A LOAD-BALANCED TOPOLOGY MAINTENANCE WITH
PARTIAL RECONSTRUCTION OF CONNECTED
DOMINATING SETS
Youn-Sik Hong, Hwa-Seok Lim and Chol-Ho Lee
Dept. of Computer Science and Engineering, University of Incheon, Incheon, 407-772, Korea
Keywords: Ad-hoc network, Connected dominating set, Load-balancing, Partial reconstruction.
Abstract: Node failure in a connected dominating set (CDS) is an event of non-negligible probability. For applications
where fault tolerance is critical, a traditional dominating-set based routing may not be a desirable form of
clustering. For a typical localized algorithm to construct CDS, it has the time complexity of
)(
3
O
, where
is the maximum degree of an input graph. In this paper we inspect the problem of load balancing in a
dominating-set based routing. The motivation of load balancing is to prolong the network lifetime, while
minimize the partitions of the network due to node failure, where they cause interruptions in communication
among nodes. The idea is that by finding alternative nodes within a restricted range and locally
reconstructing a CDS to include them, instead of totally reconstructing a new CDS. The number of nodes
which should be awaken during partial reconstruction is less than 2(-1), where is the number of nodes
from CDS and the number of neighbour of the faulty node.
1 INTRODUCTION
A connected dominating set (CDS) can create a
virtual network backbone for packet routing and
protocol. In a dominating set based routing,
messages can be routed from the source to a
neighbour in the dominating set, along the CDS to
the dominating set members closest to the
destination node, and then finally to the destination
(Blum, 2004).
A set of dominating nodes is to awake to
maintain network connectivity, while other nodes
can be put to sleep. A dominating node handles
higher traffic load and thus consumes more energy.
Without preparing load balancing strategy, a
dominating node can become a faulty node due to
shortage of its battery. Node failure in a CDS is an
event of non-negligible probability. To overcome
this, we propose a partial reconstruction of CDS. A
CDS construction is a time-consuming work and
causes heavy traffic to overall network. The idea is
that by finding alternative nodes within a restricted
range and locally reconstructing a CDS to include
them, instead of totally reconstructing a new CDS.
Figure 1 shows an illustrative example to give an
insight how to partial reconstruction will be applied.
Figure 1: An example of partial topology reconstruction in
the case of node failure.
In Section 2, we review the related work in CDS
construction. The proposed partial topology
reconstruction algorithm will be explained in more
detail in Section 3. Section 4 presents some
experimental results.
2 REALTAED WORKS
Guha and Kuller (Guha, 1998) proposed two
centralized CDS construction algorithms. However,
for sensor networks and ad-hoc networks, distributed
CDS construction is more effective due to the lack
of a centralized administration. Various distributed
approaches that seek to balance the competing
65
Hong Y., Lim H. and Lee C..
A LOAD-BALANCED TOPOLOGY MAINTENANCE WITH PARTIAL RECONSTRUCTION OF CONNECTED DOMINATING SETS.
DOI: 10.5220/0003484400650068
In Proceedings of the International Conference on Wireless Information Networks and Systems (WINSYS-2011), pages 65-68
ISBN: 978-989-8425-73-7
Copyright
c
2011 SCITEPRESS (Science and Technology Publications, Lda.)
requirements of complexity, running time, stability,
and overhead have been proposed. Notice that
finding a minimum-sized dominating set is NP-hard.
Wu et al’s work (Wu, 2002) proposes a
completely localized algorithm to construct CDS in
general graphs. A node having two unconnected
neighbours is chosen as a dominating node. They
also present two pruning rules to minimize the
number of dominating nodes.
In a weakly CDS (WCDS), the vertex set is
partitioned into a set of cluster-heads and cluster
members, such that each cluster member is within
radio range of at least one cluster-head. Chen et al
(Chen, 2002) propose approximation algorithms for
computing a small WCDS. Blum et el (Blum, 2004)
gives performance comparison for distributed CDS
construction algorithms in lately proposed methods.
A CARCODS
(Cho, 2005)
tries to minimize
reconstruction
of CDS by delaying neighbour set
advertisement message broadcast in proportion to
residual energy, mobility and the number of
neighbour nodes.
3 A PARTIAL TOPOLOGY
RECONSTRUCTION
3.1 CDS Maintenance Algorithm
An ad-hoc network can be modeled as a graph G =
(V, E), where V is the set of vertices (nodes) and E
the set of edges (links) which represents the
available communication. If a node v is a physical
neighbor of a node u, then there exists an edge (u, v).
That means v is within the communication range R
of a u and thus receives its messages.
}),(|),{(
2
RvudVvuE
(1)
),( vud
is the Euclidean distance between nodes u
and v. We define the neighbor set N (u) of a node u
as:
}),(|{)( EvuuvVvuN
(2)
Then, we will explain our proposed algorithm in a
stepwise execution style by taking an illustrative
example as shown in Figure 2. Let
c
n be the faulty
node. In Figure 2, there are four dominating nodes
{2, 5, 7, 9}. Assume that the current battery level of
the node 5 is under a given threshold. Notice that
without loss of generality we assume that an initial
CDS construction is built. Thus our proposed
method is applied after initial CDS construction.
STEP 1: Check the Coverage of a Faulty Node.
Node 5 is
c
n and it informs its neighbor dominating
nodes {2, 7}. Since
)5(N
were covered with {2, 7},
there are no more nodes to be covered by them
(Figure 2 (b)).
(5, )
(5) (2) (5) (7) (5)
{2,3,4,7,8}{3,4}{8}{2,7}
jEd
NN NN N j



(3)
Where,
d
E is the set of edges which belong to the
CDS.
STEP 2: Find an Alternative Node to maintain
the Connectivity among the Existing Dominating
Nodes. For the one-hop neighbor dominating nodes
{2, 7} for
c
n , search process begins to see whether
there is an alternative node or not to find a possible
routing path to connect them. There is no alternative
path.
}9,8{}4,3,1{)7()2( NN
(4)
Then by extending to the 2-hop neighbors of
c
n ,
search process continues to find an alternative node.
The set of neighbor nodes of node 2 represent the 2-
hop neighbors of
c
n . Notice that one of them can be
connected to the dominating node 9 (Figure. 2 (c)).
Ej
NjN
),2(
}9{}9,8{}9,6,4,2{)7()(
(5)
We can do perform the search process for the set of
neighbor nodes of node 7, instead of node 2,
(7, )
(2) ( ) {1, 3, 4} {4, 7, 8, 9,10,11} {4}
kE
NNk

(6)
If the process fails for the above cases, search
process continues for the set of neighbor nodes of
)2(N
and
)7(N
.
EkEj
kNjN
),7(),2(
)()(
(7)
STEP 3: Select the Alternative Node. If there is
more than one node to choose, the priority of node i
can be calculated by the following equation.
iii
NDELP
(8)
where,
i
EL
and
i
ND
is the current energy level and
the node degree of node i, respectively. In addition,
both
and
indicates the weighting factors.
WINSYS 2011 - International Conference on Wireless Information Networks and Systems
66
Figure 2: An example of partial reconstruction of CDS.
3.2 Duration of Partial Reconstruction
The duration of a partial reconstruction of CDS
(abbreviated as PRCDS) is shorter than that of a
CDS construction. With a shorter duration of
PRCDS the possibility of maintaining a connected
dominating set becomes higher.
As shown in Figure 3 (a), in a CDS construction
none-CDS nodes have regular intervals of both sleep
mode and wake-up mode. However, in the case of
PRCDS, they have shorter period of sleep mode. In
PRCDS, the number of nodes which should be
awaken during reconstruction is less than 2(-1),
where is the number of dominating nodes and the
number of neighbors of the faulty node. In most
cases, an alternative node was found by just
searching 2-hop neighbors of the faulty node.
Our simulation results show that execution time
of PRCDS is faster than that of CDS by 40%. For a
typical localized algorithm to construct CDS, it has
the time complexity of
)(
3
O
, where is the
maximum degree of an input graph.
4 EXPERIMENTAL RESULTS
AND ANALYSIS
For the purpose of simulation QualNet Exata 4.0
(http://www.scalable-networks.com) is modified to
incorporate with the proposed algorithms. The
performance evaluation is based on the comparison
of three different metrics: node mobility, packet
receive ratio, and energy consumption. These
metrics are also evaluated for SDAA (Wu, 2002)
and CARCODS (Cho, 2005) for comparison
purposes.
Figure 3: Duration of CDS construction: (a) CDS full
construction (b) PRCDS.
Nodes begin to move again after specified pause
time. In our experiments we varied it between 0 and
600 seconds. The network between the pause times 0
to 150 have a high mobility, whereas the network
beyond 450 have a low mobility.
As the node mobility becomes high, the packet
receive ratio decreases due to network instability.
However, PRCDS tries to maintains network
connectivity by establishing partial reconstrction of
CDS. In the case of high mobility PRCDS is
remarkable better than the two methods as shown in
Figure 4.
There is no clear distinction for power
consumption with respect to node mobility in Figure
5. We can say that a frequently partial reconstruction
of CDS is not a energy-consuming work. In
addition, with PRCDS an average remaining battery
level of nodes is higher and the standard deviation
from its mean is smaller than the other methods as
shown in Figure 6.
Figure 4: Packet receive rate versus node mobility.
A LOAD-BALANCED TOPOLOGY MAINTENANCE WITH PARTIAL RECONSTRUCTION OF CONNECTED
DOMINATING SETS
67
Figure 5: Power consumption versus node mobility.
5 CONCLUSIONS
We propose a partial reconstruction of CDS when
applying dominating set based routing in wireless
ad-hoc networks. Since a dominating node in a CDS
is a gateway node, a failure happened in such a node
causes a serious problem on network-wide
connectivity. PRCDS searches a restricted area
within 2-hop distance of a faulty node to find an
alternative node.
Our proposed algorithm shows a remarkable
performance in the case of high mobility. It
guarantees more stable network connectivity by
frequently reconstruction of CDS. In addition, it
does not consume more energy but balance average
energy consumption per node compared to the CDS
construction methods.
Figure 6: The comparison results of remaining battery
level of nodes.
REFERENCES
S. Guha and S. Khuller, Approximation algorithms for
connected dominating sets, Algorithmica, 20(4),
pp.374-387, 1998.
J. Wu, F. Dai, M, Gao, and I. Stojmenovic. “On
Calculating Power-Aware Connected Dominating Sets
for Efficient Routing in Ad Hoc Wireless Networks,”
Journal of Communications and Networks, Vol.4,
No.1, March, 2002.
Y. Chen, and A. Liestman, “Approximating minimum size
weakly-connected dominating sets for clustering
mobile ad hoc networks, in Proc. ACM MobiHoc, June,
2002.
J. Blum, M. Ding, A. Thaeler, and X. Cheng, Connected
dominating set in sensor networks and MANETs,
Handbook of Combinatorial Optimization, Kluwer
Academic Pub., pp329-369, 2004.
H-S., Cho, and S-J., Yoo, “Power, mobility and wireless
channel condition aware connected dominating set
construction algorithm in the wireless ad-hoc
network,” Domestic Journal, Vol.30, No.5B, May,
2005.
http://www.scalable-networks.com
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