Double partition: (6∈+∈ε)-approximation for minimum weight dominating set in unit disk graphs

Abstract

We introduce a new technique on partition, called double partition. With this new type of partition, we obtain a polynomial time (6∈+∈ε)- approximation (ε>∈0) for the minimum weight dominating set problem in unit disk graphs, which improves a recent result of a 72-approximation given by Ambühl et al. for solving a long-standing open problem. As a corollary, we obtain a (9.875∈+∈ε)-approximation for the minimum weight connected dominating set problem in unit disk graphs. © 2008 Springer-Verlag Berlin Heidelberg.