A local algorithm for dominating sets of quasi-unit disk graphs

Authors:
Yonatan Cohen;Jaroslav Opatrny
Affiliations:
University of British Colombia, Vancouver, Canada;Concordia University, Montreal, QC, Canada
Venue:
C3S2E '09 Proceedings of the 2nd Canadian Conference on Computer Science and Software Engineering
Year:
2009

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Abstract

A quasi-unit disk graph has been used as a realistic model of an ad-hoc or a sensor wireless network. A wireless ad-hoc network is location aware if each node knows its geographic coordinates. Some network backbones proposed for data gathering in a wireless network are based on dominating sets of the network graph. The location awareness of ad-hoc networks corresponding to unit disk graph was used in [6] to obtain a local algorithm for a dominating set of a unit disk graph. In this paper we generalize this algorithm to location aware ad-hoc networks corresponding to quasi-unit graphs. The competitive ratio of the algorithm is determined for several ranges of the parameter r of an r--quasi-unit disk graph. For each range of r the competitive ratio is shown to be a constant value. An experimental evaluation of the algorithm is also carried out, which confirms very good performance of our algorithm.