A Weight-Based Clustering Algorithm for mobile Ad Hoc network

Wei-dong Yang, Guang-zhao Zhang Department of Electronic and Communication Engineering

SUN Yat-sen University, Guangzhou, China ywdyar@163.com

Abstract

Ad Hoc network is a kind of multi-hop self-organizing network, which is dynamic in nature due to the mobility of nodes. Many mobile ad hoc applications depend on the hierarchical structure, and clustering is the most popular method to impose a hierarchical structure in the mobile ad hoc networks. Only is some single factor is considered in most existing clustering algorithms, they have very limited application scenarios. In this paper, we propose a novel weight-based clustering algorithm (WBCA). The proposed clustering algorithm takes the mean connectivity degree and battery power of mobile nodes into consideration. Analysis and simulation of the algorithm have been implemented and validity of the algorithm has been proved. 1. Introduction

Current wireless cellular networks solely rely on the wired backbone by which all base stations are connected, implying that networks are fixed and constrained to a geographical area with a pre-defined boundary. However, ad hoc is a self-organized and self-configuring multihop wireless network. It does not rely on a fixed infrastructure and works in a share wireless media. So it plays a critical role in places where a wired (central) backbone is neither available nor economical to build. Due to the nature of the network, it can be widely used in temporary and emergency scenarios. For example, ad hoc networks can be applied to battlefield, disaster recovery situations, emergency search-and-rescue operations, and so on[1,2].

The clustering algorithm presents a logical topology to the routing algorithm, and it accepts feedback from routing algorithm in order to adjust that logical topology and make clustering decisions. So clustering algorithm plays a crucial role in ad hoc wireless networks.

Many clustering schemes [3~13] have been proposed out of special issues in recent years. The Lowest-ID[3,4] (LOWID) is known as identifier-based clustering. In this algorithm, each node is assigned a distinct ID. Periodically, the node broadcasts the list of nodes that it can be heard (including itself). Among the neighbors, the node with lowest-ID is selected as clusterhead. LOWID calculates simply, implements easily and converges quickly. However, the drawback of this heuristic is its bias towards nodes with smaller IDs which may lead to the battery drainage of certain nodes. And it does not attempt to balance the load uniformly across all the nodes. The Highest-Degree [5] is known as connectivity-based clustering. The degree of a node is computed based on its distance from others. Each node broadcasts its ID to the nodes that are within its transmission range. The node with maximum number of neighbors (i.e., maximum degree) is chosen as a clusterhead. The neighbors of a clusterhead become members of that cluster and can no longer participate in the election process. It can reduce the number of clusters, the mean-hop of source-destination pairs and delay of packet forward. However ratio which be used in space of channel is lower because of the fewer number of the cluster. Not having any restriction on the upper bound on the number of nodes in a cluster, the throughput drops and the system performance degrades gradually when the number of nodes in a cluster is increased. In Node-Weight heuristic [6], each node is assigned weights based on its suitability of being a clusterhead. A node is chosen to be a clusterhead if its weight is higher than any of its neighbor’s weight; otherwise, it joins a neighboring clusterhead. The smaller node ID is chosen in case of a tie. This means that a node decides to become a clusterhead or stay as an ordinary node depending on the weights of its one-hop neighbors. However, the drawback of this algorithm is that computing the clusterheads becomes very expensive and there are no optimizations on the system parameters such as throughput and power control. Weighted Clustering Algorithm [7-10] is depended on weight of the nodes in

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the network. In these algorithms, the node with highly weight among the neighbors is selected as clusterhead. Although it can increase stability of the cluster, the proportion of every factor in the weight is uncertain. Furthermore calculation and storage of the weight are costly. Clustering algorithm based on global positioning system [11-13] depends on the distance which is calculated according to the physical coordinate of the nodes in the network. This algorithm need not keep the topology information of the network. Owing to these, the cost of the network is fewer and it can fleetly adapt to the topology change of the network. Because of obtaining the local information by GPS, its application is limited.

By studying existing clustering algorithm, this paper proposes a novel weight-based clustering algorithm (WBCA). It takes the mean connectivity degree and battery power of mobile nodes into consideration.

The rest of the paper is organized as following: In section 2, we propose the weight-based clustering

algorithm (WBCA). Section 3 presents the performance results and we

conclude our paper in section 4. 2. Weight-based Clustering Algorithm (WBCA)

2.1 The goal of the clustering algorithm

The goal of the clustering algorithm is that some

nodes among the given nodes are selected as clusterheads based on the election rule. The clusters are made of these clusterheads and their 1-hop neighbor nodes. They cover the whole network.

2.2 some definitions:

1) Definition 1: 1-hop neighbor nodes –An ad hoc network can be represented by an undirected graph

. Here G consists of a finite set V of objects called nodes, a finite set

),( EVG =E of objects called

logical edge. Let’s suppose that Vx∈ and Vy∈ . A logical edge ( x , ) means that y x and can communicate with each other. We consider that node

y

x is node ’s 1-hop neighbor nodes. y2) Definition 2: non-overlapped cluster –We definite

a cluster that is a set of nodes. is the least hops between

VCi ⊂ iC ),( yxdx and . And any two nodes y

x , fill that . We call that

and are non-overlapped clusters if and

y iC∈ 2),( ≤yxd iC

jC iiCUV =

Φ=ji CC I ，( ji ≠ ).

3) Definition 3: node’s degree- –Degree of a node is the number of its neighborhood.

nd

4) Definition 4: mean connectivity degree- –A

node’s is depended on degrees of its own and its

neighbors, here

nP

nP

11

+

+=∑=

n

n

d

ini

n d

ddP

n

. Where is the

degree of neighbor of node .

nid

thi n5) Definition 5: isolated node –If a node hasn’t any

1-hop neighbor, we call it isolated node. 6) Definition 6: T –Time of a period. 7) Definition 7: – Cumulative time of a node

which acts as a clusterhead. nT

2.3 some assumptions:

The clusterhead election procedure is periodic.

Every node has a unique ID and knows the IDs and weigh of its 1-hop neighbors by exchanging HELLO message periodically. If a node n is a clusterhead and its 1-hop neighbor’s number is in a period, its consumed battery power is . Where e is the consumed battery power per degree for clusterhead in a period. We assume that the consumed battery power of a clusterhead is related with its degrees. At the beginning, battery power of every node in the network is the same.

kkeEn =

2.4 Proposed algorithm

Based on the existing algorithm, we propose an algorithm called weight-based clustering algorithm (WBCA) which takes the mean degree and battery power of mobile nodes into consideration. Clusterhead election procedure is described below:

Step 1. Find the neighbors of each node (i.e., nodes within its transmission range) which defines its degree as , then calculate .

n

nd nPStep 2. Calculate the degree-difference,

|| nnn PdD −= , for every node . n

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Step 3. Calculate the consumed energy of a

node n , where = . Here is the times of

period which a node acts as clusterhead and is

the degree of a node acts as clusterhead at times. implies how much battery power has been

consumed during a node acts as clusterhead. is

related with its when it acts as clusterhead.

nE

nE ∑=

q

knk ed

1q

n nkdn thk

nEn nE

ndStep 4. Calculate the cumulative time, , during

which a node n acts as a clusterhead, where

= . Here indicates the times of period

which a node n acts as clusterhead.

nT

nT ∑=

q

k

T1

q

Step 5. Calculate the weight for each node ,

where , where and are

weighing factors and + =1. Value of and can be adjusted according to the system requirements.

nW n

nnn EcDcW 21 += 1c 2c

1c 2c 1c 2c

Step 6. Choose that node with the smallest as the clusterhead. All the neighbors of the chosen clusterhead are no longer allowed to participate in the election procedure.

nW

Step 7. If a node is an isolated node, it becomes a clusterhead automatically.

Step 8. Repeat steps 2–7 for the remaining nodes not yet selected as a clusterhead or assigned to a cluster.

According to step 6, it is a non-overlapped cluster.

3. Simulation Experiments and Results 3.1 Simulation Environment and performance index

We simulate our clustering algorithm by OPNET

10.5. The random waypoint model[14] is used in the simulation runs. In this model, a node selects a destination randomly within the roaming area and moves towards that destination at a speed uniform distributed between 0m/s and m/s, where is the maximum speed of the node. Once the node reaches the destination, it selects another destination randomly and moves towards it after a predefined pause time. We simulate a system of

maxV maxV

N nodes on a 100mⅹ100m area. Simulation time is 10000s.

We compare the performance of WBCA with that of LOWID and Highest-Degree. We compare three parameters in the follow: (1) the number of clusterheads, (2) load balancing factor ( LBF ), and (3)

. We define the LBF as the inverse of the variance of the cardinality of the clusters. Here,

nT

∑=

−=

cn

ii

c

ux

nLBF

1

2)(, where is the number of

clusterheads, is the cardinality of cluster i , and

cn

ix

c

c

nnNu −

= , ( N being the total number of nodes in

the system) is the average number of neighbors of a clusterhead. Clearly, a higher value of LBF signifies a better load distribution and it tends to infinity for a perfectly balanced system.

3.2 Simulation Results

In our simulation experiments, N was 32, T was 4s, was 2, battery power of initialization of every node was 100000, was 5m/s and the transmission range was varied between 5m and 60m (The transmission range was 25m in Figure 1.). The weight values used for simulation were =0.4 and = 0.6. Note that these values are arbitrary at this time and should be adjusted according to the system requirements. For example, we can increase the weighing factor of battery energy (here is ) properly when battery energy plays a critical role in the network.

emaxV

1c 2c

2c

Figure 1 The time of a node acting as a clusterhead

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Figure 1 shows that , the cumulative time which a node n acts as a clusterhead, is different remarkably in LOWID. of a node with smaller ID is much longer than that of node with bigger ID because LOWID inclines to choose the node with smaller ID as clusterhead. This may lead to the battery energy of the node with smaller ID used up easily. Thus the node with smaller ID may become the bottleneck of the network communication. The Highest-Degree is inclined to choose node with maximum degree as clusterhead. Comparing with LOWID, The Highest-Degree improves. However, the improvement is limited. Because of having not any tendency to choose node as clusterhead, the improvement of WBCA is much greater than that of LOWID and Hghest-Degree.

distributing of a node in ad hoc network is much more uniform. The reason for this is that WBCA considers the mean connectivity degree and battery power. The chance of node being selected as clusterhead is much more uniform.

nT

nT

nT

Table 1 Statistic value of LBF for three

clustering algorithms (average)

Average statistic value of LBF for three clustering algorithms is listed in Table 1. Here N was 32, was 5m/s and the transmission range was 20m, 30m and 40m. The result shows that LBF of WBCA is biggest and LBF of Highest-Degree is smallest. LBF of LOWID is smaller than that of WBCA but bigger than that of Highest-Degree. That is to say, load balancing of WBCA is the best and that of Highest-Degree is the worst. The reason for this is that WBCA constrains the connectivity degrees of clusterheads by mean connectivity degree and considers battery power of clusterheads. This makes the distributing of clusterheads be much more uniform and the load balancing of clusterheads be much better. However, nodes with maximum degree are inclined to be selected as clusterhead in Highest-Degree and connectivity degree of node isn’t constrained. This makes the numbers of node in each cluster is not uniform. So the load balancing of Highest-degree is worst.

maxV

Figure 2 relation between number of

clusterheads and transmission range Figure 2 shows that the average number of

clusterheads decreases with the increase in the transmission range. This is due to the fact that a clusterhead with a large transmission range will cover a larger area. The decreasing speed of clusterhead’s number becomes lower when transmission range is larger than 30. The average number of clusterhead in Highest-Degree is smallest. Highest-Degree can reduce the number of clusters, the mean-hop of source-destination pairs and delay of packet forward. Because of having not any restriction on the upper bound of the number of nodes in a cluster, it can not adapt to some special networks. For example, Bluetooth employs a Master-Slave model where the clusterhead is the master and can handle up to seven slaves[2]. Typically, each cluster is assigned some resources which is shared among the members of that cluster on a round-robin basis. As the number of nodes in a cluster is increased, the throughput drops. The curve trend of LOWID and WBCA is similar. Comparing with LOWID, the numbers of clusterhead is a little bigger when transmission range is larger than 45. When transmission range is 40, the average degree of Highest-Degree is about 8 and the average degree of LOWID and WBCA is about 5.7. When transmission range is 50, the average degree of Highest-Degree is about 12 and the average degree of LOWID and WBCA is about 6.4. When transmission range is 60, the average degree of Highest-Degree is about 14, the average degree of LOWID is about 8.4 and the average degree of WBCA is about 6.9. 4. Conclusion

In this paper, we propose a novel weight-based clustering algorithm (WBCA) which the mean degree

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and battery power of mobile nodes takes into consideration. It makes clusterhead’s selection become reasonable. It also overcomes the limitation of most existing clustering algorithms which only take into consideration certain factor which affects network. It can improve its applicability and universality. The simulation results show that the performances of our clustering algorithm are better than that of the Highest-Degree and the Lowest-ID heuristics. 5. References [1] Ljubica B, Levente B, Srdjan C, et al. Self-organization in mobile Ad Hoc network: the approach of terminodes [J]. IEEE Communication Magazine, 2001, 39(6): 166-174. [2] Magnus Frodigh, Per Johansson. Wireless Ad Hoc networking－The art of networking without a network [J]. Ericsson Review, 2000(4): 248-262. [3] Gerla M , Tsai J T C. Multicluster, mobile, multimedia radio network [J]. Wireless Networks, 1995, 1(3) : 255-265. [4] LIN C R, GERLA M. Adaptive clustering for mobile wireless networks [J]. IEEE Journal on Selected Areas in Communications, 1997, 15(7): 1265-1275. [5] Parekh A K. Selecting routers in ad-hoc wireless networks [C]. Proceedings of the SBT/IEEE International Telecommunications Symposium, August 1994. [6] S Bassagni. Distributed Clustering for Ad Hoc Networks [A]. Proc of Int’ l Symp on Parallel Architectures, Algorithms and Networks[C]. 1999,310-315.

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