\begin{abstract}
One of the fundamental challenges in Wireless Sensor Networks (WSNs)
-is coverage preservation and extension of the network lifetime
+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 rounds during which a small number of nodes, remaining
active for sensing, is selected to ensure coverage. Each round
\noindent Recent years have witnessed significant advances in wireless
communications and embedded micro-sensing MEMS technologies which have
-made emerge wireless sensor networks as one of the most promising
+led to the emergence of wireless sensor 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
+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.
%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.
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 benefit
-from the overlapping sensing regions of some sensor nodes to save
+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.
Obviously, the deactivation of nodes is only relevant if the coverage
-of the monitored area is not affected. Consequently, future software
+of the monitored area is not affected. Consequently, future softwares
may need to adapt appropriately to achieve acceptable quality of
-service for applications. In this paper we concentrate on area
+service for applications. 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
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 much node failures.
+ 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 suitable manner a sensor node to
+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.
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.
+this problem is subject to a wide range of interpretations, we have chosen
+to recall the main definitions and assumptions related to our work.
%\begin{itemize}
%\item Area Coverage: The main objective is to cover an area. The area coverage requires
The most discussed coverage problems in literature can be classified
into two types \cite{ma10}: area coverage (also called full or blanket
coverage) and target coverage. An area coverage problem is to find a
-minimum number of sensors to work such that each physical point in the
+minimum number of sensors to work, such that each physical point in the
area is within the sensing range of at least one working sensor node.
Target coverage problem is to cover only a finite number of discrete
points called targets. This type of coverage has mainly military
applications. Our work will concentrate on the area coverage by design
and implementation of a strategy which efficiently selects the active
nodes that must maintain both sensing coverage and network
-connectivity and in the same time improve the lifetime of the wireless
+connectivity and at the same time improve the lifetime of the wireless
sensor network. But requiring that all physical points of the
considered region are covered may be too strict, especially where the
sensor network is not dense. Our approach represents an area covered
{\bf Lifetime}
Various definitions exist for the lifetime of a sensor
-network~\cite{die09}. Main definitions proposed in the literature are
-related to the remaining energy of the nodes or to the percentage of
-coverage. The lifetime of the network is mainly defined as the amount
-of time that the network can satisfy its coverage objective (the
+network~\cite{die09}. The main definitions proposed in the literature are
+related to the remaining energy of the nodes or to the coverage percentage.
+The lifetime of the network is mainly defined as the amount
+of time during which the network can satisfy its coverage objective (the
amount of time that the network can cover a given percentage of its
area or targets of interest). In this work, we assume that the network
is alive until all nodes have been drained of their energy or the
Activity scheduling is to schedule the activation and deactivation of
sensor nodes. The basic objective is to decide which sensors are in
-what states (active or sleeping mode) and for how long, such that the
+what states (active or sleeping mode) and for how long, so that the
application coverage requirement can be guaranteed and the 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
+scheduling. In distributed algorithms, each node in the network
autonomously makes decisions on whether to turn on or turn off itself
only using local neighbor information. In centralized algorithms, a
central controller (a node or base station) informs every sensors of
Some distributed algorithms have been developed
in~\cite{Gallais06,Tian02,Ye03,Zhang05,HeinzelmanCB02} to perform the
scheduling. 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
+a predetermined duration. At the beginning of each round, a sensor
+exchanges information with its neighbors and makes a decision to either
remain turned on or to go to sleep for the round. This decision is
-basically based on simple greedy criteria like the largest uncovered
+basically made 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 containing node ID
-and node location to its neighbors at the beginning of each round. A
+a sensing phase. Each sensor broadcasts a message containing the node ID
+and the node location to its neighbors at the beginning of each round. A
sensor determines its status by a rule named off-duty eligible rule
which tells him to turn off if its sensing area is covered by its
neighbors. A back-off scheme is introduced to let each sensor delay
the decision process with a random period of time, in order to avoid
-that nodes make conflicting decisions simultaneously and that a part
-of the area is no longer covered.
+simultaneous conflicting decisions between nodes and lack of coverage on any area.
\cite{Prasad:2007:DAL:1782174.1782218} defines a model for capturing
the dependencies between different cover sets and proposes localized
heuristic based on this dependency. The algorithm consists of two
phases, an initial setup phase during which each sensor computes and
-prioritize the covers and a sensing phase during which each sensor
+prioritizes the covers and a sensing phase during which each sensor
first decides its on/off status, and then remains on or off for the
rest of the duration. 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 is being maintained. This algorithm works in
+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 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
+Some other approaches do not consider a synchronized and predetermined
period of time where the sensors are active or not. Indeed, each
-sensor maintains its own timer and its time wake-up is randomized
+sensor maintains its own timer and its wake-up time is randomized
\cite{Ye03} or regulated \cite{cardei05} over time.
%A ecrire \cite{Abrams:2004:SKA:984622.984684}p33
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
+The 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
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.
+of covers that includes 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.
