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 + ?)-approximation (?> 0) for the minimum weight dominating set problem in unit disk graphs, which improves a recent result of a 72-approximation given by Ambuhl et al. for solving a long-standing open problem. As a corollary, we obtain a (9.875 + ?)-approximation for the minimum weight connected dominating set problem in unit disk graphs.