\hyphenation{op-tical net-works semi-conduc-tor}
-
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%
% paper title
of sensor node activity is planned for each subregion. The proposed
scheduling considers rounds during which a small number of nodes,
remaining active for sensing, is selected to ensure coverage. Each
-round consists of four phases: (i)~Information Exchange, (ii)~Leader
+round consists in four phases: (i)~Information Exchange, (ii)~Leader
Election, (iii)~Decision, and (iv)~Sensing. The decision process is
carried out by a leader node, which solves an integer program.
Simulation results show that the proposed approach can prolong the
\section{Introduction}
-\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
+%\indent 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{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. Thelimited energy of sensors represents the main challenge
+%in the WSNs design~\cite{Sudip03}, 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.
+
+Recent years have witnessed significant advances in wireless
+communications and embedded micro-sensing MEMS technologies which have
+led to the emergence of Wireless Sensor Networks (WSNs) as one of the
+most promising technologies \cite{Akyildiz02}. In fact, they present
+huge potential in several domains ranging from health care
+applications to military applications. A sensor network is composed of
+a large number of tiny sensing devices deployed in a region of
+interest. Each device has processing and wireless communication
+capabilities, which enable it to sense its environment, to compute, to
+store information and to deliver report messages to a base station
+\cite{Sudip03}. One of the main design issues in WSNs is to prolong
+the network lifetime, while achieving acceptable quality of service
+for applications. Indeed, sensors nodes have limited resources in
+terms of memory, energy and computational power.
+
+Since sensor nodes have limited battery life and since it is impossible to
+replace batteries, especially in remote and hostile environments, it
+is desirable that a WSN should be deployed with high density because
+spatial redundancy can then be exploited to increase the lifetime of
+the network. In such a high density network, if all sensor nodes were
+to be activated at the same time, the lifetime would be reduced. 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}.
+Obviously, the deactivation of nodes is only relevant if the coverage
+of the monitored area is not affected. In this paper, we concentrate
+on the area coverage problem \cite{Nayak04}, 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.
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
+In \cite{chin2007}, 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}. 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.
+Greedy Algorithm (DTGA) to solve it. They take in particular advantage
+from both temporal and spatial correlations between data sensed by
+different sensors.
+
+The works presented in \cite{Bang, Zhixin, Zhang} focus on the
+definition of coverage-aware, distributed energy-efficient and
+distributed clustering methods respectively. They aim to extend the
+network lifetime while ensuring the coverage. S. Misra et al.
+\cite{Misra05} proposed a localized algorithm which conserves energy and
+coverage by activating the subset of sensors with the minimum
+overlapping area. It preserves the network connectivity thanks to the
+formation of the network backbone. J.~A.~Torkestani \cite{Torkestani}
+designed a Learning Automata-based Energy-Efficient Coverage protocol
+(LAEEC) to construct a Degree-constrained Connected Dominating Set
+(DCDS) in WSNs. He showed 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:
+to build a scheduling strategy.\\
%\begin{itemize}
%\item
-{\bf How must the phases for information exchange, decision and
- sensing be planned over time?} Our algorithm divides the time line
- into a number of rounds. Each round contains 4 phases: Information
- Exchange, Leader Election, Decision, and Sensing.
+{\indent \bf How must the phases for information exchange, decision
+ and sensing be planned over time?} Our algorithm divides the timeline into rounds. Each round contains 4 phases: Information Exchange,
+Leader Election, Decision, and Sensing.
%\item
{\bf What are the rules to decide which node has to be turned on
objectives.
%\item
-{\bf Which node should make such a decision?} As mentioned in
- \cite{pc10}, both centralized and distributed algorithms have their
- own advantages and disadvantages. Centralized coverage algorithms
- have the advantage of requiring very low processing power from the
- sensor nodes, which have usually limited processing capabilities.
- Distributed algorithms are very adaptable to the dynamic and
- scalable nature of sensors network. Authors in \cite{pc10} conclude
- that there is a threshold in terms of network size to switch from a
- localized to a centralized algorithm. Indeed, the exchange of
- messages in large networks may consume a considerable amount of
- energy in a centralized approach compared to a distributed one. Our
- work does not consider only one leader to compute and to broadcast
- the scheduling decision to all the sensors. When the network size
- increases, the network is divided into many subregions and the
- decision is made by a leader in each subregion.
+{\bf Which node should make such a decision?} A leader node should
+make such a decision. Our work does not consider only one leader to
+compute and to broadcast the scheduling decision to all the sensors.
+When the network size increases, the network is divided into many
+subregions and the decision is made by a leader in each subregion.
%\end{itemize}
-
-
\section{Activity scheduling}
\label{pd}
simultaneously. Our protocol works in rounds fashion as shown in
figure~\ref{fig1}.
-%Given the interested Area $A$, the wireless sensor nodes set $S=\lbrace s_1,\ldots,s_N \rbrace $ that are deployed randomly and uniformly in this area such that they are ensure a full coverage for A. The Area A is divided into regions $A=\lbrace A^1,\ldots,A^k,\ldots, A^{N_R} \rbrace$. We suppose that each sensor node $s_i$ know its location and its region. We will have a subset $SSET^k =\lbrace s_1,...,s_j,...,s_{N^k} \rbrace $ , where $s_N = s_{N^1} + s_{N^2} +,\ldots,+ s_{N^k} +,\ldots,+s_{N^R}$. Each sensor node $s_i$ has the same initial energy $IE_i$ in the first time and the current residual energy $RE_i$ equal to $IE_i$ in the first time for each $s_i$ in A. \\
-
\begin{figure}[ht!]
\centering
\includegraphics[width=85mm]{FirstModel.eps} % 70mm
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 is
-at least twice the size of the sensing range. 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.
-%To calculate the coverage ratio for the area of interest, we can propose the following coverage model which is called Wireless Sensor Node Area Coverage Model to ensure that all the area within each node sensing range are covered. We can calculate the positions of the points in the circle disc of the sensing range of wireless sensor node based on the Unit Circle in figure~\ref{fig:cluster1}:
+covered by this sensor. We also assume that the communication range $R_c \geq 2R_s$ ~\cite{Zhang05}.
+
+
%\begin{figure}[h!]
%\centering
%\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{Sensor node represented by 13 primary points}
\label{fig2}
\end{figure}
\section{Coverage problem formulation}
\label{cp}
-%We can formulate our optimization problem as energy cost minimization by minimize the number of active sensor nodes and maximizing the coverage rate at the same time in each $A^k$ . This optimization problem can be formulated as follow: Since that we use a homogeneous wireless sensor network, we will assume that the cost of keeping a node awake is the same for all wireless sensor nodes in the network. We can define the decision parameter $X_j$ as in \eqref{eq11}:\\
-%To satisfy the coverage requirement, the set of the principal points that will represent all the sensor nodes in the monitored region as $PSET= \lbrace P_1,\ldots ,P_p, \ldots , P_{N_P^k} \rbrace $, where $N_P^k = N_{sp} * N^k $ and according to the proposed model in figure ~\ref{fig:cluster2}. These points can be used by the wireless sensor node leader which will be chosen in each region in A to build a new parameter $\alpha_{jp}$ that represents the coverage possibility for each principal point $P_p$ of each wireless sensor node $s_j$ in $A^k$ as in \eqref{eq12}:\\
-
\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
guarantee that the maximum number of points are covered during each
round.
-%In equation \eqref{eq15}, there are two main objectives: the first one using the Overcoverage parameter to minimize the number of active sensor nodes in the produced final solution vector $X$ which leads to improve the life time of wireless sensor network. The second goal by using the Undercoverage parameter to maximize the coverage in the region by means of covering each primary point in $SSET^k$.The two objectives are achieved at the same time. The constraint which represented in equation \eqref{eq16} refer to the coverage function for each primary point $P_p$ in $SSET^k$ , where each $P_p$ should be covered by
-%at least one sensor node in $A^k$. The objective function in \eqref{eq15} involving two main objectives to be optimized simultaneously, where optimal decisions need to be taken in the presence of trade-offs between the two conflicting main objectives in \eqref{eq15} and this refer to that our coverage optimization problem is a multi-objective optimization problem and we can use the BPSO to solve it. The concept of Overcoverage and Undercoverage inspired from ~\cite{Fernan12} but we use it with our model as stated in subsection \ref{Sensing Coverage Model} with some modification to be applied later by BPSO.
-%\subsection{Notations and assumptions}
-
-%\begin{itemize}
-%\item $m$ : the number of targets
-%\item $n$ : the number of sensors
-%\item $K$ : maximal number of cover sets
-%\item $i$ : index of target ($i=1..m$)
-%\item $j$ : index of sensor ($j=1..n$)
-%\item $k$ : index of cover set ($k=1..K$)
-%\item $T_0$ : initial set of targets
-%\item $S_0$ : initial set of sensors
-%\item $T $ : set of targets which are not covered by at least one cover set
-%\item $S$ : set of available sensors
-%\item $S_0(i)$ : set of sensors which cover the target $i$
-%\item $T_0(j)$ : set of targets covered by sensor $j$
-%\item $C_k$ : cover set of index $k$
-%\item $T(C_k)$ : set of targets covered by the cover set $k$
-%\item $NS(i)$ : set of available sensors which cover the target $i$
-%\item $NC(i)$ : set of cover sets which do not cover the target $i$
-%\item $|.|$ : cardinality of the set
-
-%\end{itemize}
-
\section{Simulation results}
\label{exp}
\parskip 0pt
\begin{figure}[h!]
\centering
-\includegraphics[scale=0.5]{TheCoverageRatio150g.eps} %\\~ ~ ~(a)
+\includegraphics[scale=0.37]{CR1.eps} %\\~ ~ ~(a)
\caption{The impact of the number of rounds on the coverage ratio for 150 deployed nodes}
\label{fig3}
\end{figure}
\begin{figure}[h!]
\centering
-\includegraphics[scale=0.5]{TheActiveSensorRatio150g.eps} %\\~ ~ ~(a)
+\includegraphics[scale=0.37]{ASR1.eps} %\\~ ~ ~(a)
\caption{The impact of the number of rounds on the active sensors ratio for 150 deployed nodes }
\label{fig4}
\end{figure}
usually continues the optimization process, and this extends the
lifetime of the network.
-\subsection{The impact of the number of rounds on the energy saving ratio}
+\subsection{Impact of the number of rounds on the energy saving ratio}
In this experiment, we consider a performance metric linked to energy.
This metric, called Energy Saving Ratio (ESR), is defined by:
%\centering
% \begin{multicols}{6}
\centering
-\includegraphics[scale=0.5]{TheEnergySavingRatio150g.eps} %\\~ ~ ~(a)
+\includegraphics[scale=0.37]{ESR1.eps} %\\~ ~ ~(a)
\caption{The impact of the number of rounds on the energy saving ratio for 150 deployed nodes}
\label{fig5}
\end{figure}
\begin{figure}[h!]
\centering
-\includegraphics[scale=0.5]{TheNumberofStoppedSimulationRuns150g.eps}
+\includegraphics[scale=0.36]{SR1.eps}
\caption{The percentage of stopped simulation runs compared to the number of rounds for 150 deployed nodes }
\label{fig6}
\end{figure}
\begin{figure}[h!]
\centering
-\includegraphics[scale=0.5]{TheEnergyConsumptiong.eps}
+\includegraphics[scale=0.37]{EC1.eps}
\caption{The energy consumption}
\label{fig7}
\end{figure}
distributed method is clearly required.
\begin{table}[ht]
-\caption{THE EXECUTION TIME(S) VS THE NUMBER OF SENSORS}
+\caption{EXECUTION TIME(S) VS. NUMBER OF SENSORS}
% title of Table
\centering
Finally, we have defined the network lifetime as the time until all
nodes have been drained of their energy or each sensor network
-monitoring an area has become disconnected. In figure~\ref{fig8}, the
+monitoring an area has become disconnected. In figure~\ref{fig8}, the
network lifetime for different network sizes and for both strategy
-with two leaders and the simple heuristic is illustrated.
- We do not consider anymore the centralized strategy with one
- leader, because, as shown above, this strategy results in execution
- times that quickly become unsuitable for a sensor network.
+with two leaders and the simple heuristic is illustrated. We do not
+consider anymore the centralized strategy with one leader, because, as
+shown above, this strategy results in execution times that quickly
+become unsuitable for a sensor network.
\begin{figure}[h!]
%\centering
% \begin{multicols}{6}
\centering
-\includegraphics[scale=0.5]{TheNetworkLifetimeg.eps} %\\~ ~ ~(a)
+\includegraphics[scale=0.37]{LT1.eps} %\\~ ~ ~(a)
\caption{The network lifetime }
\label{fig8}
\end{figure}
As highlighted by figure~\ref{fig8}, the network lifetime obviously
-increases when the size of the network increases, with our approach
-that leads to the larger lifetime improvement. By choosing the best
-suited nodes, for each round, to cover the region of interest and by
+increases when the size of the network increases, with our approach
+that leads to the larger lifetime improvement. By choosing the best
+suited nodes, for each round, to cover the region of interest and by
letting the other ones sleep in order to be used later in next rounds,
-our strategy efficiently prolonges the network lifetime. Comparison shows that
-the larger the sensor number is, the more our strategies outperform
-the simple heuristic. Strategy~2, which uses two leaders, is the best
-one because it is robust to network disconnection in one subregion. It
-also means that distributing the algorithm 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{Conclusion and future works}
+our strategy efficiently prolonges the network lifetime. Comparison
+shows that the larger the sensor number is, the more our strategies
+outperform the simple heuristic. Strategy~2, which uses two leaders,
+is the best one because it is robust to network disconnection in one
+subregion. It also means that distributing the algorithm 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{Conclusion and future work}
\label{sec:conclusion}
-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
+In this paper, we have addressed the problem of the coverage and the
+lifetime optimization in WSNs. 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 multi-rounds coverage protocol
will optimize 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
-protocol in terms of lifetime, coverage ratio, active sensors ratio,
-energy saving, 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 propose 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 protocol, which
-computes all active sensor schedules in one time, using
-optimization methods such as swarms optimization or evolutionary
-algorithms. 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.
+the best representative active nodes. Results from simulations show
+the relevance of the proposed protocol in terms of lifetime, coverage
+ratio, active sensors ratio, energy saving, 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
+propose 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 a coverage protocol which computes all active sensor
+schedules in only one step for many rounds, using optimization methods
+such as swarms optimization or evolutionary algorithms.
% use section* for acknowledgement
%\section*{Acknowledgment}
-
-
-
\bibliographystyle{IEEEtran}
\bibliography{bare_conf}
-
\end{document}
