannot transmit any information regarding an observed
+ event in the area that it monitors.
+
\item {{\bf Coverage Ratio (CR)}:} 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
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,
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
+ 18} (respectively {\bf 46}), whereas the other versions of DiLCO, DESK, and GAF
ensure a coverage ratio above 50\% for subsequent periods. We believe that the
results obtained with these two methods can be explained by a high consumption
of energy and we will check this assumption in the next subsection.
