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Proceedings ArticleDOI

A Distributed Greedy Algorithm for Constructing Connected Dominating Sets in Wireless Sensor Networks

01 Jan 2014-pp 181-187

TL;DR: This paper presents a distributed greedy algorithm for constructing a CDS that is up to 30% smaller in size than K2 that operates in two phases, first constructing a dominating set and then connecting the nodes in this set.

AbstractA Connected Dominating Set (CDS) of the graph representing a Wireless Sensor Network can be used as a virtual backbone for routing in the network. Since sensor nodes are constrained by limited on-board batteries, it is desirable to have a small CDS for the network. However, constructing a minimum size CDS has been shown to be a NP-hard problem. In this paper we present a distributed greedy algorithm for constructing a CDS that we call Greedy Connect. Our algorithm operates in two phases, first constructing a dominating set and then connecting the nodes in this set. We evaluate our algorithm using simulations and compare it to the two-hop K2 algorithm in the literature. Depending on the network topology, our algorithm generally constructs a CDS that is up to 30% smaller in size than K2.

Summary (2 min read)

1 INTRODUCTION

  • Wireless Sensor Networks (WSNs) have attracted considerable research interest in the past decade (Iyengar and Brooks, 2004) (Akyildiz et al., 2002) (Chong and Kumar, 2003).
  • They have evolved from research to deployment with many environmental, security, energy and other applications.
  • Each sensor serves as both a data gathering source and a router, forwarding messages from other nodes.
  • A key approach to solve the problem of data gathering and communication involves the construction of a connected dominating set (CDS) that serves as a virtual backbone for the network.
  • The construction of a CDS provides the network with a virtual backbone over which routing, multicast and broadcast can be performed since every node is either in the backbone or has a neighbor in the backbone.

3 Greedy Connect Algorithm for CDS construction

  • Distributed algorithm for constructing a connected dominating set.the authors.
  • The authors also assume every sensor node to have a unique identifier.
  • The sensor nodes fields as used in their algorithm are shown in Table 1.

3.1 Phase 1: Greedy construction of a dominating set

  • Phase 1 uses node coloring to implement its greedy approach.
  • Initially the authors start out with all nodes being colored white.
  • At this point, the node with the highest white neighbor count adds itself to the dominating set by changing its color to black and changing the color of its white neighbors to grey.
  • The second pass looks at only those nodes that are still white and essentially repeats the process to ensure that the set is dominating.
  • Request the white neighbor count for every neighbor u ∈ N(v) if v.

3.2 Phase 2: Connecting the Dominating Set

  • In this subsection the authors will present their connection algorithm.
  • Assume there is a component separated from all other components by at least three vertices at the end of the algorithm, also known as Lemma Proof.
  • The authors can visualize this scenario as COMP1− a− b− c−COMP2 where a,b,c are the three vertices separating COMP1 and COMP2.
  • The authors make the assumption that every sensor has a unique identifier associated with it.
  • As can be seen from the algorithm below, the authors initialize the component id of each grey sensor to -1 and for every connected dominating component, they initialize its component number to that of the highest id sensor in that connected component.

3.3 An example

  • The figure shows the sensors and the resulting graph representing the network.
  • As mentioned in (Zhang and Hou, 2005), the transmission radius is double the sensing radius.
  • In the first round of Phase 1 each vertex checks if it has the highest (or tied highest) white neighbor count in its neighborhood.
  • At this point the authors have a Dominating Set with two components (each of the two black nodes being a separate component).
  • This node will assume the component id of the higher of these two nodes (i.e., 5) and this component id will propagate across the CDS resulting in all the black nodes having a component id of 5 as shown in the second figure of Figure 3.

4 Results

  • For their simulation setup, the authors create networks of sensors with 100 nodes scattered randomly in a 100x100m area.
  • Each data point in the figure represents an average of the ten graphs generated for that size.
  • The authors plot the size of the CDS for both algorithms in each of the random networks they generated with this range.
  • As can be seen from the figure, their algorithm is consistently better than K2.
  • One major point to note is that the authors have not yet conducted simulation studies on the impact of their algorithm on the lifetime of the network.

5 CONCLUSIONS

  • In conclusion, in this paper the authors present a 2-phase algorithm that starts with greedy coloring scheme to form a dominating set which they then connect using the sensor id’s of the disconnected component.
  • In simulation studies their approach has been shown to result in a smaller CDS than a popular 2-hop algorithm in the literature.

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A Distributed Greedy Algorithm for Constructing
Connected Dominating Sets in Wireless Sensor
Networks
Akshaye Dhawan
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Nicholas A. Scoville
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Michelle Tanco
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A Distributed Greedy Algorithm for Constructing Connected
Dominating Sets in Wireless Sensor Networks
Akshaye Dhawan, Michelle Tanco and Nicholas Scoville
Department of Mathematics and Computer Science, Ursinus College, 610 E Main Street, Collegeville, PA, USA
{adhawan, mitanco, nscoville}@ursinus.edu
Keywords:
Wireless Sensor Networks, Dominating Sets, Distributed Algorithms
Abstract:
A Connected Dominating Set (CDS) of the graph representing a Wireless Sensor Network can be used as a
virtual backbone for routing in the network. Since sensor nodes are constrained by limited on-board batteries,
it is desirable to have a small CDS for the network. However, constructing a minimum size CDS has been
shown to be a NP-hard problem. In this paper we present a distributed greedy algorithm for constructing a
CDS that we call Greedy Connect. Our algorithm operates in two phases, first constructing a dominating
set and then connecting the nodes in this set. We evaluate our algorithm using simulations and compare it
to the two-hop K2 algorithm in the literature. Depending on the network topology, our algorithm generally
constructs a CDS that is up to 30% smaller in size than K2.
1 INTRODUCTION
Wireless Sensor Networks (WSNs) have attracted
considerable research interest in the past decade
(Iyengar and Brooks, 2004) (Akyildiz et al., 2002)
(Chong and Kumar, 2003). They have evolved from
research to deployment with many environmental, se-
curity, energy and other applications. WSNs consist
of a number of low-cost sensors scattered in a geo-
graphical area of interest and connected by a wire-
less RF interface. Sensors gather information about
the monitored area and send this information to gate-
way nodes known as sinks. Most common network
models consist of a distributed and localized control
with no central management. Each sensor serves as
both a data gathering source and a router, forward-
ing messages from other nodes. In order to keep their
cost low, the sensors are equipped with limited energy
(Feeney and Nilsson, 2001) (Feeney, 2001) and com-
putational resources. The energy supply is typically in
the form of a battery and once the battery exhausted,
the sensor is considered to be dead. A key approach
to solve the problem of data gathering and communi-
cation involves the construction of a connected domi-
nating set (CDS) that serves as a virtual backbone for
the network.
In this paper, we use a graph G = (V, E) to repre-
sent the wireless sensor network, where V is the set
of sensors in the network and an edge (u, v) E rep-
resent a link between two sensors u, v that are within
communicating distance of each other. We also as-
sume that all sensors are deployed on a 2-dimensional
plane and have a uniform transmission range. The re-
sulting graph is known as a Unit-Disk Graph (UDG)
(Clark et al., 1990) since the uniform transmission
range results in edges of equal (or unit) weight. We
also assume that the transmission range is at least
twice the sensing range since as shown in (Zhang and
Hou, 2005) a covered network is also connected if this
is true.
Given such a representation of a sensor network,
a dominating set (DS) of a graph G is a subset D V
such that for all u V either u D or u is adjacent to a
node in D (i.e., (u, w) E for some w D). Nodes in
the dominating set D are referred to as dominators and
the remaining nodes in V D are referred to as dom-
inatees. A Connected Dominating Set (CDS) is a set
that is dominating and induces a connected subgraph.
In other words, it is a set of nodes C V such that the
nodes in C are both dominating and connected.
The construction of a CDS provides the network
with a virtual backbone over which routing, multicast
and broadcast can be performed since every node is
either in the backbone or has a neighbor in the back-
bone. Also, the construction of a CDS, allows the net-
work to adapt to changes in the topology since only
the nodes in the CDS need to be aware of routing
information. By being connected the backbone can
relay a message to either the destination directly (if
the destination is in the CDS) or through the domi-

nator of the destination. Since the nodes in the CDS
are actively draining their batteries by serving as re-
lay nodes for the network, it is desirable to construct
a minimum size CDS. However this has been shown
to be a NP-hard problem in (Clark et al., 1990). Much
attention has been given to centralized algorithms
based on the use of a maximal independent set (MIS)
to construct a CDS. The current best performance ra-
tio of 4.8 + ln5 was shown in (Li et al., 2005).
In this paper, we present a two-phase distributed
and localized greedy algorithm that first constructs a
dominating set (Phase 1) and then connects it (Phase
2). Our algorithm assumes that each sensor has a
unique identifier. The resulting CDS has been shown
to be significantly smaller in size to that of a compara-
ble distributed algorithm in the literature that we call
K2 (Dai and Wu, 2004).
The remainder of this paper is organized as fol-
lows in Section 2, we look at the literature on con-
struction of connected dominating sets. In Section 3
we explain our two phase algorithm. We look at a
simulation evaluation of our algorithm in Section 4.
Finally, we conclude in Section 5.
2 Related Work
In this section we briefly summarize related work in
this area. Considerable work has been done in the
development of both centralized and distributed algo-
rithms for CDS construction in the literature. Below
we focus mostly on distributed algorithms.
The applications of a connected dominating set
to routing in ad hoc networks were first outlined in
(Ephremides et al., 1987) where they presented the
idea of constructing a virtual backbone and its appli-
cation to routing. This paper led to several papers that
design approximation algorithms for this problem. A
coloring scheme similar to the one we use is a com-
mon theme in many of these papers with all nodes be-
ing white initially, with dominator’s being black and
dominatee’s being grey at the conclusion of these al-
gorithms.
(Guha and Khuller, 1998) presents a centralized
algorithm with a O(H) approximation factor where
is the maximum degree and H is the harmonic func-
tion. In (Ruan et al., 2004) the authors present a 1-
phase greedy algorithm that has a performance ra-
tion of 2 + ln. (Funke et al., 2006) was one of the
first distributed algorithms to show an improved anal-
ysis of the relationship between the size of a maximal
independent set and a minimum CDS in a unit disk
graph, which yields better bounds for many other al-
gorithms. (Wan et al., 2002) presents a distributed al-
gorithm for CDS construction by constructing a span-
ning tree first and then labeling every node in the tree
as a dominator or dominatee. The Performance Ra-
tio for this algorithm was shown to be 8. In (Alzoubi
et al., 2002) the same authors noticed the difficulty
of maintaining a CDS and designed a localized 2-
phase algorithm that uses a Maximal Independent Set
but this algorithm has a PR of 192. (Li et al., 2005)
presents the best known PR of 4.8 + ln5 in a central-
ized algorithm. The algorithm is known as S-MIS and
uses a Steiner Tree to construct a CDS. In this algo-
rithm they build a Maximal Independent Set in Phase
1. Then in Phase 2, they employ a greedy algorithm
to construct a Steiner tree with minimal number of
Steiner nodes to connect the nodes in the MIS. They
mention that a distributed implementation is possible
but do not elaborate on this algorithm or its PR.
(Wu and Li, 1999) presents an earlier version of a
pruning algorithm that the authors refined into the K2
algorithm. Finally, we look at the K2 algorithm (Dai
and Wu, 2004) that we compare ourselves against.
The algorithm is a two phase algorithm which first
creates a connected dominating set and then reduces
the size of the set. In phase one, each sensor adds
itself to the dominating set if any two of its neigh-
bors are not neighbors. It is clear that if we start
with a connected graph we will get a connected dom-
inating set since any two non-connected sensors that
share a neighbor will be connected. However, this
set is likely to contain many more nodes than neces-
sary since the marking process was very simple. In
order to reduce the size of the set, the authors use a
k-reduction (where k is the number of hops the al-
gorithm is looking at) to remove unnecessary sensors
from the set. For each sensor in the dominating set we
consider every k-hop group of neighbors where each
member of the group is in the dominating set. If one
of these groups contains every neighbor of the origi-
nal sensor in its neighbor set, we remove the original
sensor from the dominating set. The dominating set
is still connected by the group of k neighbors. We
call this the K2 algorithm because we compare our-
selves against the 2-hop version of this algorithm. As
k increases, the size of the connected dominating set
decreases. However, the message and time complex-
ity increase since we have to check each size k group
of neighbors for each sensor. For the purposes of this
paper we let k = 2, since an algorithm cannot be lo-
calized and use a reasonable number of messages if it
requires more than 2-hops of information. This algo-
rithm has the benefit of the CDS being easy to main-
tain.

3 Greedy Connect Algorithm for
CDS construction
In this section we present our greedy, distributed al-
gorithm for constructing a connected dominating set.
The algorithm is a two-phase algorithm. In Phase 1,
we construct a dominating set and in Phase 2, we con-
nect the dominating set to form a connected dominat-
ing set. We begin by presenting Phase 1 - a greedy
approach to constructing a dominating set.
In this section, we will use a graph G = (V, E) to
represent the sensor network. We will also use the
notation N(u) to denote the one-hop neighbor set of
node u V . We also assume every sensor node to
have a unique identifier. The sensor nodes fields as
used in our algorithm are shown in Table 1.
Table 1: Fields for a given sensor node v
Field Meaning
v.COLOR The current color of the sensor
v.ID Unique identifier for the sensor
v.WhiteCount Number of white nodes in N(v)
3.1 Phase 1: Greedy construction of a
dominating set
Phase 1 uses node coloring to implement its greedy
approach. We summarize the meaning of the colors
in Table 2. Initially we start out with all nodes be-
ing colored white. The heuristic is greedy because
our criteria for adding nodes to the dominating set is
to pick the node that dominates the highest number
of non-dominated nodes. The color white represents
nodes that have not been dominated. When a node is
added to the dominating set, it is colored black and its
neighbors are colored grey to indicate that they have
been dominated.
Table 2: Node color assignments for Phase 1.
Color Meaning
White Undiscovered by the Dominating Set
Grey Dominated but has white neighbors
Black Dominated and has no white neighbors
In the first pass, every node every node exchanges
its white neighbor count with its neighbors. At this
point, the node with the highest white neighbor count
adds itself to the dominating set by changing its color
to black and changing the color of its white neighbors
to grey. Since this pass happens asynchronously, there
is a possibility (as shown by the example in Section
3.3) that some nodes have not yet been dominated.
The second pass looks at only those nodes that are
still white and essentially repeats the process to en-
sure that the set is dominating.
Require: v V v.COLOR WHITE
if v.COLOR ==WHITE then
*Initially every node will do this once*
Request the white neighbor count for every neigh-
bor u N(v)
if v.WhiteCount >= u.WhiteCount
u N(v) then
v.COLOR BLACK
for every neighbor u N(v) do
if u.COLOR == WHITE then
u.COLOR GREY
end if
end for
end if
end if
if v.COLOR==WHITE then
Request the white neighbor count for every neigh-
bor u N(v)
high The node with the highest WhiteCount
high.COLOR BLACK
for every neighbor u N(high) do
if u.COLOR == WHITE then
u.COLOR GREY
end if
end for
end if
When the above algorithm concludes, we are left
with a dominating set that is possibly fragmented into
disconnected components. In Phase 2 we will connect
these components. The time complexity of this phase
is O(n), where is the maximum degree of a node in
V . This is because the first pass takes O(n) since ev-
ery sensor exchanges information with its neighbors
and the second pass takes O(w) where w is the num-
ber of white nodes left after the first pass and w n.
Lemma 1: The nodes colored Black at the end of
Phase 1 represent a Dominating Set for the graph G.
Proof: Assume that at the end of Phase 1, there
exists a node that is still colored white (i.e., it is not
adjacent to a black node or colored black itself). In the
second pass (that every white sensor goes through),
each sensor either adds either itself or a neighbor to
the dominating set. If a sensor is added to the dom-
inating set, all its white neighbors are colored grey.
Hence all white nodes must be either grey or black
when the second pass of Phase 1 concludes. There-
fore, such a node cannot exist and the set of black
nodes is dominating.

3.2 Phase 2: Connecting the
Dominating Set
In this subsection we will present our connection al-
gorithm. However, before we can do so, we need
to prove some properties of the dominating set con-
structed at the end of Phase 1 since we rely on
these properties to come up with the construction
that connects the disconnected dominating compo-
nents formed at the end of Phase 1.
Lemma 2: Any component of a dominating set is
separated by at most two vertices from another com-
ponent.
Proof: Assume there is a component separated
from all other components by at least three vertices
at the end of the algorithm. We can visualize this sce-
nario as COMP1 a b c COMP2 where a, b, c
are the three vertices separating COMP1 and COMP2.
Clearly the nodes a and c are dominated by the two
components. Also, by Lemma 1, b must be adjacent
to or in the dominating set. If b is dominated by a dif-
ferent component, this would create a path of length
two from both COMP1 and COMP2 to the component
dominating b, thereby leading to a contradiction.
Lemma 3: Connecting the dominating set created
by the greedy algorithm takes adding at most 2(n 1)
vertices to the dominating set where n is the number
of components of the dominating set.
Proof: Base Case: Consider a dominating set of
two components. By Lemma 2 there are at most two
vertices need to connect this set. Thus the base case
holds: to connect a set of two components we need
at most 2 = 2(2 1) vertices. By the inductive hy-
pothesis a dominating set of n 1 components can
be connected with 2((n 1) 1) = 2(n 2) = 2n 4
components. By Lemma 2, another component is at
most 2 vertices away. Then the limit for n components
is 2n 4 +2 = 2n 2 = 2(n 1) vertices.
Based on these two lemmas we now present the
connection phase of our algorithm. We make the as-
sumption that every sensor has a unique identifier as-
sociated with it. As can be seen from the algorithm
below, we initialize the component id of each grey
sensor to -1 and for every connected dominating com-
ponent, we initialize its component number to that of
the highest id sensor in that connected component.
This allows every component to have an associated
id - that of the highest id sensor in that component.
Now, if a grey is connected to two components with
different id’s, it colors itself black (in order to connect
these two components). It also updates its id to that
of the largest of these components. Since two compo-
nents can be at most two hops away (by Lemma 2), in
the next for loop, we check if any pair of sensors con-
nects two disconnected dominating components and
color this pair black.
Require: Recursively compute a component number
based on the id of the largest id sensor for that com-
ponent. Initialize all dominatees (grey) to an com-
ponent number of -1.
for all non-dominating (grey) nodes in V do
if v is connected to two dominating components
with different IDs then
v.COLOR BLACK
v.ID max component ID of the compo-
nents it connects
end if
end for
for every pair (u,v) of non-dominating connected
sensors do
highU max(N(u).ID)
highV max(N(v).ID)
if (highU 6= highV) then
u.COLOR BLACK
v.COLOR BLACK
change v.ID and u.ID to the component ID of
the component they joined
end if
end for
3.3 An example
We will now look at an example of both phases in
operation. We use the network shown in Figure 1 as
our exemplar. The figure shows the sensors and the
resulting graph representing the network. As men-
tioned in (Zhang and Hou, 2005), the transmission ra-
dius is double the sensing radius. At the start of the
algorithm all vertices are colored white (shown here
in yellow). The number next to each sensor indicates
its white neighbor count which at initialization is just
the degree of each node.
In the first round of Phase 1 each vertex checks if it
has the highest (or tied highest) white neighbor count
in its neighborhood. If so, it adds itself to the dom-
inating set (denoted in black) and tells all its neigh-
bors they have been dominated (denoted in gray). If
not, the vertex waits for round two. Since each ver-
tex is discovering its white neighbor count simultane-
ously, in this example only the vertex of white neigh-
bor count ve will add itself. The vertex connected to
two leaves was not added since it had a neighbor with
a higher white count. In the second pass, each of the
white sensors checks which neighbor has the highest
count (including itself) and tells that neighbor to add
itself to the dominating set. The coloring at the end of
each pass of Phase 1 along with the component id’s of
the two black nodes is shown in Figure 2. Here we as-

Citations
More filters

01 Jan 2005
TL;DR: This paper presents a very simple distributed algorithm for computing a small CDS, improving upon the previous best known approximation factor of 8 and implying improved approximation factors for many existing algorithm.
Abstract: Several routing schemes in ad hoc networks first establish a virtual backbone and then route messages via back-bone nodes. One common way of constructing such a backbone is based on the construction of a minimum connected dominating set (CDS). In this paper we present a very simple distributed algorithm for computing a small CDS. Our algorithm has an approximation factor of at most 6.91, improving upon the previous best known approximation factor of 8 due to Wan et al. [INFOCOM'02], The improvement relies on a refined analysis of the relationship between the size of a maximal independent set and a minimum CDS in a unit disk graph. This subresult also implies improved approximation factors for many existing algorithm.

151 citations


Proceedings ArticleDOI
01 Nov 2018
TL;DR: To improve packet delivery ratio, this work considers three different relay selection mechanisms and develops their extensions that are capable to operate in a distributed fashion and is evaluated via extensive simulations.
Abstract: Bluetooth Mesh (BM) is a new communication standard, which is designed for the upcoming Internet of Things. It builds on the Bluetooth Low Energy (BLE) protocol and allows devices to extend the range and create a mesh network. BM introduces a publisher/ observer structure where a publisher node can broadcast a packet, known also as an advertisement, and all observers can receive the packet. Typically, in BM networks flooding is used to propagate the advertisements. Flooding is known to suffer from broadcast storm problem and be nonreli-able. To improve packet delivery ratio we propose an approach where only a few nodes, relays, are involved in packet forwarding. Selection of the relay nodes, which is a focus of the paper, is a nontrivial task: on the one hand, a minimization of number of relays is desired, on the other hand, using a minimum dominated set would not provide redundancy. We consider three different relay selection mechanisms and develop their extensions that are capable to operate in a distributed fashion. Their performance is evaluated via extensive simulations.

10 citations


Cites background or methods from "A Distributed Greedy Algorithm for ..."

  • ...Greedy Connect by [9] creates a minimised connected dominating set in a greedy fashion....

    [...]

  • ...Therefore, descriptions presented below slightly deviate from the original descriptions in [9], [10], [11]....

    [...]


Proceedings ArticleDOI
01 Dec 2015
TL;DR: Three randomized algorithms for constructing a minimal CDS are presented that are generally equivalent in size to those constructed by K2 while being asymptotically better in time and message complexity.
Abstract: A Connected Dominating Set (CDS) of a graph representing a Wireless Sensor Network can be used as a virtual backbone for routing through the network. Since the sensors in the network are constrained by limited battery life, we desire a minimal CDS for the network, a known NP-hard problem. In this paper we present three randomized algorithms for constructing a CDS. We evaluate our algorithms using simulations and compare them to the two-hop K2 algorithm and two other greedy algorithms from the literature. After pruning, the randomized algorithms construct a CDS that are generally equivalent in size to those constructed by K2 while being asymptotically better in time and message complexity. This shows the potential of significant energy savings in using a randomized approach as a result of the reduced complexity.

4 citations


Proceedings ArticleDOI
01 Dec 2015
TL;DR: This work has developed an algorithm specifically targeted towards the non-total type of PIDS, the Total Positive Influence Dominating Set (TPIDS), which consistently generates smaller PIDS than both existing algorithms.
Abstract: Current algorithms in the Positive Influence Dominating Set (PIDS) problem domain are focused on a specific type of PIDS, the Total Positive Influence Dominating Set (TPIDS). We have developed an algorithm specifically targeted towards the non-total type of PIDS. In addition to our new algorithm, we adapted two existing TPIDS algorithms to generate PIDS. We ran simulations for all three algorithms, and our new algorithm consistently generates smaller PIDS than both existing algorithms, with our algorithm generating PIDS approximately 5% smaller than the better of the two existing algorithms.

3 citations


Cites background from "A Distributed Greedy Algorithm for ..."

  • ...While the topic of dominating sets has several years of research behind it in particular for backbone formation in Wireless Sensor Networks [7] [8] [9], the problem of Positive Influence Dominating Sets (PIDS) in social networks has been studied relatively recently....

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Journal ArticleDOI
TL;DR: This paper proposes a fault-tolerant distributed algorithm for a minimal capacitated CDS (CapCDS) construction in WSNs, and is believed to be the first distributed self-stabilizing CapCDS algorithm.
Abstract: Energy efficiency is one of the major issues in wireless sensor networks (WSNs) that lack a fixed infrastructure and centralized control. In order to prolong the network lifetime, a connected dominating set (CDS) has been widely used as a virtual backbone in WSNs. The sensor nodes in WSNs are prone to failure due to a lack of battery, hardware damage, link failure, or environmental interference. Therefore, designing an energy-efficient and fault-tolerant CDS algorithm is quite vital in WSNs. A non-masking fault tolerance method denoted self-stabilizing tolerates any finite number of transient faults. In this paper, we propose a fault-tolerant distributed algorithm for a minimal capacitated CDS (CapCDS) construction in WSNs. To the best of our knowledge, this is the first distributed self-stabilizing CapCDS algorithm. It makes an illegitimate system legitimate at most ( n 2 3 + 2 n ) moves by using an unfair distributed scheduler where n is the number of nodes. The performance of the algorithm is validated through extensive experimental testbeds and simulations.

2 citations


References
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Journal ArticleDOI
TL;DR: The current state of the art of sensor networks is captured in this article, where solutions are discussed under their related protocol stack layer sections.
Abstract: The advancement in wireless communications and electronics has enabled the development of low-cost sensor networks. The sensor networks can be used for various application areas (e.g., health, military, home). For different application areas, there are different technical issues that researchers are currently resolving. The current state of the art of sensor networks is captured in this article, where solutions are discussed under their related protocol stack layer sections. This article also points out the open research issues and intends to spark new interests and developments in this field.

13,726 citations


"A Distributed Greedy Algorithm for ..." refers background in this paper

  • ...Wireless Sensor Networks (WSNs) have attracted considerable research interest in the past decade (Iyengar and Brooks, 2004) (Akyildiz et al., 2002) (Chong and Kumar, 2003)....

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Journal ArticleDOI
11 Aug 2003
TL;DR: The history of research in sensor networks over the past three decades is traced, including two important programs of the Defense Advanced Research Projects Agency (DARPA) spanning this period: the Distributed Sensor Networks (DSN) and the Sensor Information Technology (SensIT) programs.
Abstract: Wireless microsensor networks have been identified as one of the most important technologies for the 21st century. This paper traces the history of research in sensor networks over the past three decades, including two important programs of the Defense Advanced Research Projects Agency (DARPA) spanning this period: the Distributed Sensor Networks (DSN) and the Sensor Information Technology (SensIT) programs. Technology trends that impact the development of sensor networks are reviewed, and new applications such as infrastructure security, habitat monitoring, and traffic control are presented. Technical challenges in sensor network development include network discovery, control and routing, collaborative signal and information processing, tasking and querying, and security. The paper concludes by presenting some recent research results in sensor network algorithms, including localized algorithms and directed diffusion, distributed tracking in wireless ad hoc networks, and distributed classification using local agents.

3,178 citations


Proceedings ArticleDOI
22 Apr 2001
TL;DR: A series of experiments are described which obtained detailed measurements of the energy consumption of an IEEE 802.11 wireless network interface operating in an ad hoc networking environment, and some implications for protocol design and evaluation in ad hoc networks are discussed.
Abstract: Energy-aware design and evaluation of network protocols requires knowledge of the energy consumption behavior of actual wireless interfaces. But little practical information is available about the energy consumption behavior of well-known wireless network interfaces and device specifications do not provide information in a form that is helpful to protocol developers. This paper describes a series of experiments which obtained detailed measurements of the energy consumption of an IEEE 802.11 wireless network interface operating in an ad hoc networking environment. The data is presented as a collection of linear equations for calculating the energy consumed in sending, receiving and discarding broadcast and point-to-point data packets of various sizes. Some implications for protocol design and evaluation in ad hoc networks are discussed.

1,788 citations


"A Distributed Greedy Algorithm for ..." refers background in this paper

  • ...In order to keep their cost low, the sensors are equipped with limited energy (Feeney and Nilsson, 2001) (Feeney, 2001) and computational resources....

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Journal Article
TL;DR: A decentralized density control algorithm, Optimal Geographical Density Control (OGDC), is devised for density control in large scale sensor networks and can maintain coverage as well as connectivity, regardless of the relationship between the radio range and the sensing range.
Abstract: In this paper, we address the issues of maintaining sensing coverage and connectivity by keeping a minimum number of sensor nodes in the active mode in wireless sensor networks. We investigate the relationship between coverage and connectivity by solving the following two sub-problems. First, we prove that if the radio range is at least twice the sensing range, complete coverage of a convex area implies connectivity among the working set of nodes. Second, we derive, under the ideal case in which node density is sufficiently high, a set of optimality conditions under which a subset of working sensor nodes can be chosen for complete coverage. Based on the optimality conditions, we then devise a decentralized density control algorithm, Optimal Geographical Density Control (OGDC), for density control in large scale sensor networks. The OGDC algorithm is fully localized and can maintain coverage as well as connectivity, regardless of the relationship between the radio range and the sensing range. Ns-2 simulations show that OGDC outperforms existing density control algorithms [25, 26, 29] with respect to the number of working nodes needed and network lifetime (with up to 50% improvement), and achieves almost the same coverage as the algorithm with the best result.

1,522 citations


"A Distributed Greedy Algorithm for ..." refers background in this paper

  • ...tioned in (Zhang and Hou, 2005), the transmission radius is double the sensing radius....

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  • ...As mentioned in (Zhang and Hou, 2005), the transmission radius is double the sensing radius....

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  • ...We also assume that the transmission range is at least twice the sensing range since as shown in (Zhang and Hou, 2005) a covered network is also connected if this is true....

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Journal ArticleDOI
TL;DR: It is shown that many standard graph theoretic problems remain NP-complete on unit disks, including coloring, independent set, domination, independent domination, and connected domination; NP-completeness for the domination problem is shown to hold even for grid graphs, a subclass of unit disk graphs.
Abstract: Unit disk graphs are the intersection graphs of equal sized circles in the plane: they provide a graph-theoretic model for broadcast networks (cellular networks) and for some problems in computational geometry. We show that many standard graph theoretic problems remain NP-complete on unit disk graphs, including coloring, independent set, domination, independent domination, and connected domination; NP-completeness for the domination problem is shown to hold even for grid graphs, a subclass of unit disk graphs. In contrast, we give a polynomial time algorithm for finding cliques when the geometric representation (circles in the plane) is provided.

1,454 citations


"A Distributed Greedy Algorithm for ..." refers background in this paper

  • ...The resulting graph is known as a Unit-Disk Graph (UDG) (Clark et al., 1990) since the uniform transmission range results in edges of equal (or unit) weight....

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  • ...However this has been shown to be a NP-hard problem in (Clark et al., 1990)....

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