Maximal Independent Set and Minimum Connected Dominating Set in Unit Disk Graphs

Abstract

In ad hoc wireless networks, the 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 construction of maximal independent set. The relation between the size mis(G) of a maximum independent set and the size cds(G) of 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 graph G. In this paper, we improve it by showing mis(G)<=3.8*cds(G)+1.2.