+
\documentclass[conference]{IEEEtran}
\ifCLASSINFOpdf
-
+
\else
-
+
\fi
\hyphenation{op-tical net-works semi-conduc-tor}
-\usepackage{float}
+
+\usepackage{etoolbox}
+\usepackage{float}
\usepackage{epsfig}
\usepackage{calc}
\usepackage{times,amssymb,amsmath,latexsym}
\usepackage{epsfig}
\usepackage{caption}
\usepackage{multicol}
+\usepackage{times}
+\usepackage{graphicx,epstopdf}
+\epstopdfsetup{suffix=}
+\DeclareGraphicsExtensions{.ps}
+\DeclareGraphicsRule{.ps}{pdf}{.pdf}{`ps2pdf -dEPSCrop -dNOSAFER #1 \noexpand\OutputFile}
\begin{document}
+%
+% paper title
+% can use linebreaks \\ within to get better formatting as desired
+\title{Coverage and Lifetime Optimization in Heterogeneous Energy Wireless Sensor Networks}
-\title{Energy-Efficient Activity Scheduling in Heterogeneous Energy Wireless Sensor Networks}
-
-
-% author names and affiliations
-% use a multiple column layout for up to three different
-% affiliations
-\author{\IEEEauthorblockN{Ali Kadhum Idrees, Karine Deschinkel, Michel Salomon, and Raphael Couturier }
-\IEEEauthorblockA{FEMTO-ST Institute, UMR CNRS, University of Franche-Comt\'e, Belfort, France \\
-Email:$\lbrace$ali.idness, karine.deschinkel, michel.salomon,raphael.couturier$\rbrace$@femto-st.fr}
-%\email{\{ali.idness, karine.deschinkel, michel.salomon, raphael.couturier\}@univ-fcomte.fr}
-%\and
-%\IEEEauthorblockN{Homer Simpson}
-%\IEEEauthorblockA{FEMTO-ST Institute, UMR CNRS, University of Franche-Comte, Belfort, France}
-%\and
-%\IEEEauthorblockN{James Kirk\\ and Montgomery Scott}
-%\IEEEauthorblockA{FEMTO-ST Institute, UMR CNRS, University of Franche-Comte, Belfort, France}
-}
-
+\author{\IEEEauthorblockN{Ali Kadhum Idrees, Karine Deschinkel, Michel Salomon, and Rapha\"el Couturier}
+\IEEEauthorblockA{FEMTO-ST Institute, UMR 6174 CNRS \\
+University of Franche-Comt\'e \\
+Belfort, France\\
+Email: ali.idness@edu.univ-fcomte.fr, $\lbrace$karine.deschinkel, michel.salomon, raphael.couturier$\rbrace$@univ-fcomte.fr}}
\maketitle
\begin{abstract}
One of the fundamental challenges in Wireless Sensor Networks (WSNs)
-is coverage preservation, while extending the network lifetime
-continuously and effectively during monitoring a certain area (or
-region) of interest. In this paper a coverage optimization protocol to
+is the coverage preservation and the extension of the network lifetime
+continuously and effectively when monitoring a certain area (or
+region) of interest. In this paper, a coverage optimization protocol to
improve the lifetime in heterogeneous energy wireless sensor networks
is proposed. The area of interest is first divided into subregions
-using a divide-and-conquer method and then scheduling of sensor node
+using a divide-and-conquer method and then the scheduling of sensor node
activity is planned for each subregion. The proposed scheduling
-considers activity 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
+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
Election, (iii)~Decision, and (iv)~Sensing. The decision process is
-carried out by a leader node which solves an integer program.
+carried out by a leader node, which solves an integer program.
Simulation results show that the proposed approach can prolong the
network lifetime and improve the coverage performance.
\end{abstract}
- %\keywords{Area Coverage, Wireless Sensor Networks, lifetime Optimization, Distributed Protocol.}
+\begin{IEEEkeywords}
+Wireless Sensor Networks, Area Coverage, Network lifetime, Optimization, Scheduling.
+\end{IEEEkeywords}
+%\keywords{Area Coverage, Network lifetime, Optimization, Distributed Protocol}
- \IEEEpeerreviewmaketitle
+\IEEEpeerreviewmaketitle
+
\section{Introduction}
-\noindent Recent years have witnessed significant advances in wireless
-communications and embedded micro-sensing MEMS technologies which have
-made emerge wireless ensor networks as one of the most promising
-technologies~\cite{asc02}. 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 to
-sense its environment, to compute, to store information and to deliver
-report messages to a base station.
-%These sensor nodes run on batteries with limited capacities. To achieve a long life of the network, it is important to conserve battery power. Therefore, lifetime optimisation is one of the most critical issues in wireless sensor networks.
-One of the main design challenges in wireless sensor networks is to
-prolong the network lifetime, while achieving acceptable quality of
-service for applications. Indeed, sensor nodes have limited resources
-in terms of memory, energy and computational power.
-
-%\medskip
-Since sensor nodes have limited battery life and without being able to replace
-batteries, especially in remote and hostile environments,
-it is desirable that a WSN should be deployed with
-high density and thus redundancy can 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. Consequently,
-future software may need to adapt appropriately to achieve acceptable quality of service for applications.
-In this paper we concentrate on area coverage problem, with the objective of maximizing the network lifetime by using an adaptive scheduling. Area of interest is divided into subregions and an activity scheduling for sensor nodes is planned for each subregion.
-Our scheduling scheme works in round which includes a discovery phase to exchange information between sensors of the subregion, then a sensor is chosen in suitable manner to carry out a coverage strategy. This coverage strategy involves the resolution of an integer program which provides the activation of the sensors for the next round.
-
-
-The remainder of the paper is organized as follows.
-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 conducted on OMNET++, that fully demonstrate the usefulness of the proposed approach. Finally, we give concluding remarks in Section~\ref{sec:conclusion}.
-
-\section{\uppercase{Related work}}
-\label{rw}
-\noindent
-This section is dedicated to the various approaches proposed in the literature for the coverage lifetime maximization problem where the objective is to optimally schedule sensors'activities in order to extend network lifetime in a randomly deployed network. As this problem is subject to a wide range of interpretations, we suggest to recall main definitions and assumptions related to our work.
-{\bf Coverage}
+\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 work with the coverage lifetime maximization problem, where the objective is to optimally schedule sensors' activities in
+order to extend network lifetime in WSNS. Authors in \cite{chin2007} propose a novel
+distributed heuristic named Distributed Energy-efficient Scheduling
+for k-coverage (DESK) so that the energy consumption among all the
+sensors is balanced, and network lifetime is maximized while the
+coverage requirement is being maintained. This algorithm works in
+round, requires only 1-sensing-hop-neighbor information, and a sensor
+decides its status (active/sleep) based on the perimeter coverage
+model, which proposed in \cite{Huang:2003:CPW:941350.941367}.
+Shibo et al.\cite{Shibo} studied the coverage problem, which is formulated as a minimum weight submodular set cover problem. To address this problem,
+ a distributed truncated greedy algorithm (DTGA) is proposed. They exploited from the
+temporal and spatialcorrelations among the data sensed by different sensor nodes and leverage
+prediction to extend the WSNs lifetime.
+Bang et al. \cite{Bang} proposed a coverage-aware clustering protocol(CACP), which used computation method for the optimal cluster size to minimize the average energy consumption rate per unit area. They defied in this protocol a cost metric that prefer the redundant sensors
+with higher power as best candidates for cluster heads and select the active sensors that cover the area of interest more efficiently.
+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. We give a brief answer to these three questions
+to describe our approach before going into details in the subsequent
+sections.
%\begin{itemize}
-%\item Area Coverage: The main objective is to cover an area. The area coverage requires
-%that the sensing range of working Active nodes cover the whole targeting area, which means any
-%point in target area can be covered~\cite{Mihaela02,Raymond03}.
-
-%\item Target Coverage: The objective is to cover a set of targets. Target coverage means that the discrete target points can be covered in any time. The sensing range of working Active nodes only monitors a finite number of discrete points in targeting area~\cite{Mihaela02,Raymond03}.
-
-%\item Barrier Coverage An objective to determine the maximal support/breach paths that traverse a sensor field. Barrier coverage is expressed as finding one or more routes with starting position and ending position when the targets pass through the area deployed with sensor nodes~\cite{Santosh04,Ai05}.
+%\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.
+
+%\item
+{\bf What are the rules to decide which node has to be turned on
+ or off?} Our algorithm tends to limit the overcoverage of points of
+ interest to avoid turning on too many sensors covering the same
+ areas at the same time, and tries to prevent undercoverage. The
+ decision is a good compromise between these two conflicting
+ 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.
%\end{itemize}
-The most discussed coverage problems in literature can be classified into two types \cite{} : area coverage and targets coverage. An area coverage problem is to find a minimum number of sensors to work such that each physical point in the area is monitored by at least a working sensor. Target coverage problem is to cover only a finite number of discrete points called targets.
- Our work will concentrate on the area coverage by design and implement a strategy which efficiently select the active nodes that must maintain both sensing coverage and network connectivity and in the same time improve the lifetime of the wireless sensor network. But requiring that all physical points are covered may be too strict, specially where the sensor network is not dense.
-Our approach represents an area covered by a sensor as a set of primary points and tries to maximize the total number of primary points that are covered in each round, while minimizing overcoverage (points covered by multiple active sensors simultaneously).\\
-{\bf Lifetime}\\
-Various definitions exist for the lifetime of a sensor network. Main definitions proposed in the literature are related to the remaining energy of the nodes \cite{} or to the percentage of coverage \cite{}. The lifetime of the network is mainly defined as the amount of time that 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 our simulation we assume that the network is alive until all nodes have been drained of their energy or the sensor network disconnected and we measure the coverage ratio during the process.
-
-{\bf Activity scheduling}\\
-Activity scheduling is to schedule the activation and deactivation of nodes 'sensor units. The basic objective is to decide which sensors are in which states (active or sleeping mode) and for how long a time such that the application coverage requirement can be guaranteed and network lifetime can be prolonged. Various approaches, including centralized, distributed and localized algorithms, have been proposed for activity scheduling. In the distributed algorithms, each node in the network autonomously makes decisions on whether to turn on or turn off itself only using local neighbour information. In centralized algorithms, a central controller (node or base station) informs every sensor of the time intervals to be activated.
-
-{\bf Distributed approaches}
-
-Some distributed algorithms have been developed in~\cite{Gallais06,Tian02,Ye03,Zhang05,HeinzelmanCB02}. Distributed algorithms typically operate in rounds for predetermined duration. At the beginning of each round, a sensor exchange information with its neighbors and makes a decision to either turn on or go to sleep for the round. This decision is basically based on simple greedy criteria like the largest uncovered area \cite{Berman05efficientenergy}, maximum uncovered targets \cite{1240799}.
-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 to its neighbours containing node ID and node location at the beginning of each round. 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 neighbours. A back-off scheme is introduced to let each sensor delay the decision process with a random period of time, in order to avoid that nodes make conflicting decisions simultaneously and that a part of the area is no longer covered.
-\cite{Prasad:2007:DAL:1782174.1782218} propose a model for capturing the dependencies between different cover sets and propose localized heuristic based on this dependency. The algorithm consists of two phases, an initial setup phase during which each sensor calculates and prioritize 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.
-Authors in \cite{chin2007} propose a novel distributed heuristic named distributed Energy-efficient Scheduling for k-coverage (DESK) so that the energy consumption among all the sensors is balanced, and network lifetime is maximized while the coverage requirements being maintained. This algorithm works in round, requires only 1-sensing-hop-neighbour information, and a sensor decides its status (active/sleep) based on its perimeter coverage computed through the k-Non-Unit-disk coverage algorithm proposed in \cite{Huang:2003:CPW:941350.941367}.\\
-
-Some others approaches do not consider synchronized and predetermined period of time where the sensors are active or not. Each sensor maintains its own timer and its time wake-up is randomized \cite{Ye03} or regulated \cite{cardei05} over time.
-%A ecrire \cite{Abrams:2004:SKA:984622.984684}p33
-
-
-%The scheduling information is disseminated throughout the network and only sensors in the active state are responsible
-%for monitoring all targets, while all other nodes are in a low-energy sleep mode. The nodes decide cooperatively which of them will remain in sleep mode for a certain
-%period of time.
-
- %one way of increasing lifeteime is by turning off redundant nodes to sleep mode to conserve energy while active nodes provide essential coverage, which improves fault tolerance.
-
-%In this paper we focus on centralized algorithms because distributed algorithms are outside the scope of our work. Note that centralized coverage algorithms have the advantage of requiring very low processing power from the sensor nodes which have usually limited processing capabilities. Moreover, a recent study conducted in \cite{pc10} concludes 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 localized approach compared to a centralized one.
-
-{\bf Centralized approaches}\\
-Power efficient centralized schemes differ according to several criteria \cite{Cardei:2006:ECP:1646656.1646898}, such as the coverage objective (target coverage or area coverage), the node deployment method (random or deterministic) and the heterogeneity of sensor nodes (common sensing range, common battery lifetime). The major approach is to divide/organize the sensors into a suitable number of set covers where each set completely covers an interest region and to activate these set covers successively.
-
-First algorithms proposed in the literature consider that the cover sets are disjoint: a sensor node appears in exactly one of the generated cover sets. For instance Slijepcevic and Potkonjak \cite{Slijepcevic01powerefficient} propose an algorithm which allocates sensor nodes in mutually independent sets to monitor an area divided into several fields. Their algorithm constructs a cover set by including in priority the sensor nodes which cover critical fields, that is to say fields that are covered by the smallest number of sensors. The time complexity of their heuristic is $O(n^2)$ where $n$ is the number of sensors. ~\cite{cardei02} present
-a graph coloring technique to achieve energy savings
-by organizing the sensor nodes into a maximum number of disjoint
-dominating sets which are activated successively. The dominating
-sets do not guarantee the coverage of the whole region of interest.
-Abrams et al.\cite{Abrams:2004:SKA:984622.984684} design three approximation algorithms for a variation of the set k-cover problem, where the objective is
-to partition the sensors into covers such that the number of
-covers that include an area, summed over all areas, is maximized. Their work builds upon previous work in~\cite{Slijepcevic01powerefficient} and the generated cover sets do not provide complete coverage of the monitoring zone.
-
-
-%examine the target coverage problem by disjoint cover sets but relax the requirement that every cover set monitor all the targets and try to maximize the number of times the targets are covered by the partition. They propose various algorithms and establish approximation ratio.
-
-In~\cite{Cardei:2005:IWS:1160086.1160098}, the authors propose a heuristic to
-compute the disjoint set covers (DSC). In order to compute the maximum number of covers, they
-first transform DSC into a maximum-flow problem ,
-which is then formulated as a mixed integer programming problem
-(MIP). Based on the solution of the MIP, they design a heuristic
-to compute the final number of covers. The results show a slight performance
-improvement in terms of the number of produced DSC in comparison to~\cite{Slijepcevic01powerefficient} but it incurs
-higher execution time due to the complexity of the mixed integer programming resolution.
- %Cardei and Du \cite{Cardei:2005:IWS:1160086.1160098} propose a method to efficiently compute the maximum number of disjoint set covers such that each set can monitor all targets. They first transform the problem into a maximum flow problem which is formulated as a mixed integer programming (MIP). Then their heuristic uses the output of the MIP to compute disjoint set covers. Results show that these heuristic provides a number of set covers slightly larger compared to \cite{Slijepcevic01powerefficient} but with a larger execution time due to the complexity of the mixed integer programming resolution.
-Zorbas et al. \cite{Zorbas2007} present B\{GOP\}, a centralized coverage algorithm introducing sensor candidate categorisation depending on their coverage status and the notion of critical target to call targets that are associated with a small number of sensors. The total running time of their heuristic is $0(m n^2)$ where $n$ is the number of sensors, and $m$ the number of targets. Compared to algorithm's results of Slijepcevic and Potkonjak \cite{Slijepcevic01powerefficient}, their heuristic produces more cover sets with a slight growth rate in execution time.
-%More recently Manju and Pujari\cite{Manju2011}
-
-In the case of non-disjoint algorithms \cite{Manju2011}, sensors may participate in more than one cover set.
-In some cases this may prolong the lifetime of the network in comparison to the disjoint cover set algorithms but designing algorithms for non-disjoint cover sets generally incurs a higher order of complexity. Moreover in case of a sensor's failure, non-disjoint scheduling policies are less resilient and less reliable because a sensor may be involved in more than one cover sets. For instance, Cardei et al.~\cite{cardei05bis} present a linear programming (LP) solution
-and a greedy approach to extend
-the sensor network lifetime by organizing the sensors into a
-maximal number of non-disjoint cover sets. Simulation results show that by allowing sensors to
-participate in multiple sets, the network lifetime
-increases compared with related work~\cite{Cardei:2005:IWS:1160086.1160098}. In~\cite{berman04}, the authors have formulated the lifetime problem and suggested another (LP) technique to solve this problem. A centralized provably near
-optimal solution based on the Garg-K\"{o}nemann algorithm~\cite{garg98} is also proposed.
-
-{\bf Our contribution}
-%{decoupage de la region en sous region, selection de noeud leader, formulation %et resolution du probleme de couverture, planification périodique
-There are three main questions which should be answered to build a scheduling strategy. We give a brief answer to these three questions to describe our approach before going into details in the subsequent sections.
-\begin{itemize}
-\item {\bf How must be planned the
-phases for information exchange, decision and sensing over time?}
-Our algorithm partitions the time line into a number of 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 turn on or off?}
-Our algorithm tends to limit the overcoverage of points of interest to avoid turning on too much sensors covering the same areas at the same time, and tries to prevent undercoverage. The decision is a good compromise between these two conflicting objectives.
-\item {\bf Which node should make such 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} concludes 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 localized approach compared to a centralized one. Our work does not consider only one leader to compute and to broadcast the schedule decision to all the sensors. When the size of network increases, the network is divided in many subregions and the decision is made by a leader in each subregion.
-\end{itemize}
+\section{Activity scheduling}
+\label{pd}
+We consider a randomly and uniformly deployed network consisting of
+static wireless sensors. The wireless sensors are deployed in high
+density to ensure initially a full coverage of the interested area. We
+assume that all nodes are homogeneous in terms of communication and
+processing capabilities and heterogeneous in term of energy provision.
+The location information is available to the sensor node either
+through hardware such as embedded GPS or through location discovery
+algorithms. The area of interest can be divided using the
+divide-and-conquer strategy into smaller areas called subregions and
+then our coverage protocol will be implemented in each subregion
+simultaneously. Our protocol works in rounds fashion as shown in
+figure~\ref{fig1}.
- \section{\uppercase{Activity scheduling}}
-\label{pd}
-We consider a randomly and uniformly deployed network consisting of static wireless sensors. The wireless sensors are deployed in high density to ensure initially a full coverage of the interested area. We assume that all nodes are homogeneous in terms of communication and processing capabilities and heterogeneous in term of energy. The location information is available to the sensor node either through hardware such as embedded GPS or through location discovery algorithms.
-The area of interest can be divided using the divide-and-conquer strategy into smaller area called subregions and then our coverage protocol will be implemented in each subregion simultaneously. Our protocol works in rounds fashion as in figure \ref{fig:4}.
%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=70mm]{FirstModel.eps}
-\caption{Multi-Round Coverage Protocol}
-\label{fig:4}
+\includegraphics[width=85mm]{FirstModel.eps} % 70mm
+\caption{Multi-round coverage protocol}
+\label{fig1}
\end{figure}
-Each round is divided into 4 phases : Information (INFO) Exchange, Leader Election, Decision, and Sensing. For each round there is exactly one set cover responsible for sensing task. This protocol is more reliable against the unexpectedly node failure because it works into rounds, and if the node failure is detected before taking the decision, the node will not participate in decision and if the node failure occurs after the decision, the sensing task of the network will be affected temporarily only during the period of sensing until starting new round, since a new set cover will take charge of the sensing task in the next round. The energy consumption and some other constraints can easily be taken into account since the sensors can update and then exchange the information (including their residual energy) at the beginning of each round. However, the preprocessing phase (INFO Exchange, leader Election, Decision) are energy consuming for some nodes even when they not join the network to monitor the area. We describe each phase in more detail.
-
-\subsection{\textbf INFO Exchange Phase}
-
-Each sensor node $j$ sends its position, remaining energy $RE_j$, number of local neighbours $NBR_j$ to all wireless sensor nodes in its subregion by using INFO packet and listen to the packets sent from other nodes. After that, each node will have information about all the sensor nodes in the subregion. In our model, the remaining energy corresponds to the time that a sensor can live in the active mode.
-
+Each round is divided into 4 phases : Information (INFO) Exchange,
+Leader Election, Decision, and Sensing. For each round there is
+exactly one set cover responsible for the sensing task. This protocol is
+more reliable against an unexpected node failure because it works
+in rounds. On the one hand, if a node failure is detected before
+making the decision, the node will not participate to this phase, and,
+on the other hand, if the node failure occurs after the decision, the
+sensing task of the network will be temporarily affected: only during
+the period of sensing until a new round starts, since a new set cover
+will take charge of the sensing task in the next round. The energy
+consumption and some other constraints can easily be taken into
+account since the sensors can update and then exchange their
+information (including their residual energy) at the beginning of each
+round. However, the pre-sensing phases (INFO Exchange, Leader
+Election, Decision) are energy consuming for some nodes, even when
+they do not join the network to monitor the area. Below, we describe
+each phase in more details.
+
+\subsection{Information exchange phase}
+
+Each sensor node $j$ sends its position, remaining energy $RE_j$, and
+the number of local neighbours $NBR_j$ to all wireless sensor nodes in
+its subregion by using an INFO packet and then listens to the packets
+sent from other nodes. After that, each node will have information
+about all the sensor nodes in the subregion. In our model, the
+remaining energy corresponds to the time that a sensor can live in the
+active mode.
%\subsection{\textbf Working Phase:}
%The working phase works in rounding fashion. Each round include 3 steps described as follow :
-\subsection{\textbf Leader Election Phase}
-This step includes choosing the Wireless Sensor Node Leader (WSNL) which will be responsible of executing coverage algorithm to choose the list of active sensor nodes that contribute in covering the subregion.
-All the sensor nodes cooperates to select WSNL. After the phase of information exchange , each sensor have all information about the other nodes in the same subregion, after that each node will execute the leader election procedure to determine who is the leader?(each node will know who is the leader) where all the nodes in the same subregion will select the same leader based on the received information from all other nodes in the same subregion.The leader will be selected as follow: It will select the node that have maximum number of neighbour as a leader.If there are more than one node have the same maximum number of neighbours , it will take all these nodes and then select the node that have larger remaining energy. If there are more than one node have the same maximum number of neighbours and the same remaining energy then it will select the node with larger index among them. Each subregion in the area of interest will select its own WSNL independently for each round.
-
-\subsection{\textbf Decision Phase}
-The WSNL will solve an integer program (see section \ref{cp}) to select which sensors will be activated in the next round to cover the subregion. WSNL will send Active-Sleep packet to each sensor in the subregion based on algorithm's results.
+\subsection{Leader election phase}
+This step includes choosing the Wireless Sensor Node Leader (WSNL),
+which will be responsible for executing the coverage algorithm. Each
+subregion in the area of interest will select its own WSNL
+independently for each round. All the sensor nodes cooperate to
+select WSNL. The nodes in the same subregion will select the leader
+based on the received information from all other nodes in the same
+subregion. The selection criteria in order of priority are: larger
+number of neighbours, larger remaining energy, and then in case of
+equality, larger index.
+
+\subsection{Decision phase}
+The WSNL will solve an integer program (see section~\ref{cp}) to
+select which sensors will be activated in the following sensing phase
+to cover the subregion. WSNL will send Active-Sleep packet to each
+sensor in the subregion based on the algorithm's results.
%The main goal in this step after choosing the WSNL is to produce the best representative active nodes set that will take the responsibility of covering the whole region $A^k$ with minimum number of sensor nodes to prolong the lifetime in the wireless sensor network. For our problem, in each round we need to select the minimum set of sensor nodes to improve the lifetime of the network and in the same time taking into account covering the region $A^k$ . We need an optimal solution with tradeoff between our two conflicting objectives.
%The above region coverage problem can be formulated as a Multi-objective optimization problem and we can use the Binary Particle Swarm Optimization technique to solve it.
-\\
-
-\subsection{\textbf Sensing Phase}
- Active sensors in the round will execute their sensing task to preserve maximal coverage in the region of interest. We will assume that the cost of keeping a node awake (or sleep) for sensing task is the same for all wireless sensor nodes in the network. Each sensor received Active-Sleep packet will go to awake or sleep for a time equal to the period of sensing until starting new round.
-
+\subsection{Sensing phase}
+Active sensors in the round will execute their sensing task to
+preserve maximal coverage in the region of interest. We will assume
+that the cost of keeping a node awake (or asleep) for sensing task is
+the same for all wireless sensor nodes in the network. Each sensor
+will receive an Active-Sleep packet from WSNL informing it to stay
+awake or to go to sleep for a time equal to the period of sensing until
+starting a new round.
%\subsection{Sensing coverage model}
%\label{pd}
%\noindent We try to produce an adaptive scheduling which allows sensors to operate alternatively so as to prolong the network lifetime. For convenience, the notations and assumptions are described first.
%The wireless sensor node use the binary disk sensing model by which each sensor node will has a certain sensing range is reserved within a circular disk called radius $R_s$.
-\noindent We consider a boolean disk coverage model which is the most 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 of the sensing range. In fact, Zhang and Zhou ~\cite{Zhang05} prove that if the transmission range is at least twice of the sensing range, a complete coverage of a convex area implies connectivity among the working nodes in the active mode.
+\indent We consider a boolean disk coverage model which is the most
+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}:
%\begin{figure}[h!]
%We choose to representEach wireless sensor node will be represented into a selected number of primary points by which we can know if the sensor node is covered or not.
% Figure ~\ref{fig:cluster2} shows the selected primary points that represents the area of the sensor node and according to the sensing range of the wireless sensor node.
-\noindent Instead of working with area coverage, we consider for each sensor a set of points called primary points. And we assume the sensing disk defined by a sensor is covered if all primary points of this sensor are covered.
-
+\indent Instead of working with the coverage area, we consider for each
+sensor a set of points called primary points. We also assume that the
+sensing disk defined by a sensor is covered if all the primary points of
+this sensor are covered.
%\begin{figure}[h!]
%\centering
%\begin{tabular}{cc}
%\caption{Wireless Sensor Node Area Coverage Model.}
%\label{fig:cluster2}
%\end{figure}
-
-
-
-\noindent By knowing the position (point center :($p_x,p_y$) of the wireless sensor node and its $R_s$ , we calculate the primary points directly based on proposed model. We use these primary points (that can be increased or decreased as if it is necessary) as references to ensure that the monitoring area of the region is covered by the selected set of sensors instead of using the all points in the area.
-
- \begin{figure}[h!]
-%\centering
-% \begin{multicols}{6}
-\centering
-%\includegraphics[scale=0.10]{fig21.pdf}\\~ ~ ~(a)
-%\includegraphics[scale=0.10]{fig22.pdf}\\~ ~ ~(b)
-\includegraphics[scale=0.2]{principles13.eps}
-%\includegraphics[scale=0.10]{fig25.pdf}\\~ ~ ~(d)
-%\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 }
-\label{fig3}
-\end{figure}
-
-\noindent We can calculate the positions of the selected primary points in the circle disk of the sensing range of wireless sensor node in figure ~\ref{fig3} as follow:\\
-$p_x,p_y$ = point center of wireless sensor node. \\
+By knowing the position (point center: ($p_x,p_y$)) of a wireless
+sensor node and its $R_s$, we calculate the primary points directly
+based on the proposed model. We use these primary points (that can be
+increased or decreased if necessary) as references to ensure that the
+monitored region of interest is covered by the selected set of
+sensors, instead of using all the points in the area.
+
+\indent We can calculate the positions of the selected primary
+points in the circle disk of the sensing range of a wireless sensor
+node (see figure~\ref{fig2}) as follows:\\
+$(p_x,p_y)$ = point center of wireless sensor node\\
$X_1=(p_x,p_y)$ \\
$X_2=( p_x + R_s * (1), p_y + R_s * (0) )$\\
$X_3=( p_x + R_s * (-1), p_y + R_s * (0)) $\\
$X_{10}=( p_x + R_s * (\frac{-\sqrt{2}}{2}), p_y + R_s * (\frac{\sqrt{2}}{2})) $\\
$X_{11}=( p_x + R_s * (\frac{\sqrt{2}}{2}), p_y + R_s * (\frac{\sqrt{2}}{2})) $\\
$X_{12}=( p_x + R_s * (0), p_y + R_s * (\frac{\sqrt{2}}{2})) $\\
-$X_{13}=( p_x + R_s * (0), p_y + R_s * (\frac{-\sqrt{2}}{2})) $\\
-
-
+$X_{13}=( p_x + R_s * (0), p_y + R_s * (\frac{-\sqrt{2}}{2})) $.
+ \begin{figure}[h!]
+%\centering
+% \begin{multicols}{6}
+\centering
+%\includegraphics[scale=0.10]{fig21.pdf}\\~ ~ ~(a)
+%\includegraphics[scale=0.10]{fig22.pdf}\\~ ~ ~(b)
+\includegraphics[scale=0.25]{principles13.eps}
+%\includegraphics[scale=0.10]{fig25.pdf}\\~ ~ ~(d)
+%\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}
+\label{fig2}
+\end{figure}
-\section{\uppercase{Coverage problem formulation}}
+\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}:\\
-
-\noindent 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 propose a integer program which forces undercoverage and overcoverage of targets to become minimal at the same time. They use binary variables $x_{s,l}$ to indicate if the sensor $s$ belongs to cover set $l$. In our model, we consider binary variables $X_{j}$ which determine the activation of sensor $j$ in the round. We also consider primary points as targets. The set of primary points is denoted by P, and the set of sensors by J. \\
-\noindent For a primary point $p$, let $\alpha_{jp}$ denote the indicator function of whether the point $p$ is covered, that is, \\
+\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
+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 variables $X_{j}$, which determine the
+activation of sensor $j$ in the sensing phase of the round. We also
+consider primary points as targets. The set of primary points is
+denoted by $P$ and the set of sensors by $J$.
+
+\noindent For a primary point $p$, let $\alpha_{jp}$ denote the
+indicator function of whether the point $p$ is covered, that is:
\begin{equation}
\alpha_{jp} = \left \{
\begin{array}{l l}
1 & \mbox{if the primary point $p$ is covered} \\
- & \mbox{by active sensor node $j$} \\
- 0 & \mbox{Otherwise}\\
+ & \mbox{by sensor node $j$}, \\
+ 0 & \mbox{otherwise.}\\
\end{array} \right.
%\label{eq12}
\end{equation}
-The number of sensors that are covering point $p$ is equal to $\sum_{j \in J} \alpha_{jp} * X_{j}$ where :
+The number of active sensors that cover the primary point $p$ is equal
+to $\sum_{j \in J} \alpha_{jp} * X_{j}$ where:
\begin{equation}
X_{j} = \left \{
\begin{array}{l l}
- 1& \mbox{if sensor $j$ is active} \\
- 0 & \mbox{otherwise}\\
+ 1& \mbox{if sensor $j$ is active,} \\
+ 0 & \mbox{otherwise.}\\
\end{array} \right.
%\label{eq11}
\end{equation}
-We define the Overcoverage variable $\Theta_{p}$ .\\
-
+We define the Overcoverage variable $\Theta_{p}$ as:
\begin{equation}
\Theta_{p} = \left \{
\begin{array}{l l}
- 0 & \mbox{if point p is not covered}\\
- \left( \sum_{j \in J} \alpha_{jp} * X_{j} \right)- 1 & \mbox{otherwise}\\
+ 0 & \mbox{if the primary point}\\
+ & \mbox{$p$ is not covered,}\\
+ \left( \sum_{j \in J} \alpha_{jp} * X_{j} \right)- 1 & \mbox{otherwise.}\\
\end{array} \right.
\label{eq13}
\end{equation}
-
-
-\noindent$\Theta_{p}$ represents the number of active sensor nodes minus one that cover the primary point $p$.\\
-The Undercoverage variable $U_{p}$ of the primary point $p$ is defined as follow :\\
-
+\noindent More precisely, $\Theta_{p}$ represents the number of active
+sensor nodes minus one that cover the primary point $p$.\\
+The Undercoverage variable $U_{p}$ of the primary point $p$ is defined
+by:
\begin{equation}
U_{p} = \left \{
\begin{array}{l l}
- 1 &\mbox{if point } $p$ \mbox{ is not covered} \\
- 0 & \mbox{otherwise}\\
+ 1 &\mbox{if the primary point $p$ is not covered,} \\
+ 0 & \mbox{otherwise.}\\
\end{array} \right.
\label{eq14}
\end{equation}
-\noindent Our coverage optimization problem can be formulated as follow.\\
+\noindent Our coverage optimization problem can then be formulated as follows\\
\begin{equation} \label{eq:ip2r}
\left \{
\begin{array}{ll}
\right.
\end{equation}
\begin{itemize}
-\item $X_{j}$ : indicating whether or not sensor $j$ is active in the round (1 if yes and 0 if not)
-\item $\Theta_{p}$ : {\it overcoverage}, the number of sensors minus one that are covering point $p$
-\item $U_{p}$ : {\it undercoverage}, indicating whether or not point $p$ is being covered (1 if not covered and 0 if covered)
+\item $X_{j}$ : indicates whether or not the sensor $j$ is actively
+ sensing in the round (1 if yes and 0 if not);
+\item $\Theta_{p}$ : {\it overcoverage}, the number of sensors minus
+ one that are covering the primary point $p$;
+\item $U_{p}$ : {\it undercoverage}, indicates whether or not the primary point
+ $p$ is being covered (1 if not covered and 0 if covered).
\end{itemize}
-The first group of constraints indicates that some point $p$ should be covered by at least one sensor and, if it is not always the case, overcoverage and undercoverage variables help balance the restriction equation by taking positive values. Second group of contraints ensures for each sensor that the amount of energy consumed during its activation periods will be less than or equal to its remaining energy.
-There are two main objectives. We limit overcoverage of primary points in order to activate a minimum number of sensors and we prevent that parts of the subregion are not monitored by minimizing undercoverage. The weights $w_{\theta}$ and $w_{U}$ must be properly chosen so as to guarantee that the maximum number of points are covered during each round.
+
+The first group of constraints indicates that some primary point $p$
+should be covered by at least one sensor and, if it is not always the
+case, overcoverage and undercoverage variables help balancing the
+restriction equations by taking positive values. There are two main
+objectives. First, we limit the overcoverage of primary points in order to
+activate a minimum number of sensors. Second we prevent the absence of monitoring on
+ some parts of the subregion by minimizing the undercoverage. The
+weights $w_\theta$ and $w_U$ must be properly chosen so as to
+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.
%\item $|.|$ : cardinality of the set
%\end{itemize}
-\section{\uppercase{Simulation Results}}
+
+\section{Simulation results}
\label{exp}
-In this section, we conducted a series of simulations to evaluate the efficiency of our approach
-based on the discrete event simulator OMNeT++ (http://www.omnetpp.org/). We conduct simulations for five
-different densities varying from 50 to 250 nodes. Experimental results were obtained from randomly generated
-networks in which nodes are deployed over a $ 50\times25(m^2) $sensing field. For each network deployment, we
-assume that the deployed nodes can fully cover the sensing field with the given sensing range. 10 simulation runs are performed with different network topologies. The results presented hereafter are the average of these 10 runs. Simulation ends when there all the nodes are dead or the sensor network becomes disconnected (some nodes may not be able to sent to a base station an event they sense) . Our proposed coverage protocol use the Radio energy dissipation model that defined by~\cite{HeinzelmanCB02} as energy consumption model by each wireless sensor node for transmitting and receiving the packets in the network. The energy of each node in the network is initialized randomly within the range 24-60 joules, and each sensor will consumes 0.2 watts during the sensing period of 60 seconds. Each active node will consumes 12 joules during sensing phase and each sleep node will consume 0.002 joules. Each sensor node will not participate in the next round if it's remaining energy less than 12 joules. In all experiments the parameters are given by $R_s = 5m $ , $ w_{\Theta} =1$ and $w_{U} = |P^2|$.
-We evaluate the efficiency of our approach using some performance metrics such as : coverage ratio, number of
-active nodes ratio, energy saving ratio, Energy Consumption,network lifetime, execution time and the number of stopped simulation runs.
-Our approach is called Strategy (with Two Leaders) will be compared with two approaches: The first one called Strategy (with One Leader) that use the same our approach method but it implemented in $ 50\times25(m^2) $sensing field with one leader. The second method called Simple Heuristic which consists in dividing uniformly the region into squares $(5 * 5)m^2$ . During the pre-sensing phase, in each square, a sensor is chosen randomly, and will be turned on for the next round.
-In our simulation the sensing field is subdivided into two subregions each one equal to $ 25\times25)m^2 $ of the sensing field.
-
-\subsection{The impact of the Number of Rounds on Coverage Ratio:}
-In this experiment,the Coverage ratio measures how much area of a sensor field is covered. In our case, the coverage ratio is regarded as the number of primary points covered among the set of all primary points within the field. Fig. \ref{fig3} shows the impact of the number of rounds on the average coverage ratio for 150 deployed nodes for the three approaches.
-The comparison shows that the Strategy (with One Leader) gives the same or better than the Strategy (with Two Leaders) for rounds from 1 to 14. after that the Strategy (with One Leader) will suffer from the sensor network becomes disconnected more than Strategy (with Two Leaders) leads to give the advantage for Strategy (with Two Leaders) that will give better coverage and more network lifetime for the rest last rounds because the Strategy (with Two Leaders) subdivide the region into 2 subregions and if on of the two subregion becomes disconnected, it not leads to stop the the responsibility of coverage optimization in the other subregion.
+
+In this section, we conducted a series of simulations to evaluate the
+efficiency and the relevance of our approach, using the discrete event
+simulator OMNeT++ \cite{varga}. We performed simulations for five
+different densities varying from 50 to 250~nodes. Experimental results
+were obtained from randomly generated networks in which nodes are
+deployed over a $(50 \times 25)~m^2 $ sensing field.
+More precisely, the deployment is controlled at a coarse scale in
+ order to ensure that the deployed nodes can fully cover the sensing
+ field with the given sensing range.
+10~simulation runs are performed with
+different network topologies for each node density. The results
+presented hereafter are the average of these 10 runs. A simulation
+ends when all the nodes are dead or the sensor network becomes
+disconnected (some nodes may not be able to send, to a base station, an
+event they sense).
+
+Our proposed coverage protocol uses the radio energy dissipation model
+defined by~\cite{HeinzelmanCB02} as energy consumption model for each
+wireless sensor node when transmitting or receiving packets. The
+energy of each node in a network is initialized randomly within the
+range 24-60~joules, and each sensor node will consume 0.2 watts during
+the sensing period, which will last 60 seconds. Thus, an
+active node will consume 12~joules during the sensing phase, while a
+sleeping node will use 0.002 joules. Each sensor node will not
+participate in the next round if its remaining energy is less than 12
+joules. In all experiments, the parameters are set as follows:
+$R_s=5~m$, $w_{\Theta}=1$, and $w_{U}=|P^2|$.
+
+We evaluate the efficiency of our approach by using some performance
+metrics such as: coverage ratio, number of active nodes ratio, energy
+saving ratio, energy consumption, network lifetime, execution time,
+and number of stopped simulation runs. Our approach called strategy~2
+(with two leaders) works with two subregions, each one having a size
+of $(25 \times 25)~m^2$. Our strategy will be compared with two other
+approaches. The first one, called strategy~1 (with one leader), works
+as strategy~2, but considers only one region of $(50 \times 25)$ $m^2$
+with only one leader. The other approach, called Simple Heuristic,
+consists in uniformly dividing the region into squares of $(5 \times
+5)~m^2$. During the decision phase, in each square, a sensor is
+randomly chosen, it will remain turned on for the coming sensing
+phase.
+
+\subsection{The impact of the number of rounds on the coverage ratio}
+
+In this experiment, the coverage ratio measures how much the area of a
+sensor field is covered. In our case, the coverage ratio is regarded
+as the number of primary points covered among the set of all primary
+points within the field. Figure~\ref{fig3} shows the impact of the
+number of rounds on the average coverage ratio for 150 deployed nodes
+for the three approaches. It can be seen that the three approaches
+give similar coverage ratios during the first rounds. From the
+9th~round the coverage ratio decreases continuously with the simple
+heuristic, while the two other strategies provide superior coverage to
+$90\%$ for five more rounds. Coverage ratio decreases when the number
+of rounds increases due to dead nodes. Although some nodes are dead,
+thanks to strategy~1 or~2, other nodes are preserved to ensure the
+coverage. Moreover, when we have a dense sensor network, it leads to
+maintain the full coverage for a larger number of rounds. Strategy~2 is
+slightly more efficient than strategy 1, because strategy~2 subdivides
+the region into 2~subregions and if one of the two subregions becomes
+disconnected, the coverage may be still ensured in the remaining
+subregion.
+
\parskip 0pt
\begin{figure}[h!]
-%\centering
-% \begin{multicols}{6}
\centering
-\includegraphics[scale=0.5]{TheCoverageRatio150.pdf} %\\~ ~ ~(a)
-
-\caption{The impact of the Number of Rounds on Coverage Ratio for 150 deployed nodes }
+\includegraphics[scale=0.5]{TheCoverageRatio150g.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
-% \begin{multicols}{6}
-\centering
-%\includegraphics[scale=0.10]{fig21.pdf}\\~ ~ ~(a)
-%\includegraphics[scale=0.10]{fig22.pdf}\\~ ~ ~(b)
-\includegraphics[scale=0.5]{TheCoverageRatio250.pdf} %\\~ ~ ~(a)
-%\includegraphics[scale=0.5]{CR2R2L_2.eps} %\\~ ~ ~(b)
-%\includegraphics[scale=0.10]{fig26.pdf}\\~ ~ ~(e)
-%\includegraphics[scale=0.10]{fig27.pdf}\\~ ~ ~(f)
-%\end{multicols}
-\caption{The impact of the Number of Rounds on Coverage Ratio for 250 deployed nodes }
-\label{fig4}
-\end{figure}
-
-Fig. \ref{fig4} represents the average coverage ratio provided by
-Strategy (with Two Leaders),Strategy (with One Leader) and Simple Heuristic for 250 deployed nodes while
-varying the number of rounds. We made the same observation as in Fig. \ref{fig3}, i.e. Strategy (with One Leader) guarantee a good coverage in the beginning the same or equal to Strategy (with Two Leaders) then when the number of rounds increases, the coverage ratio decreases due to network becomes disconnected. Meanwhile,the Strategy (with Two Leaders) ensures better coverage despite the variation in rounds number.\\
-\parskip 0pt
-As shown in Fig. \ref{fig3} and Fig. \ref{fig4},the Strategy (with Two Leaders) gives a full average coverage ratio or more than 90\% in the first rounds and then it decreases when the number of rounds increases due to dead nodes.Although some nodes are dead, sensor activity scheduling in each subregion choose other nodes to ensure the coverage. Moreover, when we have a dense sensor network, it leads to maintain the full coverage for larger number of rounds.\\
-
-\subsection{The impact of the Number of Rounds on Active Sensor Ratio:}
-It is important to have as few active nodes as possible in each round in order to minimize the communication
-overhead and maximize the network lifetime. The Active Sensor Ratio(\%) = ((the no. of active sensor during this round) / (Total number of sensors in the network for the subregion)) * 100. Fig. \ref{fig5} and \ref{fig6} shows the average number of active nodes ratio versus rounds for 150 and 250 deployed nodes respectively.
+\subsection{The impact of the number of rounds on the active sensors ratio}
+
+It is important to have as few active nodes as possible in each round,
+in order to minimize the communication overhead and maximize the
+network lifetime. This point is assessed through the Active Sensors
+Ratio (ASR), which is defined as follows:
+\begin{equation*}
+\scriptsize
+\mbox{ASR}(\%) = \frac{\mbox{Number of active sensors
+during the current sensing phase}}{\mbox{Total number of sensors in the network
+for the region}} \times 100.
+\end{equation*}
+Figure~\ref{fig4} shows the average active nodes ratio versus rounds
+for 150 deployed nodes.
\begin{figure}[h!]
-%\centering
-% \begin{multicols}{6}
\centering
-\includegraphics[scale=0.5]{TheActiveSensorRatio150.pdf} %\\~ ~ ~(a)
-\caption{The impact of the Number of Rounds on Active Sensor Ratio for 150 deployed nodes }
-\label{fig5}
-\end{figure}
-\begin{figure}[h!]
-%\centering
-% \begin{multicols}{6}
-\centering
-\includegraphics[scale=0.46]{TheActiveSensorRatio250.pdf} %\\~ ~ ~(a)
-\caption{The impact of the Number of Rounds on Active Sensor Ratio for 250 deployed nodes }
-\label{fig6}
+\includegraphics[scale=0.5]{TheActiveSensorRatio150g.eps} %\\~ ~ ~(a)
+\caption{The impact of the number of rounds on the active sensors ratio for 150 deployed nodes }
+\label{fig4}
\end{figure}
-The results in Fig. \ref{fig5} shows the superior of the Strategy (with Two Leaders) and the Strategy (with One Leader) on Simple Heuristic. The Strategy (with One Leader) uses minimum number of active nodes than the Strategy (with Two Leaders) until the last rounds because it uses central control on all the sensing field , the advantage of the Strategy (with Two Leaders) approach is that even if a network is disconnected in a one subregion the other one usually continues the optimization and this leads to extend the lifetime of the network.
-In Fig. \ref{fig6}, we see the same observation that we saw on fig. \ref{fig5} but in the last rounds the Strategy (with Two Leaders) will be the better because the effect of disconnected network increases and it becomes near or equal to the Strategy (with One Leader) leads to give minimum average of active nodes.
-
-\subsection{The impact of the Number of Rounds on Energy Saving Ratio:}
-
-In this experiment, the Energy saving ratio ESR(\%) =( (No. of alive sensors in the network during this round) / (total number of sensors in the network for the subregion)) * 100. Fig. \ref{fig5} and \ref{fig6} shows the average number of active nodes ratio versus rounds for all three approach and for 150 and 250 deployed nodes respectively.
+The results presented in figure~\ref{fig4} show the superiority of
+both proposed strategies, the strategy with two leaders and the one
+with a single leader, in comparison with the simple heuristic. The
+strategy with one leader uses less active nodes than the strategy with
+two leaders until the last rounds, because it uses central control on
+the whole sensing field. The advantage of the strategy~2 approach is
+that even if a network is disconnected in one subregion, the other one
+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}
+
+In this experiment, we consider a performance metric linked to energy.
+This metric, called Energy Saving Ratio (ESR), is defined by:
+\begin{equation*}
+\scriptsize
+\mbox{ESR}(\%) = \frac{\mbox{Number of alive sensors during this round}}
+{\mbox{Total number of sensors in the network for the region}} \times 100.
+\end{equation*}
+The longer the ratio is, the more redundant sensor nodes are
+switched off, and consequently the longer the network may live.
+Figure~\ref{fig5} shows the average Energy Saving Ratio versus rounds
+for all three approaches and for 150 deployed nodes.
\begin{figure}[h!]
%\centering
% \begin{multicols}{6}
\centering
-\includegraphics[scale=0.5]{TheEnergySavingRatio150.pdf} %\\~ ~ ~(a)
-\caption{The impact of the Number of Rounds on Energy Saving Ratio for 150 deployed nodes }
+\includegraphics[scale=0.5]{TheEnergySavingRatio150g.eps} %\\~ ~ ~(a)
+\caption{The impact of the number of rounds on the energy saving ratio for 150 deployed nodes}
\label{fig5}
\end{figure}
+The simulation results show that our strategies allow to efficiently
+save energy by turning off some sensors during the sensing phase. As
+expected, the strategy with one leader is usually slightly better than
+the second strategy, because the global optimization permits to turn
+off more sensors. Indeed, when there are two subregions more nodes
+remain awake near the border shared by them. Note that again as the
+number of rounds increases the two leaders' strategy becomes the most
+performing one, since it takes longer to have the two subregion networks
+simultaneously disconnected.
+
+\subsection{The percentage of stopped simulation runs}
+
+We will now study the percentage of simulations, which stopped due to
+network disconnections per round for each of the three approaches.
+Figure~\ref{fig6} illustrates the percentage of stopped simulation
+runs per round for 150 deployed nodes. It can be observed that the
+simple heuristic is the approach, which stops first because the nodes
+are randomly chosen. Among the two proposed strategies, the
+centralized one first exhibits network disconnections. Thus, as
+explained previously, in case of the strategy with several subregions
+the optimization effectively continues as long as a network in a
+subregion is still connected. This longer partial coverage
+optimization participates in extending the network lifetime.
+
\begin{figure}[h!]
-%\centering
-% \begin{multicols}{6}
\centering
-\includegraphics[scale=0.46]{TheEnergySavingRatio250.pdf} %\\~ ~ ~(a)
-\caption{The impact of the Number of Rounds on Energy Saving Ratio for 150 deployed nodes }
+\includegraphics[scale=0.5]{TheNumberofStoppedSimulationRuns150g.eps}
+\caption{The percentage of stopped simulation runs compared to the number of rounds for 150 deployed nodes }
\label{fig6}
\end{figure}
-Simulation results explain the efficiency of the Strategy (with Two Leaders) to save the energy during larger number of rounds that seems to be very near the central approach (Strategy (with One Leader))which it be better in general.
-
-\subsection{The Network Lifetime:}
-we can define the network lifetime as the time until all nodes have been drained of their energy or the sensor network disconnected. In Fig. \ref{fig7}, the network lifetime for different network sizes and for the three approaches is illustrated.
+\subsection{The energy consumption}
+
+In this experiment, we study the effect of the multi-hop communication
+protocol on the performance of the strategy with two leaders and
+compare it with the other two approaches. The average energy
+consumption resulting from wireless communications is calculated
+by taking into account the energy spent by all the nodes when transmitting and
+receiving packets during the network lifetime. This average value,
+which is obtained for 10~simulation runs, is then divided by the
+average number of rounds to define a metric allowing a fair comparison
+between networks having different densities.
+
+Figure~\ref{fig7} illustrates the energy consumption for the different
+network sizes and the three approaches. The results show that the
+strategy with two leaders is the most competitive from the energy
+consumption point of view. A centralized method, like the strategy
+with one leader, has a high energy consumption due to many
+communications. In fact, a distributed method greatly reduces the
+number of communications thanks to the partitioning of the initial
+network in several independent subnetworks. Let us notice that even if
+a centralized method consumes far more energy than the simple
+heuristic, since the energy cost of communications during a round is a
+small part of the energy spent in the sensing phase, the
+communications have a small impact on the network lifetime.
\begin{figure}[h!]
-%\centering
-% \begin{multicols}{6}
\centering
-\includegraphics[scale=0.46]{TheNetworkLifetime.pdf} %\\~ ~ ~(a)
-\caption{The Network Lifetime }
+\includegraphics[scale=0.5]{TheEnergyConsumptiong.eps}
+\caption{The energy consumption}
\label{fig7}
\end{figure}
-As shown in fig. \ref{fig7}, the network lifetime increase when the size of the network increase because the efficient of our approach in choosing the best representative nodes that will cover all the subregion and let the others nodes to sleep to be used later in the next rounds. Comparison shows that our approach is better than the other two methods in improving the network lifetime and this shows us by distributing the algorithm in each node in the network and subdivide the sensing field into many subregions to be managed independently and simultaneously can be more powerful against the sensor network disconnected in some subregions leads to maximize the lifetime of the network obviously.
-
-\subsection{The Energy Consumption:}
-In this experiment, we study the effect of the multi-hop communication protocol on the performance of our approach and compare it with other two approaches. The average energy consumption calculated based only on the energy consumed by transmitting and receiving packets by all sensor nodes in the network and during the lifetime of the network for 10 simulation runs divided by the average number of rounds and for different sizes of the network.We took the total energy consumption in both subregions for Strategy (with Two Leaders) and Simple heuristic. Fig. \ref{fig8} illustrates the Energy Consumption for different network sizes and for the three approaches.
-
-\begin{figure}[h!]
-\centering
-\includegraphics[scale=0.46]{TheEnergyConsumption.pdf}
-\caption{The Energy Consumption }
-\label{fig8}
-\end{figure}
-
-The results show that our approach consume less energy during the lifetime of the network by using multi-hop communication protocol in comparison with other two approaches especially Strategy (with One Leader) in spite of our approach make the network live for a longer time.
-
-\subsection{The impact of Number of Sensors on Execution Time:}
-It is important to have time efficient algorithm to be executed in sensor node because the limited resources in the sensor node. We took the total Execution Time of algorithms in both subregions for Strategy (with Two Leaders) and Simple heuristic. Table \ref{table1} exhibits the execution time for three approaches using different number of sensors.
+\subsection{The impact of the number of sensors on execution time}
+
+A sensor node has limited energy resources and computing power,
+therefore it is important that the proposed algorithm has the shortest
+possible execution time. The energy of a sensor node must be mainly
+used for the sensing phase, not for the pre-sensing ones.
+Table~\ref{table1} gives the average execution times in seconds
+on a laptop of the decision phase (solving of the optimization problem)
+during one round. They are given for the different approaches and
+various numbers of sensors. The lack of any optimization explains why
+the heuristic has very low execution times. Conversely, the strategy
+with one leader, which requires to solve an optimization problem
+considering all the nodes presents redhibitory execution times.
+Moreover, increasing the network size by 50~nodes multiplies the time
+by almost a factor of 10. The strategy with two leaders has more
+suitable times. We think that in distributed fashion the solving of
+the optimization problem in a subregion can be tackled by sensor
+nodes. Overall, to be able to deal with very large networks, a
+distributed method is clearly required.
\begin{table}[ht]
-\caption{The Execution Time(s) vs The Number of Sensors }
+\caption{THE EXECUTION TIME(S) VS THE NUMBER OF SENSORS}
% title of Table
\centering
% used for centering table
-\begin{tabular}{|c| c| c| c |}
+\begin{tabular}{|c|c|c|c|}
% centered columns (4 columns)
-\hline\hline
+ \hline
%inserts double horizontal lines
-Sensors Number & Strategy & Strategy & Simple Heuristic \\ [0.5ex]
- & (with Two Leaders) & (with One Leader) \\ [0.5ex]
+Sensors number & Strategy~2 & Strategy~1 & Simple heuristic \\ [0.5ex]
+ & (with two leaders) & (with one leader) & \\ [0.5ex]
%Case & Strategy (with Two Leaders) & Strategy (with One Leader) & Simple Heuristic \\ [0.5ex]
% inserts table
%heading
\hline
200 & 4.54 & 169.469 & 0.0046 \\
\hline
-250 & 12.252 & 1581.163 & 0.0056 \\ [1ex]
-
+250 & 12.252 & 1581.163 & 0.0056 \\
% [1ex] adds vertical space
\hline
%inserts single line
% is used to refer this table in the text
\end{table}
-Table \ref{table1} shows the efficiency of our algorithm to produce the solution with good execution time though the Simple Heuristic gives the solution in less time but our approach ensure a better coverage for the region with energy saving and less energy consumption led to extend the lifetime of the network.
+\subsection{The network lifetime}
-\subsection{The Number of Stopped Simulation Runs :}
-In this study, we will shows the number of stopped simulation runs (the disconnected network) per round for 150 and 250 deployed nodes and for three approaches. Fig. \ref{fig9} and \ref{fig10} illustrate the number of stopped simulation runs per round for 150 and 250 deployed nodes respectively.
-
-\begin{figure}[h!]
-\centering
-\includegraphics[scale=0.50]{TheNumberofStoppedSimulationRuns150.pdf}
-\caption{The Number of Stopped Simulation Runs against Rounds for 150 deployed nodes }
-\label{fig9}
-\end{figure}
+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
+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.
\begin{figure}[h!]
+%\centering
+% \begin{multicols}{6}
\centering
-\includegraphics[scale=0.50]{TheNumberofStoppedSimulationRuns250.pdf}
-\caption{The Number of Stopped Simulation Runs against Rounds for 250 deployed nodes }
-\label{fig10}
+\includegraphics[scale=0.5]{TheNetworkLifetimeg.eps} %\\~ ~ ~(a)
+\caption{The network lifetime }
+\label{fig8}
\end{figure}
-The results explain the powerful of our approach against the Stopped Simulation Runs in comparison with other two approaches especially in the last rounds from the network lifetime and this will participate in extending the life time of the network.
-
-\label{Simulation Results}
-
-
-\section{\uppercase{Conclusions and Future Works}}
+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
+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}
\label{sec:conclusion}
-In this paper, we have addressed the problem of lifetime optimization in wireless sensor networks. This is a very natural and important problem, as sensor nodes have limited resources in terms of memory, energy and computational power. To cope with this problem, The field of sensing divided into smaller subregion using the concept of divide-and-conquer method and then multi-rounds coverage protocol will optimize the lifetime in each subregion.The suggested protocol joins 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 lifetime and take the responsibility of covering the subregion. The network lifetime in each subregion is divided into rounds, each round consists of four phases information exchange, Leader Election, Decision with optimization, and sensing.Our simulation results show that the proposed protocol outperforms or very near some other methods in terms of lifetime, coverage ratio, Active sensor Ratio, energy saving , energy consumption, execution time, and the number of stopped simulation runs. In future, we will study and prepare the one round coverage protocol by which all active sensor schedules will be prepared in one round using intelligent optimization methods such as swarms optimization or Evolutionary algorithms.
-
+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
+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.
% use section* for acknowledgement
-\section*{Acknowledgment}
-
-
-
-
-\begin{thebibliography}{1}
+%\section*{Acknowledgment}
-%1
-%\bibitem{wns07}
- % J. Wang, C. Niu, and R. Shen,~\emph{Randomized approach for target coverage scheduling in directional sensor network},~ICESS2007,~pp. 379-390,~2007.
-
-%2
-%\bibitem{dw60}
- % G.~B. Dantzig and P.~ Wolfe,~\emph {Decomposition principle for linear programs},~Operations Research,~pp. 101-111,~ 1960.
-
-
-\bibitem{asc02}
- I.~ Akyildiz ,~ W.~ Su ,~ Y.~Sankarasubramniam and E. Cayirci,~ emph{A survey on sensor networks},~
- IEEE Comm. Magazine,~pp. 102-114,~2002.
-
-\bibitem{pc10}
- T.~V.~ Padmavathy and M. Chitra,~emph{Extending the Network Lifetime of Wireless Sensor Networks Using Residual Energy Extraction—Hybrid Scheduling Algorithm},~Int. J. of Communications, Network and System Sciences ,~ VOL.~3,No. ~1,pp.~98-106,~2010.
-
-
-\bibitem{Slijepcevic01powerefficient}
- S.~ Slijepcevic and M.~ Potkonjak,~emph{Power Efficient Organization of Wireless Sensor Networks},~
- IEEE International conference on Communications,~pp.~472--476,~2001.
-
-\bibitem{Cardei:2005:IWS:1160086.1160098}
- M.~Cardei, and D.~ Du, ~emph {Improving wireless sensor network lifetime through power aware organization},~
- Wireless Networks,~ vol.~11,~ issue~3,~pp.~333--340,~May~2005.
-
-
-%7
-%\bibitem{Cardei05energy-efficienttarget}
-% M.~ Cardei ,~ M.~ T.~ Thai,~ Y.~ Li and W.~ Wu,~ emph{Energy-efficient target coverage in wireless sensor networks},IEEE Infocom,~pp.~1976--1984,~2005.
-
-%8
-%\bibitem{b04}
-% P.~ Berman,~ G.~ Calinescu ,~ C.~ Shah and A.~ Zelikovsky,~emph{Power efficient monitoring management in sensor networks},~Wireless Communications and Networking Conference,~ WCNC. ~2004,~2004.
-
-\bibitem{Berman05efficientenergy}
- P.~ Berman ,~ G.~ Calinescu ,~ C.~ Shah and A. Zelikovsky,~emph {Efficient energy management in sensor networks},~ Ad Hoc and Sensor Networks. Nova Science Publishers,~Nova Science Publisher,~2005.
-
-\bibitem{1240799}
- J.~ Lu and T.~ Suda,~ emph{Coverage-aware self-scheduling in sensor networks},~ Proceedings. 2003 IEEE 18th Annual Workshop on Computer Communications CCW 2003,~pp.~117-123,~2003.
-
-
-\bibitem{Prasad:2007:DAL:1782174.1782218}
- S.~K.~Prasad, and A.~Dhawan,~emph{Distributed algorithms for lifetime of wireless sensor networks based on dependencies among cover sets},~Proceedings of the 14th international conference on High performance computing ,~HiPC'07,pp.~381--392,~2007.
-
-
-%12
-%\bibitem{Zorbas:2010:SCP:1715927.1715956}
-% D.~ Zorbas ,~ D. Glynos ,~ P.~ Kotzanikolaou and C.~ Douligeris,~emph {Solving coverage problems in wireless sensor networks using cover sets},~ Ad Hoc Netw.,~ vol.~8,issue~4,~pp.~400--415,June~ 2010.
-
-%13
-%\bibitem{Garey:1990:CIG:574848}
- %M.~R.~ Garey and D.~S.~ Johnson,~ emph {Computers and Intractability; A Guide to the Theory of NP-Completeness},~ W. H. Freeman Co.,~1990.
-
-%14
-%\bibitem{Caprara98algorithmsfor}
- % A.~ Caprara ,~ M.~ Fischetti and P.~ Toth ,~ emph{Algorithms for the Set Covering Problem},~ Annals of Operations Research,~ vol.~98,~1998.
-
-%15
-%\bibitem{DBLP:journals/eor/AlfieriBBC07}
- %A.~Alfieri ,~ A.~ Bianco,~ P.~ Brandimarte and C. Chiasserini,~emph {Maximizing system lifetime in wireless sensor networks},~European Journal of Operational Research,~ vol.~181,~ No.~1,~pp.390-402,~2007.
-
-%16
-%\bibitem{Gu:2009:QTC:1673018.1673025}
-% Y.~ Gu,~ Y.~Ji,~ J. ~Li and B.~ Zhao,~emph {QoS-aware target coverage in wireless sensor networks},~Wirel. Commun. Mob. Comput.,~ vol.~9,~issue~12,~pp.~1645--1659,December~ 2009.
-
-%17
-%\bibitem{springerlink:10.1007/BF01594937}
- % Y.~ Ye,~emph{An O($n^3L$)) potential reduction algorithm for linear programming},~Mathematical Programming,~vol.~50,~issue~1,~ pp.~239-258,~ 1991.
-
-
-%18
-%\bibitem{glpk}
-% A.~ Mahkorin,~emph {GNU Linear Programming Kit, Reference Manual},~2010.
-
-%19
-%\bibitem{Garg98fasterand}
- % N.~ Garg and J.~ K\"{o}nemann,~emph {Faster and simpler algorithms for multicommodity flow and other fractional packing problems},~In Proceedings of the 39th Annual Symposium on Foundations of Computer Science,pp.~300--309,~ 1998.
-
-%20
-%\bibitem{Kuhn55}
-% H.~ W.~ Kuhn,~emph{The Hungarian Method for the assignment problem},~Naval Research Logistics Quarterly,~vol.~2,~pp.~83--97,~1955.
-
-\bibitem{Cardei:2006:ECP:1646656.1646898}
-M.~Cardei and J.~ Wu,~emph {Energy-efficient coverage problems in wireless ad-hoc sensor networks},~Comput. Commun.,~ vol.~29,~ no.~4,~pp.~413--420,~February 2006.
-
-
-\bibitem{Manju2011}
- M.~ Chaudhary and A.~ K. ~ Pujari,~emph{High-Energy-First (HEF) Heuristic for Energy-Efficient Target Coverage Problem},~International Journal of Ad hoc, Sensor and Uniquitous computing (IJASUC),~ vol.~2,
- ~no. ~1,~ 2011.
-
-
-
-\bibitem{Abrams:2004:SKA:984622.984684}
-Z.~ Abrams,~ A. ~ Goel and S.~ Plotkin, ~ emph{Set k-cover algorithms for energy efficient monitoring in wireless sensor networks},~ Proceedings of the 3rd international symposium on Information processing in sensor networks,~pp.~ 424--432,~ 2004.
-
-
-
-\bibitem{Zorbas2007}
-D.~ Zorbas ,~ D.~ Glynos ,~ P.~ Kotzanikolaou and C.~ Douligeris,~emph {B\{GOP\}: an adaptive coverage algorithm for wireless sensor networks},~Proceedings of the 13th European Wireless Conference,~Paris,~ France,~2007.
-
-\bibitem{cardei02}
- M.~ Cardei ,~D.~ MacCallum ,~M.~ X.~ Cheng ,~M.~ Min ,~X.~ Jia ,~D.~ Li and
- D.~ Du,~emph {Wireless Sensor Networks with Energy Efficient Organization},~Journal of Interconnection Networks,~ vol.~3,~ no.~3-4,pp.~213-229,~2002.
-
-
-
-\bibitem{cardei05}
- M.~ Cardei ,~ J.~ Wu, N.~ Lu and M.~O.~ Pervaiz,~emph{Maximum Network Lifetime with Adjustable Range},~WiMob,~2005.
-
-
-\bibitem{cardei05bis}
- M.~ Cardei ,~ M.~ T.~ Thai ,~Y.~ Li and W.~ Wu,~emph {Energy-efficient target coverage in wireless sensor networks},~INFOCOM,~pp.~1976-1984,~2005.
-
-
-
-\bibitem{berman04}
- P.~ Berman and G.~ Calinescu,~emph {Power Efficient Monitoring Management in Sensor Networks},~Proceedings of IEEE Wireless Communication and Networking Conference (WCNC'04),~pp.~2329--2334,~2004.
-
-
-\bibitem{garg98}
- N.~ Garg and J.~ Koenemann,~emph {Faster and Simpler Algorithms for Multicommodity Flow and other Fractional Packing Problems.},~Proceedings of the 39th Annual Symposium on Foundations of Computer Science,~pp.~300--309,~1998.
-
-
-\bibitem{Gallais06}
- A.~ Gallais,~ J.~ Carle ,~D. ~ Simplot-Ryl and I.~ Stojmenovic,~emph {Localized Sensor Area Coverage with Low Communication Overhead},~Proceedings of the Fourth Annual IEEE International Conference on Pervasive Computing and Communications,pp.~328--337,~2006.
-
-\bibitem{Tian02}
- D. ~ Tian and N.~ D.~ Georganas, ~emph {A coverage-preserving node scheduling scheme for large wireless sensor networks},~Proceedings of the 1st ACM international workshop on Wireless sensor networks and applications,~pp.~ 32--41,~2002.
-
-
-\bibitem{Ye03}
-F. ~Ye,G.~ Zhong,~J.~ Cheng,~S.~ Lu and L. ~ Zhang,~emph {PEAS: A Robust Energy Conserving Protocol for Long-lived Sensor Networks},~ Proceedings of the 23rd International Conference on Distributed Computing Systems ICDCS'03,~pp.~ 28--37,~2003.
-
-
-
-\bibitem{Huang:2003:CPW:941350.941367}
- C. ~ Huang and Y. ~ Tseng,~emph {The coverage problem in a wireless sensor network},~Proceedings of the 2nd ACM international conference on Wireless sensor networks and applications WSNA '03,~San Diego, CA, USA,~pp.~115-121,~ 2003.
-
-
-
-
-\bibitem{Zhang05}
- H.~ Zhang and J.~ C.~ Hou,~emph {Maintaining Sensing Coverage and Connectivity in Large Sensor
- Networks},~Ad Hoc {\&} Sensor Wireless Networks,~ vol.~1,no.~ 1-2,~2005.
-
-
-\bibitem{HeinzelmanCB02}
- W.~ B.~ Heinzelman ,~ A.~ P.~ Chandrakasan and H.~ Balakrishnan,~emph {An application-specific protocol architecture for wireless microsensor networks},~IEEE Transactions on Wireless Communications,~ vol. ~1,~no. ~4,pp.~ 660-670,~2002.
-
-
-
-\bibitem{pedraza2006}
- F. ~Pedraza,~A.~ L.~ Medaglia and A. ~ Garcia,~emph {Efficient coverage algorithms for wireless sensor networks},~Systems and Information Engineering Design Symposium,~ pp.~ 78 --83,~2006.
-
-
-\bibitem{chin2007}
-C.~ T. ~ Vu, ~ emph {An Energy-Efficient Distributed Algorithm for k-Coverage Problem in Wireless Sensor Networks},~GeorgiaState University,~2007.
-
-
-
-
-
-
-
-
-
-\end{thebibliography}
-
-
-
+\bibliographystyle{IEEEtran}
+\bibliography{bare_conf}
-% that's all folks
\end{document}
