Table of Contents
ISRN Sensor Networks
Volume 2013, Article ID 805635, 15 pages
Research Article

Borel Cayley Graph-Based Topology Control for Consensus Protocol in Wireless Sensor Networks

1Department of Electrical and Computer Engineering, Stony Brook University—SUNY, Stony Brook, NY 11794-2350, USA
2Intel Labs, 2111 Northeast 25th Avenue, Hillsboro, OR 97124, USA
3AT&T Laboratories, 200s Laurel Avenue, Middletown, NJ 07747, USA

Received 15 June 2013; Accepted 11 July 2013

Academic Editors: C.-Y. Chow and S. Srinivasan

Copyright © 2013 Junghun Ryu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Borel Cayley graphs have been shown to be an efficient candidate topology in interconnection networks due to their small diameter, short path length, and low degree. In this paper, we propose topology control algorithms based on Borel Cayley graphs. In particular, we propose two methods to assign node IDs of Borel Cayley graphs as logical topologies in wireless sensor networks. The first one aims at minimizing communication distance between nodes, while the entire graph is imposed as a logical topology; while the second one aims at maximizing the number of edges of the graph to be used, while the network nodes are constrained with a finite radio transmission range. In the latter case, due to the finite transmission range, the resultant topology is an “incomplete” version of the original BCG. In both cases, we apply our algorithms in consensus protocol and compare its performance with that of the random node ID assignment and other existing topology control algorithms. Our simulation indicates that the proposed ID assignments have better performance when consensus protocols are used as a benchmark application.