Minimum connected dominating sets and maximal independent sets in unit disk graphs

  • Authors:
  • Weili Wu;Hongwei Du;Xiaohua Jia;Yingshu Li;Scott C.-H. Huang

  • Affiliations:
  • Department of Computer Science, University of Texas at Dallas, Richardson, Tx;Department of Computer Science, City University of Hong Kong, Kowloon Tong, Hong Kong, China;Department of Computer Science, City University of Hong Kong, Kowloon Tong, Hong Kong, China;Department of Computer Science, Georgia State University, Atlanta, GA;Department of Computer Science, City University of Hong Kong, Kowloon Tong, Hong Kong, China

  • Venue:
  • Theoretical Computer Science
  • Year:
  • 2006

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Abstract

In ad hoc wireless networks, a connected dominating set can be used as a virtual backbone to improve the performance. Many constructions for approximating the minimum connected dominating set are based on the construction of a maximal independent set. The relation between the size mis(G) of a maximum independent set and the size cds(G) of a minimum connected dominating set in the same graph G plays an important role in establishing the performance ratio of those approximation algorithms. Previously, it is known that mis(G) ≤ 4ċcds(G) + 1 for all unit disk graphs G. In this paper, we improve it by showing mis(G) ≤ 3.8ċcds(G) + 1.2.