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

)(

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

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

 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.

}),(|),{(

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

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

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,

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

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

n ,

search process continues to find an alternative node.

The set of neighbor nodes of node 2 represent the 2-

hop neighbors of

n . Notice that one of them can be

connected to the dominating node 9 (Figure. 2 (c)).





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}

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,

and

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

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

)(

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

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

WINSYS 2011 - International Conference on Wireless Information Networks and Systems