+\noindent The fast developments in the low-cost sensor devices and
+wireless communications have allowed the emergence the WSNs. WSN
+includes a large number of small , limited-power sensors that can
+sense, process and transmit data over a wireless communication . They
+communicate with each other by using multi-hop wireless communications
+, cooperate together to monitor the area of interest, and the measured
+data can be reported to a monitoring center called, sink, for analysis
+it~\cite{Ammari01, Sudip03}. There are several applications used the
+WSN including health, home, environmental, military,and industrial
+applications~\cite{Akyildiz02}. The coverage problem is one of the
+fundamental challenges in WSNs~\cite{Nayak04} that consists in
+monitoring efficiently and continuously the area of interest. The
+limited energy of sensors represents the main challenge in the WSNs
+design~\cite{Ammari01}, where it is difficult to replace and/or
+recharge their batteries because the the area of interest nature (such
+as hostile environments) and the cost. So, it is necessary that a WSN
+deployed with high density because spatial redundancy can then be
+exploited to increase the lifetime of the network . However, turn on
+all the sensor nodes, which monitor the same region at the same time
+leads to decrease the lifetime of the network. To extend the lifetime
+of the network, the main idea is to take advantage of the overlapping
+sensing regions of some sensor nodes to save energy by turning off
+some of them during the sensing phase~\cite{Misra05}. WSNs require
+energy-efficient solutions to improve the network lifetime that is
+constrained by the limited power of each sensor node
+~\cite{Akyildiz02}. In this paper, we concentrate on the area
+coverage problem, with the objective of maximizing the network
+lifetime by using an adaptive scheduling. The area of interest is
+divided into subregions and an activity scheduling for sensor nodes is
+planned for 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 scheduling scheme considers rounds, where
+a round starts with a discovery phase to exchange information between
+sensors of the subregion, in order to choose in a suitable manner a
+sensor node to carry out a coverage strategy. This coverage strategy
+involves the solving of an integer program, which provides the
+activation of the sensors for the sensing phase of the current round.
+
+The remainder of the paper is organized as follows. The next section
+% Section~\ref{rw}
+reviews the related work in the field. Section~\ref{pd} is devoted to
+the scheduling strategy for energy-efficient coverage.
+Section~\ref{cp} gives the coverage model formulation, which is used
+to schedule the activation of sensors. Section~\ref{exp} shows the
+simulation results obtained using the discrete event simulator OMNeT++
+\cite{varga}. They fully demonstrate the usefulness of the proposed
+approach. Finally, we give concluding remarks and some suggestions
+for future works in Section~\ref{sec:conclusion}.
+
+\section{Related works}
+\label{rw}
+\indent In this section, we only review some recent works dealing with
+the coverage lifetime maximization problem, where the objective is to
+optimally schedule sensors' activities in order to extend WSNs
+lifetime.
+
+In \cite{chin2007} is proposed a novel distributed heuristic, called
+Distributed Energy-efficient Scheduling for k-coverage (DESK), which
+ensures that the energy consumption among the sensors is balanced and
+the lifetime maximized while the coverage requirement is maintained.
+This heuristic works in rounds, requires only 1-hop neighbor
+information, and each sensor decides its status (active or sleep)
+based on the perimeter coverage model proposed in
+\cite{Huang:2003:CPW:941350.941367}. More recently, Shibo et
+al. \cite{Shibo} expressed the coverage problem as a minimum weight
+submodular set cover problem and proposed a Distributed Truncated
+Greedy Algorithm (DTGA) to solve it. They take advantage from both
+temporal and spatial correlations between data sensed by different
+sensors, and leverage prediction, to improve the lifetime. A
+Coverage-Aware Clustering Protocol (CACP), which uses a computation
+method to find the cluster size minimizing the average energy
+consumption rate per unit area, has been proposed by Bang et al. in
+\cite{Bang}. Their protocol is based on a cost metric that selects the
+redundant sensors with higher power as best candidates for cluster
+heads and the active sensors that cover the area of interest the more
+efficiently.
+
+% TO BE CONTINUED
+
+Zhixin et al. \cite{Zhixin} propose a Distributed Energy- Efficient
+Clustering with Improved Coverage(DEECIC) algorithm which aims at
+clustering with the least number of cluster heads to cover the whole
+network and assigning a unique ID to each node based on local
+information. In addition, this protocol periodically updates cluster
+heads according to the joint information of nodes $’ $residual energy
+and distribution. Although DEECIC does not require knowledge of a
+node's geographic location, it guarantees full coverage of the
+network. However, the protocol does not make any activity scheduling
+to set redundant sensors in passive mode in order to conserve energy.
+
+C. Liu and G. Cao \cite{Changlei} studied how to schedule sensor
+active time to maximize their coverage during a specified network
+lifetime. Their objective is to maximize the spatial-temporal coverage
+by scheduling sensors activity after they have been deployed. They
+proposed both centralized and distributed algorithms. The distributed
+parallel optimization protocol can ensure each sensor to converge to
+local optimality without conflict with each other.
+
+S. Misra et al. \cite{Misra} proposed a localized algorithm for
+coverage in sensor networks. The algorithm conserve the energy while
+ensuring the network coverage by activating the subset of sensors,
+with the minimum overlap area.The proposed method preserves the
+network connectivity by formation of the network backbone.
+
+L. Zhang et al. \cite{Zhang} presented a novel distributed clustering
+algorithm called Adaptive Energy Efficient Clustering (AEEC) to
+maximize network lifetime. In this study, they are introduced an
+optimization, which includes restricted global re-clustering,
+intra-cluster node sleeping scheduling and adaptive transmission range
+adjustment to conserve the energy, while connectivity and coverage is
+ensured.
+
+J. A. Torkestani \cite{Torkestani} proposed a learning automata-based
+energy-efficient coverage protocol named as LAEEC to construct the
+degree-constrained connected dominating set (DCDS) in WSNs. He shows
+that the correct choice of the degree-constraint of DCDS balances the
+network load on the active nodes and leads to enhance the coverage and
+network lifetime.
+
+The main contribution of our approach addresses three main questions
+to build a scheduling strategy:
