-%{\bf Distributed approaches}
-In distributed $\&$ localized coverage algorithms, the required computation to schedule the activity of sensor nodes will be done by the cooperation among the neighbours nodes. These algorithms may require more computation power for the processing by the cooperated sensor nodes but they are more scaleable for large WSNs. Localized and distributed algorithms generally result in non-disjoint set covers.
-
-Some distributed algorithms have been developed
-in~\cite{Gallais06,Tian02,Ye03,Zhang05,HeinzelmanCB02, yardibi2010distributed} to perform the
-scheduling so as to coverage preservation. Distributed algorithms typically operate in rounds for
-a predetermined duration. At the beginning of each round, a sensor
-exchanges information with its neighbors and makes a decision to either
-remain turned on or to go to sleep for the round. This decision is
-basically made on simple greedy criteria like the largest uncovered
-area \cite{Berman05efficientenergy}, maximum uncovered targets
-\cite{lu2003coverage}. In \cite{Tian02}, the scheduling scheme is divided
-into rounds, where each round has a self-scheduling phase followed by
-a sensing phase. Each sensor broadcasts a message containing the node ID
-and the node location to its neighbors at the beginning of each round. A
-sensor determines its status by a rule named off-duty eligible rule,
-which tells him to turn off if its sensing area is covered by its
-neighbors. A back-off scheme is introduced to let each sensor delay
-the decision process with a random period of time, in order to avoid
-simultaneous conflicting decisions between nodes and lack of coverage on any area.
-\cite{prasad2007distributed} defines a model for capturing
-the dependencies between different cover sets and proposes localized
-heuristic based on this dependency. The algorithm consists of two
-phases, an initial setup phase during which each sensor computes and
-prioritizes the covers and a sensing phase during which each sensor
-first decides its on/off status, and then remains on or off for the
-rest of the duration.
-
-The authors in \cite{yardibi2010distributed} developed a distributed adaptive sleep scheduling algorithm (DASSA) for WSNs with partial coverage. DASSA does not require location information of sensors while maintaining connectivity and satisfying a user defined coverage target. In DASSA, nodes use the residual energy levels and feedback from the sink for scheduling the activity of their neighbors. This feedback mechanism reduces the randomness in scheduling that would otherwise occur due to the absence of location information.
-
-In \cite{ChinhVu}, the author 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}.
-
-
-%Our Work, which is presented in~\cite{idrees2014coverage} proposed 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 consider only distributing the coverage protocol over two subregions.
-
-The works presented in \cite{Bang, Zhixin, Zhang} focuses on a Coverage-Aware, Distributed Energy- Efficient and distributed clustering methods respectively, which aims to extend the network lifetime, while the coverage is ensured.
-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.
-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.
-
-In \cite{xu2001geography}, Xu et al. proposed an algorithm, called Geographical Adaptive Fidelity (GAF), 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.
-
-Some other approaches (outside the scope of our work) do not consider a synchronized and predetermined
-period of time where the sensors are active or not. Indeed, each
-sensor maintains its own timer and its wake-up time is randomized
-\cite{Ye03} or regulated \cite{cardei2005maximum} over time.
-
-The MuDiLCO protocol (for Multiperiod Distributed Lifetime Coverage Optimization protocol) presented in this paper is an extension of the approach explained in~\cite{idrees2014coverage}. In~\cite{idrees2014coverage}, the protocol is deployed over only two subregions. Simulation results have shown that it was more interesting to divide the area into several subregions, given the computation complexity. Compared to our previous paper, we study here the possibility of dividing the sensing phase into multiple rounds and we also add a model of energy consumption to assess the efficiency of our approach.
-%The main contributions of our MuDiLCO Protocol can be summarized as follows:
-%(1) The high coverage ratio, (2) The reduced number of active nodes, (3) The distributed optimization over the subregions in the area of interest, (4) The distributed dynamic leader election at each round based on some priority factors that led to energy consumption balancing among the nodes in the same subregion, (5) The primary point coverage model to represent each sensor node in the network, (6) 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 for a multirounds to take the mission of the coverage in each subregion, (7) The very low energy consumption, (8) The higher network lifetime.
-%\section{Preliminaries}
-%\label{Pr}
-
-
-
-
-%Network Lifetime
-
-%\subsection{Network Lifetime}
-%Various definitions exist for the lifetime of a sensor
-%network~\cite{die09}. The main definitions proposed in the literature are
-%related to the remaining energy of the nodes or to the coverage percentage.
-%The lifetime of the network is mainly defined as the amount
-%of time during which the network can satisfy its coverage objective (the
-%amount of time that the network can cover a given percentage of its
-%area or targets of interest). In this work, we assume that the network
-%is alive until all nodes have been drained of their energy or the
-%sensor network becomes disconnected, and we measure the coverage ratio
-%during the WSN lifetime. 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.
-
-
-
-
-\section{ The MuDiLCO Protocol Description}
+
+In distributed and localized coverage algorithms, the required computation to
+schedule the activity of sensor nodes will be done by the cooperation among
+neighboring nodes. These algorithms may require more computation power for the
+processing by the cooperating sensor nodes, but they are more scalable for large
+WSNs. Localized and distributed algorithms generally result in non-disjoint set
+covers.
+
+Many distributed algorithms have been developed to perform the scheduling so as
+to preserve coverage, see for example
+\cite{Gallais06,Tian02,Ye03,Zhang05,HeinzelmanCB02, yardibi2010distributed,
+ prasad2007distributed,Misra}. Distributed algorithms typically operate in
+rounds for a predetermined duration. At the beginning of each round, a sensor
+exchanges information with its neighbors and makes a decision to either remain
+turned on or to go to sleep for the round. This decision is basically made on
+simple greedy criteria like the largest uncovered area
+\cite{Berman05efficientenergy} or maximum uncovered targets
+\cite{lu2003coverage}. The Distributed Adaptive Sleep Scheduling Algorithm
+(DASSA) \cite{yardibi2010distributed} does not require location information of
+sensors while maintaining connectivity and satisfying a user defined coverage
+target. In DASSA, nodes use the residual energy levels and feedback from the
+sink for scheduling the activity of their neighbors. This feedback mechanism
+reduces the randomness in scheduling that would otherwise occur due to the
+absence of location information. In \cite{ChinhVu}, the author have designed 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 one-hop neighbor
+information, and each sensor decides its status (active or sleep) based on the
+perimeter coverage model from~\cite{Huang:2003:CPW:941350.941367}.
+
+The works presented in \cite{Bang, Zhixin, Zhang} focus on coverage-aware,
+distributed energy-efficient, and distributed clustering methods respectively,
+which aim at extending the network lifetime, while the coverage is ensured.
+More recently, Shibo et al. \cite{Shibo} have 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. In \cite{xu2001geography}, Xu et
+al. have described an algorithm, called Geographical Adaptive Fidelity (GAF),
+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.
+
+Some other approaches (outside the scope of our work) do not consider a
+synchronized and predetermined time-slot where the sensors are active or not.
+Indeed, each sensor maintains its own timer and its wake-up time is randomized
+\cite{Ye03} or regulated \cite{cardei2005maximum} over time.
+
+The MuDiLCO protocol (for Multiround Distributed Lifetime Coverage Optimization
+protocol) presented in this paper is an extension of the approach introduced
+in~\cite{idrees2014coverage}. In~\cite{idrees2014coverage}, the protocol is
+deployed over only two subregions. Simulation results have shown that it was
+more interesting to divide the area into several subregions, given the
+computation complexity. Compared to our previous paper, in this one we study the
+possibility of dividing the sensing phase into multiple rounds and we also add
+an improved model of energy consumption to assess the efficiency of our
+approach. In fact, in this paper we make a multiround optimization, while it was
+a single round optimization in our previous work. \textcolor{blue}{The idea is
+ to take advantage of the pre-sensing phase to plan the sensor's activity for
+ several rounds instead of one, thus saving energy. In addition, when the
+ optimization problem becomes more complex, its resolution is stopped after a
+ given time threshold}.
+
+
+\section{MuDiLCO protocol description}
