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

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) <= 4 (.) cds(G) + 1 for all unit disk graphs G. In this paper, we improve it by showing mis(G) <= 3.8 (.) cds(G) + 1.2. (c) 2005 Elsevier B.V. All rights reserved.