2014 Second International Symposium on Computing and Networking (CANDAR) (2014)

Shizuoka, Japan

Dec. 10, 2014 to Dec. 12, 2014

ISBN: 978-1-4799-4152-0

pp: 60-67

ABSTRACT

A connected dominating set (CDS, for short) for graph G is a dominating set which induces a connected sub graph of G. In this paper, we consider the problem of finding a minimum CDS for unit disk graphs, which have recently attracted considerable attention as a model of virtual backbone in multi-hop wireless networks. This optimization problem is known to be NP-hard and many approximation algorithms have been proposed in the literature. This paper proves a lower bound on the performance ratio of a greedy algorithm proposed by Guha and Khuller which was originally proposed for general graphs. More specifically, we show that for any fixed e > 0 and integer n0 = 1, there is a unit disk graph with bounded degree consisting of at least n0 vertices for which the output of the greedy algorithm is no better than 3 -- e times of an optimum solution to the same graph.

INDEX TERMS

Greedy algorithms, Approximation methods, Wireless networks, Spread spectrum communication, Educational institutions, Optimization, Approximation algorithms

CITATION

S. Fujita, "On Guha and Khuller's Greedy Algorithm for Finding a Minimum CDS for Unit Disk Graphs,"

*2014 Second International Symposium on Computing and Networking (CANDAR)*, Shizuoka, Japan, 2014, pp. 60-67.

doi:10.1109/CANDAR.2014.12

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