A Multi-stage Graph Approach for Efficient Clustering

in Self-Organized Wireless Sensor Networks

Abhishek Karpate and Hesham H. Ali

Department of Computer Science, College of Information Science and Technology

University of Nebraska at Omaha, Omaha, NE 68182, U.S.A.

Keywords: Wireless Sensor Networks, Self-Organized Networks, Graph Modeling, Clustering, Multi-Stage Graph

Algorithms, Energy-Aware Solutions.

Abstract: With the rapid increase in applications utilizing the current advancements of wireless sensor networks, a

number of problems related to self-organization, energy-awareness and network organizations have attracted

many researchers in the field. Various groups have proposed grouping the sensors into clusters and design

communication routes in two levels as a way to improve communication cost and better organize networks of

large sensors. In this paper, we propose a new approach to cluster wireless sensors and identify cluster heads

using multi-stage graph algorithms. The approach takes advantage of the optimally associated with finding

matching solutions in multi-stage graph networks. The proposed solution is designed to accommodate

networks with different sizes and levels of density. We tested the algorithm using different types of networks

and measure the quality of the key parameters as compared to those obtained by traditional greedy heuristics.

Obtained results show that the multi-stage graph approach produces better network organization and better

cluster head selection which leads to be more efficient self-organized networks.

1 INTRODUCTION

Wireless sensor networks (WSNs) typically consist of

a large number of sensors; sensors are small wireless

devices having limited resources like energy,

processing speed and storage. With the recent

technology advances it is possible to produce small

and low cost sensors making it economically feasible

to deploy sensors in large numbers. Sensors measure

ambient conditions or measure certain environmental

parameters and report it to processing nodes. Instead

of each individual sensor being always active and

directly reporting to the processing node, the sensors

in the WSNs could be clustered in a way where

different sensors play different roles. Clustering

provides network scalability and network topology

stability in addition to possible energy saving

attributes. Due to the various schemes employed in

clustering, there is reduction in communication

overhead and interferences among the sensor nodes

(Karaki et al. 2004, Mhatre et al. 2004, Jiang et al.

2009).

There are various ways in which clustering

schemes can be classified. Clustering schemes are

categorized depending on what objective the cluster

intends to attain and what main algorithmic technique

it employs. This includes dominating-Set based

clustering, low-maintenance clustering, mobility-

aware clustering, energy-efficient clustering, load

balancing clustering, or combined based metrics

clustering (Yu and Chong 2005). The clustering

scheme has also been classified according to key cost

associated parameters like explicit control message

for clustering, ripple effect of re-clustering, stationary

assumption for cluster formation, constant

computation round and communication complexity

(Yu and Chong 2005). Clustering in networks also

depends on the type of network that is being

considered. An alternate way to classify clustering in

ad-hoc networks is based on the type of networks they

are used to cluster; single-hop or multi-hop, location

based or non-location based, synchronous or

asynchronous (depending on the network topology)

and stationary nodes or mobile nodes (Wei and Chan

2006). Clustering is performed on sensor networks

which are either homogeneous, where all the sensor

nodes are identical in built and functionality, or

heterogeneous, when the network consists of sensors

which differ from each other in built or functionality.

Both categories of networks have to deal with the

overhead of cluster construction process.

Karpate A. and Ali H..

A Multi-stage Graph Approach for Efﬁcient Clustering in Self-Organized Wireless Sensor Networks.

DOI: 10.5220/0005244700560062

In Proceedings of the 4th International Conference on Sensor Networks (SENSORNETS-2015), pages 56-62

ISBN: 978-989-758-086-4

 2015 SCITEPRESS (Science and Technology Publications, Lda.)

In this paper, we propose a new model for

distributed clustering in heterogeneous networks that

focuses on allocating sensors to cluster heads such

that the total communication cost for the entire

system is minimized. The suggested model also

provides flexibility by which the density of networks

and number of resource handling capacity of a device

can be significantly varied.

2 PROPOSED MODEL

In a heterogeneous sensor network, self-organization

continues to be a prominent feature due to increase in

the complexity in managing the network as most of

the routing paths are dynamically decided. Several

models have been proposed to take energy awareness

into consideration (Chamam and Pierre 2009, Zhange et

al. 2007, Cardei et al. 2005). Using cluster heads in wireless

sensor networks has been utilized to coordinate the process

of collecting and reporting data. In such networks, there

exist many sensors that measure the ambient

conditions or collect various parameters and report

the information they have sensed to cluster heads. The

cluster heads, in turn, process the information it

receives from all the sensors and further report it to

the processing or sink nodes (Yu et al. 2011, Nayer

and Ali 2004, Nayer and Ali 2008). The model we

propose focuses on handling the problem of

clustering sensor nodes to the cluster heads and

further clustering heads to the sink nodes. The

operation of node clustering can be modelled by

graph clustering, which groups vertices of a graph

into clusters based on certain criteria. Graph

clustering can be broadly divided into two categories:

global clustering and local clustering (Yu et al. 2011,

Camilus et al 2008, Karpate and Ali 2011). The

difference between the two types of clustering being

that in global clustering every vertex on a graph is

allocated to a cluster and in local clustering only a

certain subset of vertices is allocated to a cluster.

Applications like WSNs usually use global

clustering.

2.1 The Multi-Stage Graph Model

Multi-stage graphs are usually used in cases where

there is a connected graph optimization problem

having several stages with each stage contains a set of

nodes. The edges of the graph are used to connect

nodes in different stages. There are no edges between

nodes of the same stage or non-adjacent stage. The

entire WSN can be modelled by a multi-stage graph

having three stages as shown in Figure 1 where the

first stage of nodes represents the set of sensors, the

second stage represents the set of cluster heads and

the third stage represents the set of sink nodes. An

edge connects two nodes if that particular sensor (or

cluster head) can communicate with the particular

cluster head (or sink node). The weight on the edge

represents the distance between the two nodes. The

network can be represented by the multi-stage graph

as follows:

G = (N ∪ C ∪ S, E1 ∪ E2) where,

N  Set of sensor nodes

C  Set of cluster heads

S  Set of sink nodes

E1  Set of edges connecting N and C

E2  Set of edges connecting C and S

Figure 1: Multi-stage graph representation of

Heterogeneous Sensor Network.

As shown in the figure, there are M1 sensor nodes,

M2 cluster head nodes and M3 sink nodes. There

exists an edge that connects n1 to c1, c2, c3 up to cM2

and all the edges have respective weights associated

with them representing the distance between the two

nodes. In the allocation process, the entire system is

considered and considering the maximum number of

sensors that can be allocated to a cluster head,

appropriate edges are shortlisted and accordingly

each sensor is allocated to some particular cluster

head. A network could have more than one sink node

depending on the size of the network; if the set of

cluster heads and sink nodes are considered

depending on the distance between a particular cluster

head and sink nodes, it is clustered with one of the

sink nodes.

3 THE MATCHING ALGORITHM

The task of allocating a sensor to a cluster head and

allocating a cluster head to a sink node can be

translated to a maximum matching problem.

Maximum matching algorithm gives us an indepen-

AMulti-stageGraphApproachforEfficientClusteringinSelf-OrganizedWirelessSensorNetworks

Figure 2: Expanded graph with replicated nodes.

dent edge set with no common vertices such that the

combined weight of the edges selected is the

maximum possible for that graph. Our problem is to

find an optimal allocation of every resource in a stage

to a resource in the next stage. In terms of graph

theory, our problem can be termed as a minimum

matching problem that is a set of independent edges

where the combined weight is as minimum as

possible. Consider any stage of the multi-stage graph

like the first stage where the sensors report to cluster

heads. Assuming a cluster head can handle data from

t sensors. Replicate the set of cluster heads a number

of t times such that for every sensor, every cluster

head it was connected to is replicated t times. If we

implement the minimum-matching algorithm in this

case, we would have an optimal allocation of sensors

to cluster heads. This concept will become clearer

from the example in Figure 2, where t is given a value

of 2 in the example.

On applying the algorithm on the expanded

version, the set of independent edges selected based

on weights are (n2, c

1), (n3, c

2) and (n1, c

2). The

total cost of allocation is 15. The execution is

implemented as shown in algorithm 1 and algorithm2.

The expanded graph is created by Agorithm1 and

then is subjected to the proposed matching algorithm,

described in Algorithm2 to attain the most effective

allocation.

The proposed algorithms help in finding the most

economical assignment of sensors to cluster head as a

whole and also the most economical assignment of

cluster heads to sink nodes. In terms of time

complexity, the main algorithm is based on finding

optimal matching in Bipartite graphs which is a fast

algorithm that is quadratic in the number of nodes.

4 SIMULATION RESULTS

To illustrate the performance of the proposed

algorithm, we have compared the outputs produced

by the algorithm with the outputs produced using a

robust/greedy graph approach. The greedy approach

has a decent track record for dealing with the

clustering problem. Using the greedy approach, at any

stage when two sets of nodes are considered, a

minimum weight edge is selected at each step. Both

the models take the following inputs: number of

sensors deployed, number of cluster heads deployed

and the number of sink nodes available. The quality

and hardware superiority of the networking device

deployed determines how much data and from how

many devices can it handle the data from.

For example the better the superiority of a cluster

head the more number of sensors can report to it. Both

the algorithms implemented permit the discussed

flexibility by taking the maximum number of sensors

a cluster head can handle and the maximum number

of cluster heads a sink node can handle. The impact

of the number of sensors deployed is also considered.

Better redundancy and coverage can be expected with

the increase in the number of sensors being deployed.

In the figures below, we use the term robust algorithm

to refer to the greedy approach and the combinatorial

SENSORNETS2015-4thInternationalConferenceonSensorNetworks

Algorithm 1: Proposed Combinatorial Algorithm.

Algorithm 2: Graph expansion Algorithm

1. Start

2. Set markedUncoveredZero flag to false.

3. Create new zeros.

a. For each row, subtract its smallest element from all its elements.

b. For each column, subtract its smallest element from all its elements.

4. Assign lone zeros.

5. Consider the following cases:

a. If all the rows have been assigned.

i. Then stop.

ii. Display the allocation.

b. If the matrix is not fully covered.

i. Assign an uncovered zero.

ii. Set markedUncoveredZero flag to true.

iii. Go to step 4.

c. If the matrix is fully covered.

i. If markedUncoveredZero flag is false

1. Create new zeros by subtracting the value of the smallest uncovered cost from

all the uncovered costs.

2. Add the smallest uncovered value to all the double-covered costs.

3. Go back to step 4.

ii. Else

1. Mark all unassigned rows.

2. Mark all unmarked columns that have zero in the marked rows.

3. Mark all unmarked rows that have assignments in the marked columns.

4. Repeat 2 & 3 until no changes are observed.

5. Create new zeros by subtracting the value of the smallest uncovered cost from

all the uncovered costs.

6. Add the smallest uncovered value to all the double-covered costs.

7. Go back to step 4.

1. Start.

2. Randomly distribute the sensors, cluster heads and sink nodes in the area being

monitored.

3. Generate two arrays

a. Array 1 representing the distance between sensor and cluster head with sensors

representing rows and cluster heads representing columns.

b. Array 2 representing the distance between cluster head and sink nodes with cluster

heads representing rows and sink nodes representing columns

4. If the number of rows is greater than the number of columns in any of the array.

a. Replicate the number of columns such that the required condition is satisfied.

b. Replace the original array with the modified array.

5. Apply algorithm 2 to the arrays.

AMulti-stageGraphApproachforEfficientClusteringinSelf-OrganizedWirelessSensorNetworks

Figure 3: Graphs representing the communication cost for

sensor - cluster head communication.

Figure 4: Graphs representing the communication cost for

cluster head - sink communication.

200

400

600

800

1000

1200

1400

1600

1800

CommunicationCost

DenselyPopulatedNetworks

Proposed

Combinatorial

Approach

RobustGraph

Approach

200

400

600

800

1000

1200

1400

CommunicationCost

IntermediatelyPopulatedNetworks

Proposed

Combinatorial

Approach

RobustGraph

Approach

100

200

300

400

500

600

700

CommunicationCost

SparselyPopulatedNetworks

Proposed

Combinatorial

Approach

RobustGraph

Approach

100

200

300

400

500

600

700

800

CommunicationCost

DenselyPopulatedNetworks

Proposed

Combinatorial

Approach

RobustGraph

Approach

100

200

300

400

500

600

700

800

CommunicationCost

IntermediatelyPopulatedNetworks

Proposed

Combinatorial

Approach

RobustGraph

Approach

100

200

300

400

500

600

700

800

CommunicationCost

SparselyPopulatedNetworks

Proposed

Combinatorial

Approach

RobustGraph

Approach

SENSORNETS2015-4thInternationalConferenceonSensorNetworks

algorithm to refer to the multi-stage graph-matching

algorithm.

In our simulations there are three types of

networks – densely populated networks, moderately

populated networks and sparsely populated networks.

A network is dense if it has more than 50 sensors,

networks having sensors between 25 and 50 are

moderately populated networks and networks having

25 or less sensors are sparsely populated networks.

The cost of communication between any two

devices is directly proportional to the distance

between them. As the distance between the two

devices increases it is expected that the

communication cost between the two will increase.

The simulations are carried out assuming the cost of

communication is one unit for every one meter.

Sensors, Cluster heads and sink nodes are randomly

distributed on the area to be monitored. The proposed

algorithm is carried out on all types of network and

the results obtained. Figures 3 and 4 show the two

costs the network had to incur. Figure 3 compares the

communication cost between sensor and cluster head

for both the approaches for all the three networks

under similar conditions and Figure 4 does the same

for the communication cost between cluster heads and

sink nodes. To test the networks under different

conditions, the count of the number of cluster heads

and number of sink nodes is changed in different

cases. Case 1 has 20 cluster heads and 5 sink nodes

are deployed. Case 2 -10 cluster heads and 5 sink

nodes; case 3 – 5 cluster heads and 5 sink nodes; case

4 – 20 cluster heads and 2 sink nodes; case 5 – 10

cluster heads and 2 sink nodes and case 6 – 5 cluster

heads and 2 sink nodes are deployed.

From the above graphs, we can observe that in

most of the cases the proposed algorithm gives better

solutions as compared to the robust/greedy graph

approach. Another major advantage of the proposed

algorithm over the robust approach is that it does not

follow a greedy strategy by making choices based on

a global overview. The robust approach makes

choices that look the best at that moment. Although

most of the times the attained optimal solution by the

robust approach maybe at par with our proposed

solution, it could fail at critical conditions and hence

is not so reliable.

5 CONCLUSIONS

In this paper we propose a graph theoretic approach

to efficiently form a weight-based cluster formation

algorithm for wireless sensor networks. The network

is self-organized such that any particular sensor while

determining which cluster head to report not only

considers its physical distance from the available

cluster heads but also considers the receiving capacity

of the available cluster heads and the physical

distance of all other unallocated sensors from the

available cluster heads. The same approach is used

while determining which cluster head should report to

which sink node. In this attempt we manage to find

an allocation that consider the system as a whole and

provides gives energy-aware solutions. The

efficiency of the algorithm is measured by comparing

it with a robust graph approach, which is a greedy

approach for solving the problem. The efficiency of

the proposed combinatorial optimization algorithm is

better than that of the greedy algorithm in most of the

cases; it also avoids the local short-sighted issues that

are dealt with while using the greedy approach. One

of the disadvantages it has over the robust graph

approach is that it takes a longer time to process the

best allocation of resources. The graph theoretic

model can be further enhanced to increase the level of

redundancy by deciding how many resources can a

particular resource report to, this feature is very useful

when the area being monitored is of high priority and

if due to certain factors, some signals or data is lost it

can be retrieved from an alternate source.

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