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 ) ⩽ 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 .
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