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.
Wu et al. REF introduced a distributed CDS construction algorithm that relies on the relation between the maximumal independent set (MIS) and the connected dominating set.
Minimum connected dominating sets and maximal independent sets in unit disk graphs
Mathematics Computer Science