An Adaptive Energy-efficient Area Coverage Algorithm

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An Adaptive Energy-efficient Area Coverage Algorithm

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An adaptive energy-efficient area coverage algorithm for
wireless sensor networks
Javad Akbari Torkestani

Young Researchers Club, Arak Branch, Islamic Azad University, Arak, Iran
a r t i c l e i n f o
Article history:
Received 3 August 2012
Received in revised form 1 February 2013
Accepted 9 March 2013
Available online 19 March 2013
Keywords:
Area coverage
Minimum weight CDS
Degree-constrained CDS
WSN
Learning automata
a b s t r a c t
The connected dominating set (CDS) concept has recently emerged as a promising
approach to the area coverage in wireless sensor network (WSN). However, the major
problem affecting the performance of the existing CDS-based coverage protocols is that
they aim at maximizing the number of sleep nodes to save more energy. This places a
heavy load on the active sensors (dominators) for handling a large number of neighbors.
The rapid exhaustion of the active sensors may disconnect the network topology and leave
the area uncovered. Therefore, to make a good trade-off between the network connectivity,
coverage, and lifetime, a proper number of sensors must be activated. This paper presents a
degree-constrained minimum-weight extension of the CDS problem called DCDS to model
the area coverage in WSNs. The proper choice of the degree-constraint of DCDS balances
the network load on the active sensors and significantly improves the network coverage
and lifetime. A learning automata-based heuristic named as LAEEC is proposed for finding
a near optimal solution to the proxy equivalent DCDS problem in WSN. The computational
complexity of the proposed algorithm to find a
1

optimal solution of the area coverage
problem is approximated. Several simulation experiments are conducted to show the supe-
riority of the proposed area coverage protocol over the existing CDS-based methods in
terms of the control message overhead, percentage of covered area, residual energy, num-
ber of active nodes (CDS size), and network lifetime.
Ó 2013 Elsevier B.V. All rights reserved.
1. Introduction
A wireless sensor network (WSN) is a multi-hop, infra-
structureless, and self-organized network comprising a
group of small and power-constrained sensors deployed
over a vast region for different purposes such as environ-
ment monitoring, object or target tracking, industry auto-
mation and control, and etc. [1,2]. Although the recent
advances in sensor technology, micro-electromechanical
systems, and wireless communications technology have
greatly promoted the emergence of modern WSNs, they
continue to be networks with constrained resources in
terms of memory, power supply, and processing power
[3–5]. Due to the severe resource limitations in WSNs, cov-
erage is the most fundamental and challenging issue of
these networks focusing on how well the sensors cover
the monitoring region [6–8]. WSN coverage problem aims
to minimize the number of sensor nodes to be activated,
while maintaining the full coverage of the monitoring area
[9]. Besides the WSN, coverage is a well-known classic
problem in computational geometry too. The art gallery
problem [10] in which the cameras are located to monitor
every point in the art gallery, and the ocean area coverage
problem [11] in which the satellites are placed in the orbit
to provide the maximum ocean monitoring also deal with
the coverage problem [9].
Depending on the subject is covered, the coverage prob-
lem can be classified as area coverage [12,13], barrier (or
path) coverage [14–16], and target (or point) coverage
[13,17]. The area coverage deals with the problem of cov-
ering all the points within the monitoring area. The area
1570-8705/$ - see front matter Ó 2013 Elsevier B.V. All rights reserved.
http://dx.doi.org/10.1016/j.adhoc.2013.03.002

Tel./fax: +98 861 3422292.
E-mail address: [email protected]
Ad Hoc Networks 11 (2013) 1655–1666
Contents lists available at SciVerse ScienceDirect
Ad Hoc Networks
j our nal homepage: www. el sevi er . com/ l ocat e/ adhoc
coverage problem aiming at minimizing the number of ac-
tive nodes without failing to cover the entire area is the
most common form of the coverage problem [9]. Barrier
coverage is considered as monitoring a boundary region
(or barrier) within the sensor field aiming at minimizing
the probability of undetected penetration through the bar-
rier. Barrier coverage is used to detect intruders attempting
to penetrate a protected region. The target coverage prob-
lem intends to cover a set of stationary or moving points
within the sensor field [18]. All types of the coverage prob-
lem aim to minimize the required number of sensors for
covering the area, barrier or targets. A fundamental solu-
tion to the coverage problem is to place the sensors at
the predetermined locations of the sensor field determinis-
tically. Deterministic sensor placement can be applied only
to a relatively small sensor network deployed in a friendly
environment. However, when a large sensor network is de-
ployed in a hostile, harsh, and hard-to-access field, random
sensor deployment, generally scattered from an aircraft,
might be the only choice [18,19]. In random deployment,
to guarantee the complete coverage of the sensor field,
the number of sensors that must be scattered is signifi-
cantly more than that is required [18]. Under such circum-
stances, the design of a coverage protocol minimizing the
required number of active sensors significantly improves
the performance of the WSNs in terms of energy consump-
tion and network lifetime.
The connected dominating set (CDS) principle has re-
cently emerged as a new solution to the energy-efficient
coverage in WSNs. A CDS of a given graph is a connected
subset of the graph vertices such that every vertex of the
graph is either in the set or adjacent to at least one vertex
of the set. Several approaches have been proposed to solve
the CDS problem. To name just a few, Li et al. [20] and
Alzoubi et al. [21] proposed MIS (maximal independent
set)-based greedy algorithms to construct the CDS. Dai
and Wu [22] and Butenko et al. [23] presented prune-
based heuristics for the CDS problem. In a CDS-based cov-
erage protocol, a virtual backbone covering every point
within the sensor field is formed [4,9]. Misra et al. [9] pro-
posed an energy-efficient solution to maintain the cover-
age problem in WSNs. The proposed method preserves
the network connectivity by formation of the network
backbone. The proposed solution aims to cover the area
of interest and minimizing the number of active sensors
too. Wightman and Labrador [24] proposed an approxi-
mate CDS-based solution called A3 to the topology control
problem in WSNs. A3 assumes that the sensors have no
information about the position of the neighbors and so
about the network topology. In this method, the distance
between the nodes is estimated based on the received sig-
nal strength. A3 generally is composed of two processes,
neighborhood discovery process and children selection
process. However, another process called the second
opportunity process is rarely used in special cases. The
residual energy of the child node and its distance from
the parent are two metrics that A3 uses to construct the
CDS-based tree. This selection rule gives the higher priority
to the child nodes with higher energy and farther distance
from the parent node. A3 uses four messages for topology
construction, hello message sent out by the parent, parent
recognition message including the residual energy and sig-
nal strength that is sent back by the children, children rec-
ognition message including the sorted list of all children
and their timeouts sent out by the parent, and sleeping
message that is sent by the active candidate node. Wight-
man and Labrador [24] proposed an extended version of A3
called A3lite that uses only (two) hello and parent recogni-
tion messages for topology construction. A3lite avoids
sending the large size children recognition message. A3
sends a sleep message to all nodes, in the reduced tree
topology, that are within the communication area of the
other nodes. This may cause some points of the area re-
main uncovered when the sensing range is considerably
smaller than the communication range. The same authors
in [6] proposed two solutions called A3Cov and A3CovLite
for the coverage problem of A3. A3Cov first checks to see if
an unconnected node is sensing-covered by another active
node. If so, the node is sent directly to the sleeping mode.
This is because it is not needed for connectivity nor cover-
age. Otherwise, the node is asked to stay awake for an extra
period of time. If it receives a sensing coverage message
(indicating that sensing area of the node has been already
covered) from its neighbors before the timeout expires, it
goes to the sleeping mode. Otherwise, the node must re-
main active. A3CovLite [6] is a combination of A3Lite that
reduces the required number of messages as compared to
A3 original, and A3Cov that solves the area coverage prob-
lem in A3. Rizvi et al. [4] proposed a distributed energy-
efficient topology control algorithm referred to as A1 for
connected area coverage in WSNs. Similar to A3 family
protocols, A1 uses the signal strength and residual energy
as the criteria to select the dominator nodes. A1 only uses
the hello message to construct the CDS-based backbone.
A1 constructs the topology in one phase. The starting node
first discovers its neighbors. Similarly, the neighbors of the
initiator node discover their neighbors and this process
continues until the complete topology is formed with the
backbone nodes. Like A3Cove, A1 lets the children calculate
and set the timeout value independently.
Literature reviewreveals that there are critical problems
affecting the performance of the existing CDS-based con-
nected area coverage protocols. These protocols generally
aim at covering the sensor filed with the minimumnumber
of active nodes (i.e., constructing the minimum size CDS).
This reduces the energy consumption by turning off a large
number of sensors. On the other side, this significantly
shortens the sensor lifetime (even for energetic nodes) be-
cause of a heavy burden on the active sensors for handling a
large number of neighbors while the sensors severely suffer
from the limited energy, and processing power. Exhausting
the energy of the active sensors may leave the area uncov-
ered. Though the redundant active nodes (i.e., large size
CDS) extend the covered area, the overlapped sensing areas
increase the network energy consumption. This itself re-
duces the network lifetime on the other hand. Therefore,
the CDS must be constructed such that a good trade-off be-
tween the coverage (covered area) and network lifetime is
made. In this paper, the degree-constrained minimum-
weight version of the CDS, so called DCDS, is presented to
alleviate the above mentioned problems with the CDS-
based area coverage protocols. DCDS is the CDS having
1656 J. Akbari Torkestani / Ad Hoc Networks 11 (2013) 1655–1666
the minimum weight subject to a predefined degree-con-
straint. The weight associated with each node is defined
as the inverse of its residual energy. Therefore, the DCDS
maximizes the network lifetime by selection of the sensors
with the maximum residual energy. A DCDS is a CDS in
which no node has a degree greater than a predefined de-
gree-constraint. Therefore, by the proper choice of the de-
gree-constraint the DCDS is able to make a trade-off
between the percentage of the covered area and the net-
work lifetime. This paper proposes a learning automata-
based heuristic called LAEEC (short for learning automata-
based energy-efficient coverage protocol) to construct the
DCDS in the WSNs. The computational complexity of the
proposed algorithmto find a
1

optimal solution of the area
coverage problem is approximated. Extensive simulation
experiments are performed to show the performance of
the proposed area coverage algorithm. The obtained results
show the superiority of the proposed algorithm over the
best existing methods in terms of the control message over-
head, percentage of covered area, residual energy, number
of active nodes (CDS size), and network lifetime.
The rest of the paper is organized as follows. Section 2
briefly reviews the learning automata theory. In Section 3,
the proposed area coverage algorithm is presented. Sec-
tion 4 approximates the time complexity of the proposed
algorithmto find a
1

optimal solution of the area coverage
problem. Section 5 shows the performance of the proposed
algorithmthrough simulation experiments and comparison
with the existing methods. Section 6 concludes the paper.
2. Learning automata theory
A learning automaton [25,26] is an adaptive decision-
making unit that improves its performance by learning
how to choose the optimal action from a finite set of al-
lowed actions through repeated interactions with a ran-
dom environment. The action is chosen at random based
on a probability distribution kept over the action-set and
at each instant the given action is served as the input to
the random environment. The environment responds the
taken action in turn with a reinforcement signal. The action
probability vector is updated based on the reinforcement
feedback from the environment. The objective of a learning
automaton is to find the optimal action from the action-set
so that the average penalty received from the environment
is minimized. Learning automata have a wide variety of
applications in combinatorial optimization problems
[33,34,38,39], computer networks [36,37,42–45], Grid
computing [30,32,41], and Web engineering [31,35,40].
The environment can be described by a triple {a, b, c},
where a = {a
1
, a
2
, . . ., a
r
} represents the finite set of the in-
puts, b = {b
1
, b
2
, . . ., b
m
} denotes the set of the values that
can be taken by the reinforcement signal, and c = {c
1
, c
2
,
. . ., c
r
} denotes the set of the penalty probabilities, where
the element c
i
is associated with the given action a
i
. If
the penalty probabilities are constant, the randomenviron-
ment is said to be a stationary random environment, and if
they vary with time, the environment is called a non-sta-
tionary environment. The environments depending on
the nature of the reinforcement signal b can be classified
into P-model, Q-model and S-model. The environments in
which the reinforcement signal can only take two binary
values 0 and 1 are referred to as P-model environments.
Another class of the environment allows a finite number
of the values in the interval [0, 1] can be taken by the rein-
forcement signal. Such an environment is referred to as Q-
model environment. In S-model environments, the rein-
forcement signal lies in the interval [a,b].
Learning automaton can be classified into two main
families [25]: fixed structure learning automata and vari-
able structure learning automata. Variable structure learn-
ing automata are represented by a triple ¸b, a, L), where b is
the set of inputs, a is the set of actions, and L is learning
algorithm. The learning algorithm is a recurrence relation
which is used to modify the action probability vector. Let
a
i
(k) ÷ a and p(k) denote the action selected by learning
automaton and the probability vector defined over the ac-
tion set at instant k, respectively. Let a and b denote the re-
ward and penalty parameters and determine the amount
of increases and decreases of the action probabilities,
respectively. Let r be the number of actions that can be ta-
ken by learning automaton. At each instant k, the action
probability vector p(k) is updated by the linear learning
algorithm given in Eq. (1), if the selected action a
i
(k) is re-
warded by the random environment, and it is updated as
given in Eq. (2) if the taken action is penalized.
p
j
(k ÷1) =
p
j
(k) ÷ a[1 ÷ p
j
(k)[ j = i
(1 ÷ a)p
j
(k) \j –i
_
(1)
p
j
(k ÷1) =
(1 ÷ b)p
j
(k) j = i
b
r÷1
_ _
÷ (1 ÷ b)p
j
(k) \j –i
_
(2)
If a = b, the recurrence Eqs. (1) and (2) are called linear
reward-penalty (L
R÷P
) algorithm, if a ¸ b the given equa-
tions are called linear reward- penalty (L
R÷P
), and finally
if b = 0 they are called linear reward-Inaction (L
R÷I
). In the
latter case, the actionprobability vectors remainunchanged
when the taken action is penalized by the environment.
A variable action-set learning automaton is an automa-
ton in which the number of actions available at each in-
stant changes with time. It has been shown in [26] that a
learning automaton with a changing number of actions is
absolutely expedient and also -optimal, when the rein-
forcement scheme is L
R÷I
. Such an automaton has a finite
set of r actions, a = {a
1
, a
2
, . . ., a
r
}. A = {A
1
, A
2
, . . ., A
m
} de-
notes the set of action subsets and A(k) # a is the subset
of all the actions can be chosen by the learning automaton,
at each instant k. The selection of the particular action sub-
sets is randomly made by an external agency according to
the probability distribution W(k) = {W
1
(k), W
2
(k), . . .,
W
m
(k)} defined over the possible subsets of the actions,
where
W
i
(k) = prob[A(k) = A
i
[A
i
÷ A; 1 6 i 6 2
r
÷1[
^
p
i
(k) = prob[a(k) = a
i
[A(k); a
i
÷ A(k)[ denotes the proba-
bility of choosing action a
i
, conditioned on the event that
the action subset A(k) has already been selected and
a
i
÷ A(k) too. The scaled probability ^ p
i
(k) is defined as
^
p
i
(k) =
p
i
(k)
K(k)
(3)
J. Akbari Torkestani / Ad Hoc Networks 11 (2013) 1655–1666 1657
where K(k) =

a
i
÷A(k)
p
i
(k) is the sum of the probabilities of
the actions in subset A(k), and p
i
(k) = prob[a(k) = a
i
].
The procedure of choosing an action and updating the
action probabilities in a variable action-set learning
automaton can be described as follows. Let A(k) be the ac-
tion subset selected at instant k. Before choosing an action,
the probabilities of all the actions in the selected subset are
scaled as defined in Eq. (3). The automaton then randomly
selects one of its possible actions according to the scaled
action probability vector ^ p(k). Depending on the response
received from the environment, the learning automaton
updates its scaled action probability vector. Note that the
probability of the available actions is only updated. Finally,
the probability vector of the actions of the chosen subset is
rescaled as p
i
(k ÷1) =
^
p
i
(k ÷1) K(k), for all a
i
÷ A(k). The
absolute expediency and e optimality of the method de-
scribed above have been proved in [26].
3. Energy-efficient area coverage algorithm
This paper proposes the degree-constrained minimum-
weight connected dominating set (DCDS) problem for
modeling the energy-efficient coverage problem in WSNs.
The CDS size remains the primary concern of the CDS-
based coverage protocols. On one hand, MCDS (minimum
size CDS)-based coverage results in saving more energy
by maximizing the number of sleep nodes. On the other
hand, MCDS-based coverage rapidly drains the active
nodes and shortens the network lifetime. Though the
redundant active nodes extend the network lifetime, they
increase the network energy consumption. DCDS aims at
making a good trade-off between the network coverage,
lifetime, and energy consumption by an additional con-
straint on the node degree.
3.1. Problem statement
Let G¸V, E, W) be a weighted, connected, and undirected
graph, where V denotes the vertex set, E denotes the edge
set, and W denotes the set of weights associated with the
graph nodes. A CDS of a graph is a connected subset of
the graph vertices such that every vertex of the graph
either is in the set or is the adjacent to at least one vertex
of the set. MCDS is the CDS with the minimum cardinality.
The minimum weight CDS (MwCDS) is the CDS having the
minimumtotal weight. Let D
i
be the degree of vertex v
i
÷ V.
The degree of a given vertex is defined as its number of
neighboring vertices. The degree-constrained connected
dominating set of graph G is a CDS of G subject to D
i
6 d
(for all v
i
÷ V), where d is a positive integer number denot-
ing the degree-constraint. The degree-constrained mini-
mum-weight CDS (DCDS) problem seeks the CDS with
the minimum weight subject to a degree-constraint d.
Let triple ¸N; L; E) denotes the topology graph of a WSN,
where N = ¦n
1
; n
2
; . . .¦ is the set of sensor nodes,
L = ¦l
(n
i
;n
j
)
¦ #N ×N is the set of communication links,
and E = ¦E
n
i
[\n
i
÷ N¦ denotes the set of energies associ-
ated with the sensor nodes. Let E
n
i
be the residual energy
of sensor node n
i
. LAEEC aims to construct the most-stable
energy-efficient sensor network covering the monitoring
area by finding a near optimal solution to the DCDS prob-
lem, where the weight of each node is defined as its resid-
ual energy level. DCDS seeks for the set of most energetic
connected sensors whose maximum degree is bounded
above by d. Let C = ¦c
1
; c
2
; . . .¦ denotes the set of all possi-
ble degree-constrained CDSs covering the sensing area. c
+
is the optimal solution to the DCDS problem (i.e., the de-
gree-constrained CDS with the minimum weight), if
E
c+
= min
\c
i
÷C
1
min
\n
j
÷c
i
¦E
n
j
¦
_
¸
_
_
¸
_
where E
c+
denotes the energy of optimal degree-con-
strained CDS c
+
; min
\n
j
÷c
i
¦E
n
j
¦ denotes the energy of de-
gree-constrained CDS c
i
subject to constraint d. Energy of
a degree-constrained CDS is defined as the residual energy
level of the most energetic active sensor.
3.2. Degree-constrained CDS-based area coverage algorithm
In this section, a fully distributed learning automata-
based algorithm is proposed for solving the area coverage
problem in WSN by finding a near optimal solution to the
degree-constrained minimum-weight CDS problem. In this
algorithm, a group of learning automata, named as GoL, is
constituted by equipping each sensor node n
i
with a vari-
able action-set learning automaton A
i
. Duple GoL is defined
as ¸A(k), a(k)), where A(k) = ¦A
i
[\n
i
÷ N(k)¦ denotes the set
of learning automata assigned to the sensor nodes, and
a(k) = {a
i
["A
i
} denotes the set of actions that can be taken
by each learning automaton A
i
. Due to the frequent topol-
ogy changes in WSN, N; L, and E are time-variable parame-
ters. In this paper, these parameters are shown as N(k); L(k),
and E(k) for each instant k. Let a
i
denotes the set of actions
that can be taken by learning automaton A
i
÷ A(k). Each
automaton A
i
chooses the communication links incident
at the corresponding node n
i
as its actions. That is,
a
i
(k) = a
j
i
(k)
¸
¸
¸\l
(n
i
;n
j
)
÷ L(k)
_ _
. GoL is isomorphic to the net-
work topology graph, where the set of learning automata
corresponds to the set of sensor nodes and the action-set
corresponds to the set of communications links. Therefore,
action-set a
i
(k) is time-variable and its number of actions
may change at each instant k. Learning automaton is a
probabilistic learning tool that selects its actions according
to an action probability vector (APV) at random. APV is the
main component of a learning automaton that must be kept
up-to-date. The action probability vector of learning
automaton A
i
is defined as p
i
(k) = p
j
i
(k)
¸
¸
¸\a
j
i
(k) ÷ a
i
(k)
_ _
,
where p
j
i
(k) denotes the choice probability of action a
j
i
at
stage k. In this algorithm, the APV of each learning autom-
aton A
i
is set to the energy level of its neighboring nodes ini-
tially. Let e
n
i
(k) =

\l
(n
i
;n
j
)
÷L(k)
E
n
j
(k) denotes the total energy
level of the neighbors of sensor n
i
at stage k. Therefore, the
probability with which sensor n
i
selects sensor n
j
(i.e., link
l
(n
i
;n
j
)
) is defined as p
j
i
(k) =
En
j
(k)
en
i
(k)
at stage k. This activates
the sensor having the maximum energy level (in each
neighborhood) to cover the sensor field.
1658 J. Akbari Torkestani / Ad Hoc Networks 11 (2013) 1655–1666
Let us assume that the sink node n
i
starts the coverage
process. As mentioned earlier, LAEEC is a fully distributed
algorithm that is run at each sensor node independently.
Flowchart of the proposed coverage procedure running at
sensor node n
i
is shown in Fig. 1. The node that is running
the algorithm is called the current node. At each instant k,
each current node n
i
discovers its neighbors and forms its
action-set by sending an ASF (action-set formation) mes-
sage. Each node that receives the ASF message replies it.
The reply message includes the residual energy level of
the node. Current node n
i
forms its action-set based on
the received replies. Due to the network topology changes,
one node may leave (or join to) the other node at each
stage. If link l
(n
i
;n
j
)
breaks at stage k + 1, its corresponding
action (i.e., a
j
i
) must be removed from the action-set of
automaton A
i
(or action a
i
j
from automaton A
j
). Moreover,
the choice probability of the other actions (e.g., a
j
/
i
) must
be updated as p
j
/
i
(k ÷1) = p
j
/
i
(k) 1 ÷ p
j
i
(k)=1 ÷ p
j
i
(k)
_ _ _ _
in
automaton A
i
. When a new link l
(n
i
;n
j
)
is established at stage
k + 1, the choice probability of the new action is initialized
to 1/[a
i
(k + 1)[, and that of the other actions is updated as
p
j
/
i
(k ÷1) = p
j
/
i
(k) [[[a
i
(k ÷1)[ ÷1[=[a
i
(k ÷1)[[.
Let c
k
denotes the degree-constrained CDS that is con-
structed at stage k. Let c
/
k
be the set of sensor nodes cov-
ered by c
k
(or set of dominatees). c
k
is initially set to n
i
,
and c
/
k
is initialized to n
i
and its one-hop neighbors. E
c
k
is
initialized to E
n
i
. Let d
k
denotes the average degree of c
k
.
d
k
is defined (and updated) as

\n
i
÷c
k
D
i
(k)
_ _
=[c
k
[ at each
stage k, where D
i
(k) denotes the degree of node n
i
at stage
k. As shown in Fig. 1, current node n
i
selects one of its ac-
tions at random. Let us assume that action a
j
i
is selected by
node n
i
. Sensor n
i
adds sensor n
j
(corresponding to selected
action a
j
i
) to the constrained CDS c
k
and updates d
k
. Energy
of c
k
(i.e., E
c
k
) is set to min¦E
n
j
; E
c
k
¦. e
n
i
(k) = e
n
i
(k)=D
i
(k) de-
notes the average energy level of the neighbors of node n
i
at stage k. Node n
i
compares the residual energy of sensor
node n
j
with average energy level e
n
i
(k), and average de-
gree d
k
with degree-constraint d. Then, n
i
updates the
internal state of its automaton according to the following
updating rules. If the residual energy level of the node se-
lected by n
i
is higher than the average energy level of the
neighbors of n
i
(i.e., if n
j
is the most energetic neighbor of
n
i
) and d
k
does not exceed degree-constraint d, learning
automaton A
i
rewards the selected action a
j
i
by Eq. (1). If
the energy level of selected node n
j
is lower than the aver-
age energy level e
n
i
(k), and the average degree d
k
is larger
than degree-constraint d
k
, learning automaton A
i
penalizes
the selected action a
j
i
by Eq. (2). Otherwise, the APV of A
i
remains unchanged.
After learning automaton A
i
updates its APV, current
node n
i
sends an ACT (activation) message including de-
gree-constrained CDS c
k
, dominatee set c
/
k
, average degree
d
k
, and CDS energy level E
c
k
to activate the selected sensor
node n
j
. Sensor n
j
checks to see if its ID number is equal to
the receiver ID, as soon as it receives an ACT message. If so,
it adds the IDs of its one-hop neighbors to c
/
k
. If c
/
k
includes
all the network nodes (i.e., if the constructed CDS covers all
the points within the sensor field), the current iteration, k,
of the coverage process is over. Otherwise, node n
j
changes
its state to the current node and does the same operations
as node n
i
did. Sensor node n
i
in which the coverage pro-
cess completes, broadcasts a SLP (sleep) message within
the network through backbone c
k
. This message only in-
cludes degree-constrained CDS c
k
and energy level E
c
k
.
Each receiving sensor node n
i
goes to the sleep mode if it
does not find its ID in c
k
. Otherwise, it goes to the active
mode for sensing the area. The sensor network composed
of the active nodes covers the monitoring area until the
residual energy of an active sensor node falls down a pre-
defined threshold T
n
i
or one or more active sensor nodes
fail. The active node that finds its residual energy level
lower than the energy threshold T
n
i
, and the sensor node
that detects the failure of an active node are responsible
for initiating a new coverage process.
Fig. 1. Flowchart of the proposed area coverage procedure running at sensor node n
i
at stage k.
J. Akbari Torkestani / Ad Hoc Networks 11 (2013) 1655–1666 1659
4. Complexity analysis and convergence results
In this section, the computational complexity of the
proposed area coverage algorithm, LAEEC, is analyzed. To
do so, an upper bound (Lemma 1) and a lower bound (Lem-
ma 2) on the number of iterations of the algorithm for find-
ing a
1

_ _
optimal action at each node n
i
(i.e., learning
automaton A
i
) is approximated, where is the error rate.
Then, it is shown (in Theorem 1) that the time required
for finding a
1

_ _
optimal solution to the area coverage
problem is confined between the estimated lower and
upper bounds. Finally, it is proved (in Theorem 2) that
the convergence time of LAEEC to a
1

_ _
optimal area cov-
erage (i.e.,
1

c
+
) is bounded to the convergence time of the
network node with the maximum degree.
Theorem 1. Let opt
i
denotes the optimal action that can be
chosen by learning automaton A
i
. If A
i
updates its action
probability vector according to LAEEC, the time required for
finding a
1

_ _
opt
i
at node n
i
is
!
E
n+
(k)
e
n
i
(k)
_ _
6 T
i
6 !
E
n+
(k)
e
n
i
(k)
(1 ÷a)
D
i
÷1
_ _
; (4)
where
!(k) =
2
1 ÷ k ÷

[c+[
log

[c+[(1÷k)
1÷a
; (5)
÷ (0, 1) is the error rate, a denotes the learning rate of the
algorithm, [c
+
[ denotes the cardinality of the optimal degree-
constrained CDS, n

denotes the best (i.e., most energetic)
node that can be chosen by learning automaton A
i
, and D
i
de-
notes the degree of node n
i
.
Proof. Let each learning automaton A
i
updates its action
probability vector p
i
according to the updating rule of LAE-
EC. Let c
+
be the optimal area coverage and a
+
i
(n
+
) denotes
the best action (active sensor) that can be selected by
automaton A
i
(node n
i
). Before stating the proof of this the-
orem, the following two lemmas are discussed. h
Lemma 1. If each automaton A
i
updates its action probability
vector according to the proposed updating algorithm, the
upper bound on the running time for finding a
1

opt
i
is
2
1 ÷ k ÷

[c+[
log

[c+[(1÷k)
1÷a
where k Pp
+
i
(1 ÷ a)
D
i
÷1
.
Proof. Lemma 1 aims at computing the worst case running
time of the proposed algorithm. At each node n
i
, the worst
case occurs if the optimal sensor node n

(the node with
the maximum residual energy satisfying the degree-con-
straint) is chosen before all the other nodes. In this case,
the learning process is subdivided into two distinct phases:
(1) the shrinking phase, and (2) the growing phase. In the
first phase, it is assumed that all the other nodes, from
the node with the minimum energy level to the most ener-
getic node are chosen in turn and rewarded before n
i
acti-
vates the optimal node n

. Therefore, in the worst case, the
choice probability of the optimal node n

at the end of the
shrinking phase is computed as
p
+
i
(D
i
÷1) Pp
+
i
(D
i
÷2) (1 ÷ a) (6)
where p
+
i
(D
i
÷1) denotes the choice probability of the opti-
mal node n

(or optimal action a
+
i
) at stage (D
i
÷ 1), D
i
de-
notes the degree of node n
i
, a is the learning rate of the
proposed algorithm, and p
+
i
(D
i
÷1) denotes the choice
probability of the optimal node at the end of the shrinking
phase. Repeatedly substituting the recurrence function
p
+
i
(:) on the right hand side of Inequality (6), we have
p
+
i
(D
i
÷1) Pp
+
i
(1 ÷ a)
D
i
÷1
, where p
+
i
denotes the initial
choice probability of the optimal node n

. For the sake of
simplicity in notation, p
+
i
(D
i
÷1) is substituted by q
+
i
.
The growing phase starts when the optimal node n

is
chosen for the first time by node n
i
. Since the reinforce-
ment scheme by which the proposed algorithm updates
the probability vectors is L
R÷I
, the conditional expectation
of q
+
i
(k) (i.e., the choice probability of the optimal node at
stage k of the growing phase) remains unchanged when
the other nodes are selected. It increases only when the
optimal node is selected. Therefore, during the growing
phase, the changes in the conditional expectation of q
+
i
(k)
is always non-negative and as follows
q
+
i
(1) =q
+
i
÷a 1÷q
+
i
_ _
q
+
i
(2) =q
+
i
(1) ÷a 1÷q
+
i
(1)
_ _
=q
+
i
(1) (1÷a) ÷a
.
.
.
q
+
i
(k÷1) =q
+
i
(k÷2) ÷a 1÷q
+
i
(k÷2)
_ _
=q
+
i
(k ÷2) (1÷a) ÷a
q
+
i
(k) =q
+
i
(k ÷1) ÷a 1÷q
+
i
(k ÷1)
_ _
=q
+
i
(k÷1) (1÷a) ÷a
(7)
where k denotes the number of times n
i
selects the optimal
node n

before the following stop condition (derived from
the Bonferroni correction [27] to achieve an error rate low-
er than for the optimal area coverage c
+
) is met.
q
+
i
(k) = 1 ÷

[c
+
[
(8)
where [c
+
[ denotes the cardinality of the optimal area
coverage.
After substituting the recurrence function q
+
i
(k) we have
q
+
i
(k) = q
+
i
(k ÷1) (1 ÷ a) ÷ a
= q
+
i
(k ÷2) (1 ÷ a) ÷ a
_ ¸
(1 ÷ a) ÷ a
= q
+
i
(k ÷2) (1 ÷ a)
2
÷ a (1 ÷ a) ÷ a
= q
+
i
(k ÷3) (1 ÷ a) ÷ a
_ ¸
(1 ÷ a)
2
÷ a (1 ÷ a) ÷ a
= q
+
i
(k ÷2) (1 ÷ a)
3
÷ a (1 ÷ a)
2
÷ a (1 ÷ a) ÷ a
.
.
.
= q
+
i
(1) (1 ÷ a)
k÷1
÷ a (1 ÷ a)
k÷2
÷ ÷ a (1 ÷ a) ÷ a
= q
+
i
(1 ÷ a)
k
÷ a (1 ÷ a)
k÷1
÷ ÷ a (1 ÷ a) ÷ a
Hence, we have
q
+
i
(k) = q
+
i
(1 ÷ a)
k
÷ a (1 ÷ a)
k÷1
÷ ÷ a (1 ÷ a) ÷ a
(9)
After algebraic simplifications, we have
1660 J. Akbari Torkestani / Ad Hoc Networks 11 (2013) 1655–1666
q
+
i
(k) = q
+
i
(1 ÷ a)
k
÷ a (1 ÷ (1 ÷ a)÷
(1 ÷ a)
2
÷ ÷ (1 ÷ a)
k÷1
)
and
q
+
i
(k) = q
+
i
(1 ÷ a)
k
÷ a

k÷1
i=0
(1 ÷ a)
i
(10)
The second term on the right hand side of Eq. (10) is a
geometric series that sums up to a
1÷(1÷a)
k
1÷(1÷a)
_ _
, where
[1 ÷ a[ < 1. Since the learning rate a ÷ (0, 1), we have
q
+
i
(k) = q
+
i
(1 ÷ a)
k
÷ a
1 ÷ (1 ÷ a)
k
1 ÷ (1 ÷ a)
_ _
(11)
and
q
+
i
(k) = q
+
i
(1 ÷ a)
k
÷1 ÷ (1 ÷ a)
k
(12)
From Eqs. (8) and (12), we have
q
+
i
(1 ÷ a)
k
÷1 ÷ (1 ÷ a)
k
= 1 ÷

[c
+
[
(13)
and
(1 ÷ a)
k
=

[c
+
[ 1 ÷ q
+
i
_ _ (14)
Taking log
1÷a
of both sides of Eq. (14), we derive
k = log

[c+[ 1÷q
+
i
( )
1÷a
(15)
As mentioned earlier, during the growing phase, q
+
i
remains unchanged when the other nodes are penalized.
Therefore, k does not include the number of times the
other nodes are selected. Let q
+
i
be the choice probability
of the optimal node at the beginning of the growing phase.
After k iterations q
+
i
reaches 1 ÷ . On the other hand, the
choice probability of all the other nodes is initially 1 ÷ q
+
i
and reaches after the same number of iterations. There-
fore, the number of times the other nodes are selected,
before the stop condition given in Eq. (8) is met, is
1 ÷ q
+
i
÷

[c+[
1 ÷ q
+
i
÷

[c+[
k (16)
Let / denotes the total number of iterations required to
satisfy the stop condition. From Eq. (16) we have
/ =
2
1 ÷ q
+
i
÷

[c+[
k
By substituting k from Eq. (15) we have
/ =
2
1 ÷ q
+
i
÷

[c+[
log

[c+[ 1÷q
+
i
( )
1÷a
(17)
From Inequality (7) and Eq. (17), it is concluded that the
time complexity of the LAEEC for finding a
1

opt
i
is less
than
2
1 ÷ q
+
i
÷

[c+[
log

[c+[ 1÷q
+
i
( )
1÷a
(18)
where q
+
i
Pp
+
i
(1 ÷ a)
D
i
÷1
, and hence the proof of Lemma
1. h
Lemma 2. If the action probability vector p
i
(of each autom-
aton A
i
) is updated according to the updating rules of LAEEC,
the lower bound to the running time of LAEEC for finding a
1

opt
i
is greater than
2
1 ÷ p
+
i
÷

[c+[
log

[c+[ 1÷p
+
i
( )
1÷a
:
Proof. Lemma 2 considers the running time of the pro-
posed algorithm in the best case, when n
i
selects the opti-
mal node n

before the others. In this case, the learning
process does not include the shrinking phase. Therefore,
p
+
i
denotes the choice probability of the optimal node in
the beginning of the growing phase. Similar to the proof
of Lemma 1, it can be easily proved that the minimum
number of iterations required for satisfying the stop condi-
tion (8) is
2
1 ÷ q
+
i
÷

[c+[
log

[c+[ 1÷q
+
i
( )
1÷a
; (19)
where q
+
i
= p
+
i
, which completes the proof of Lemma 2. h
From Inequalities (18) and (19), it can be concluded that
2
1 ÷ q
+
i
÷

[c+[
log

[c+[ 1÷q
+
i
( )
1÷a
6 T
i
6
2
1 ÷ q
+
i
÷

[c+[
log

[c+[ 1÷q
+
i
( )
1÷a
;
where q
+
i
Pp
+
i
(1 ÷ a)
D
i
÷1
.
As described in Section 3, for each action a
j
i
, the initial
probability p
j
i
is set to
En
j
(k)
en
i
(k)
, where e
n
i
(k) =

(n
i
;n
j
)÷L(k)
E
n
j
(k). Therefore, the initial probability p
+
i
is set to
En+
(k)
en
i
(k)
.
Therefore, we have
!
E
n+
(k)
e
n
i
(k)
_ _
6 T
i
6 !
E
n+
(k)
e
n
i
(k)
(1 ÷a)
D
i
÷1
_ _
;
where
!(k) =
2
1 ÷ k ÷

[c+[
log

[c+[(1÷k)
1÷a
;
which completes the proof of the theorem.
Theorem 2. Let n
/
denotes the network node with the
maximum degree D. The time complexity of the proposed
algorithm for finding a
1

optimal solution to the coverage
problem is
!
E
n+
(k)
e
n
/
(k)
_ _
6 T 6 !
E
n+
(k)
e
n
/
(k)
(1 ÷a)
D÷1
_ _
;
where
!(k) =
2
1 ÷ k ÷

[c+[
log

[c+[(1÷k)
1÷a
Proof. As mentioned earlier, the proposed algorithm is
independently run at each node and each leaning automa-
ton locally updates its internal state to converge to the
optimal action. Therefore, node n
/
requires the maximum
number of iterations for finding
1

optimal action of
J. Akbari Torkestani / Ad Hoc Networks 11 (2013) 1655–1666 1661
learning automaton A
/
. On the other hand, from Lemmas
1 and 2, the running time of the proposed algorithm for
finding
1

optimal coverage is limited by the upper bound
and lower bound on the running time of the algorithm for
the node with the maximum degree D. Therefore, it is con-
cluded that the time taken by the proposed algorithm for
finding a
1

optimal coverage is
!
E
n+
(k)
e
n
/
(k)
_ _
6 T 6 !
E
n+
(k)
e
n
/
(k)
(1 ÷a)
D÷1
_ _
;
where!(k) =
2
1÷k÷

[c+[
log

[c+[(1÷k)
1÷a
, that completes the proof of
Theorem 2. h
5. Experiments
In this section, several simulation experiments are
conducted to show the performance of the proposed
CDS-based area coverage algorithm. The results of the
proposed method are compared with those of three
CDS-based energy efficient area coverage protocol A3
[24], A3CovLite [6], and A1 [4] in terms of control mes-
sage overhead, percentage of covered area, residual en-
ergy, number of active nodes (CDS size), and network
lifetime. In these experiments, the wireless sensor net-
work is setup as follows. The wireless sensor nodes are
uniformly and randomly distributed within a square sen-
sor deployment area of size 150(m) × 150(m) at random.
The number of sensor nodes ranges from 50 to 250 with
increment step 50. The radio transmission range of each
sensor node is set to 20(m), and the sensing range of each
node is set to 10(m). The size of each data packet is 100
bytes. The simulation time of each experiment is 1500
(s). Each sensor node has an omnidirectional antenna
with a fixed radio propagation range. IEEE 802.11 [28]
(Distributed Coordination Function) with CSMA/CA (Car-
rier Sense Multiple Access/Collision Avoidance) is used
as the medium access control protocol, and two ray
ground as the radio propagation model. The maximum
energy level of each sensor node is 2.0(J), and the initial
energy level the sensors is randomly selected from the
uniform distribution defined over interval [1.5(J), 2.0(J)].
The energy model presented by Heinzelman et al. [29]
is used for estimating the amount of energy consumption.
In this energy model that is based on the first order radio
model, each sensor node consumes 50
nJ
bit
_ _
to run the
transmitter or the receiver circuitry. Each sensor node
also consumes 100
pJ
bit
=m
2
_ _
for handling the transmit
amplifier. Therefore, the energy amount required for
receiving a k-bit data packet is estimated as
k(bit) 50
nJ
bit
_ _ _ _
= 50k(nJ)
The energy amount that is consumed to transmit a mes-
sage of length k to a destination node located x(m) far from
the transmitter is computed as
k(bit) 50
nJ
bit
_ _ _ _
÷ k(bit) 100
pJ
bit
_
m
2
_ _ _ _
x
2
(m
2
)
= 50k(nJ) ÷100 kx
2
(pJ)
In these experiments, the proposed area coverage algo-
rithm, LAEEC, is configured as follows. The environment
in which the learning automata perform is assumed to be
P-model. Each learning automaton updates its action prob-
ability vector according to reinforcement scheme L
R÷I
. In
these experiments, LAEEC is calibrated by tuning degree-
constraint d and learning rate a as follows. The covered
area and network lifetime are measured, where degree-
constraint d changes from 2 to 15. The obtained results
show that the best trade-off between the covered area
and network lifetime is made when degree-constraint d
is set to 7. The same experiment is conducted to adjust
the learning rate, where a changes from 0.05 to 0.5. The re-
sults show that LAEEC has the best performance when the
learning rate is set to 0.15. In The energy threshold T
n
i
is
defined as 0:5 E
c
k
. That is, a new coverage process initiates
when the energy level E
c
k
falls to 50% of its initial value. All
timeouts are set to 100 ms. In class A3, the weights are set
as follows: W
E
denoting the weight for the remaining en-
ergy in the node is set to 0.5, and W
D
denoting the weight
for the distance from the parent node is set to 0.5 too,
where W
D
+ W
E
= 1. For A3-based protocols, the timers
are set as t
0
= 1.5, t
1
= 30.0, t
2
= 15.0, and t
3
= 60.0.
5.1. Number of active nodes
This metric is defined as the average number of nodes
that are activated to cover the sensor field (i.e., the average
CDS size). This metric implicitly shows the number of
dominators in the CDS. The residual energy of the network
is inversely proportional to the number of active nodes.
Therefore, the energy-efficient protocols try to minimize
the number of active nodes. Fig. 2 shows the number of ac-
tive nodes (dominators in CDS) against the total number of
network nodes. From the results shown in this figure it can
be seen that A3 has the minimum number of active nodes
as compared to the other protocols. This is because A3
algorithm uses a selection metric giving the priority to
the farther nodes from the parent having higher energy le-
vel. This method considerably reduces the CDS size. As
shown in Fig. 3, this results in the lower coverage rate of
A3. A3CovLite uses extra active nodes to cover the points
of the sensor field leaved uncovered in A3. So, it requires
more active nodes than A3. Though A1 provides a higher
Fig. 2. The number of active nodes vs. the total number of network nodes.
1662 J. Akbari Torkestani / Ad Hoc Networks 11 (2013) 1655–1666
coverage rate than A3 and A3CovLite, it suffers from the
many redundant active nodes. This is due to the fact that
A1 forms the reduced topology without any metric desired
for the reduction in the size of the CDS. From the results
shown in Fig. 2, it can be seen that the number of active
nodes in LAEEC is larger than that of A3-based approaches
and smaller than that of A1. In LAEEC, the number of active
nodes is controlled by degree-constraint d. Larger values of
d reduces the number of active nodes and smaller values of
d leads to very large CDS.
5.2. Covered area
This metric shows the percentage of the sensing area
that is covered by the active sensor nodes. The coverage
percentage is a measure of the quality of service (QoS) of
the coverage protocol. Fig. 3 shows the percentage of the
sensor field covered by the selected active nodes in differ-
ent algorithms as a function of the network size. From the
results shown in this figure, it can be seen that the covered
area significantly increases as the network density (i.e., the
number of nodes in the network) increases. This is because
the number of scattered nodes within the simulation area
considerably exceeds the number of active nodes required
in optimal deployment. The obtained results depicted in
Fig. 3 also show that A3 provides the minimum area cover-
age as compared to the other protocols. This is due to the
fact that A3 sends a sleep message to the nodes within
the communication area of the other nodes in the reduced
tree topology. This may cause some points of the area re-
main uncovered when the sensing range is smaller than
the communication range. A3CovLite solves the coverage
problem with A3 by sending a node to the sleep mode if
it is sensing-covered by another active node. That is why,
the A3CovLite has a higher rate of area coverage than A3.
Comparing the results shown in Fig. 3, it is observed that
the proposed area coverage protocol LAEEC always covers
the whole monitoring area. This is because, LAEEC first
constructs a degree-constrained CDS-based backbone cov-
ering all the network points. Then, it sends all the non-
dominators to the sleep mode. A1 outperforms A3 and
A3CovLite in terms of covered area. This can be due to
using a larger number of active nodes to cover the area.
5.3. Residual energy
The residual energy is defined as the average remaining
energy of the active sensor nodes at the end of each simu-
lation experiment. Fig. 4 shows the average residual energy
of the active sensor nodes as a function of the network size.
From the results shown in this figure, it is observed that
the average residual energy level of the proposed area cov-
erage algorithm is significantly higher than the other
methods. This is due to the fact that the proposed method
makes a good trade-off between the number of active
nodes (required to cover the area) and the amount of en-
ergy consumption in each active node by selection of a
proper degree-constraint. This significantly reduces the
number of nodes covering the same points of the area,
while avoids the rapid exhaustion of the active sensors
for handling a huge number of neighbors. The results also
show that A3 has the lowest residual energy level, and
A3CovLite slightly outperforms A3. This is because A3-
based approaches reduce the number of backbone nodes
by activating the farther nodes from the parent node. This
causes a non-uniform distribution of the communication
overhead and places a heavy load on the active nodes.
Therefore, A3-based approaches result in the imbalanced
energy consumption within the network. Comparing the
results of A1 and A3, it can be seen that A1 provides a sig-
nificant higher residual energy level as compared to A3.
This is due to the fact that in A1 protocol the nodes calcu-
late the timeout with the selection criteria resulting in a
balanced virtual backbone.
5.4. Network lifetime
Network lifetime is defined as the average period of
time during which the set of active sensors remain con-
nected. Minimizing the energy consumption and maximiz-
ing the network lifetime are the major concerns of the
design of the coverage protocols. Network lifetime implic-
itly shows the energy-efficiency and load balancing of the
coverage protocol. Fig. 5 shows the changes in the network
lifetime as the number of network nodes changes from 50
to 250 with increment step 50. From the results shown in
Fig. 3. The percentage of the covered area vs. the network size.
Fig. 4. The average residual energy of the active nodes as a function of the
number of nodes.
J. Akbari Torkestani / Ad Hoc Networks 11 (2013) 1655–1666 1663
Fig. 5, it can be seen that for all coverage algorithms, the
network lifetime reduces as the network size increases.
This can be due to the fact that the backbone size grows
and it makes harder evenly distribution of the network
load on the backbone nodes. Comparing the curves de-
picted in Fig. 5, it is observed that A3 has the shortest life-
time and the proposed area coverage algorithm has the
longest lifetime. The main objective of the proposed cover-
age algorithm is to extend the lifetime of the network de-
ployed to monitor the area as much as possible. To do so, it
uses the degree-constrained minimumweight CDS concept
to activate the nodes having the maximum residual energy
level, and to evenly distribute the network load on the ac-
tive nodes. This significantly extends the lifetime of the ac-
tive nodes. As mentioned earlier, A3 tries to reduce the
required number of active nodes to cover the area. On
one hand, this reduces the total energy consumption of
the network by keeping a larger number of sensors in sleep
mode. However, on the other hand, the heavy burden
placed on the small set of active nodes drains them sooner.
This significantly shortens the network lifetime. A3CovLite
shows a better performance in Fig. 5 as compared to A3. As
shown in Fig. 2, this is achieved by adding redundant active
nodes (dominators) to the CDS. However, as the curves
show in Fig. 4, there is no significant gap between the aver-
age residual energy level of A3 and A3CovLite. A1 uses the
largest set of (redundant) active nodes to cover the area.
The results given in Fig. 5 show its superiority over A3
and A3CovLite.
5.5. Control message overhead
In this experiment, the control message overhead is
defined as the number of (extra) control messages re-
quired for coverage (degree-constrained CDS formation)
process. The extra messages are the control messages that
are used to construct the CDS-based backbone (i.e., the
message overhead of the coverage protocol). This metric
is measured as the number of control messages that must
be sent per second. Fig. 6 depicts the control message
overhead of the coverage algorithms vs. the number of
nodes. The results show that LAEEC has the lowest control
message overhead and A3 has the highest one. The results
also reveal that A3CovLite lags far behind A1. The reason
for the highly message overhead of A3 is that this proto-
col uses four messages to construct the CDS backbone.
The message complexity of A3 (in worst case) is 4n,
where n is the number of network nodes. A3 uses a chil-
dren recognition message of size 100 bytes as well as
three other messages of size 25 bytes. A3CovLite only
uses two messages of size 25 bytes. The message com-
plexity of A3CovLite is at most 2n. Therefore, it has a
meaningfully lower message overhead than A3. A1 uses
only one type of message (a hello message of size 25 by-
tes) for CDS formation (having message complexity n).
That is why, A1 outperforms A3 and A3CovLite in terms
of control message overhead. The proposed area coverage
algorithm uses only an activation (ACT) message to con-
struct the CDS structure. ACT is a variable-length message
whose size is in the interval [1; [c
k
[[ bytes. The number of
times this message is exchanged between the active
nodes is [c
k
[. Therefore, the average message complexity
of LAEEC is [c
k
[
2
=2 bytes that is significantly lower than
that of A1.
6. Conclusion
Over the past couple of decades, CDS has received a lot
of attention and found many applications in wireless net-
working such as routing, clustering, backbone formation,
and multicasting. CDS has recently emerged as an innova-
tive approach to model the area coverage problem in
wireless sensor networks and several CDS-based area cov-
erage protocols have been proposed. However, the major
problem affecting the performance of the existing CDS-
based coverage protocols is that they aim at maximizing
the number of sleep nodes to save more energy. This im-
poses a heavy burden on the active nodes for handling a
large number of neighbors. The rapid exhaustion of the
active nodes may disconnect the network topology and
leave the area uncovered. This paper proposed a degree-
constrained minimum-weight extension of the CDS prob-
Fig. 5. Network lifetime vs. the number of nodes.
Fig. 6. The control message overhead vs. the number of network nodes.
1664 J. Akbari Torkestani / Ad Hoc Networks 11 (2013) 1655–1666
lem called DCDS to model the area coverage problem in
WSNs. Selection of an optimal degree-constraint for the
DCDS balances the network load on the active nodes
and improves the network coverage, connectivity, and
lifetime. This paper designed a learning automata-based
heuristic called LAEEC for finding a near optimal solution
to the proxy equivalent DCDS problem in WSN. The com-
putational complexity of the proposed algorithm to find a
1

optimal solution of the area coverage problem is
approximated. Several simulation experiments were per-
formed to show the performance of the proposed area
coverage algorithm. The results show that LAEEC outper-
forms the existing CDS-based coverage protocols in terms
of the control message overhead, percentage of covered
area, residual energy, number of active nodes (CDS size),
and network lifetime.
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Javad Akbari Torkestani received the B.S. and
M.S. degrees in Computer Engineering in Iran,
in 2001 and 2004, respectively. He also
received the Ph.D. degree in Computer Engi-
neering from Science and Research University,
Iran, in 2009. Currently, he is an assistant
professor in Computer Engineering Depart-
ment at Arak Azad University, Arak, Iran. Prior
to the current position, he joined the faculty
of the Computer Engineering Department at
Arak Azad University as a lecturer. His
research interests include wireless networks,
multi-hop networks, fault tolerant systems, grid computing, learning
systems, parallel algorithms, and soft computing.
1666 J. Akbari Torkestani / Ad Hoc Networks 11 (2013) 1655–1666

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