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

It was a long-standing open problem whether the minimum weight dominating set in unit disk graphs has a polynomial-time constant-approximation. In 2006, Ambuhl et al solved this problem by presenting a 72-approximation for the minimum weight dominating set and also a 89-approximation for the minimum weight connected dominating set in unit disk graphs. In this paper, we improve their results by giving a (6 + epsilon)-approximation for the minimum weight dominating set and a (10 + epsilon)-approximation for the minimum weight connected dominating set in unit disk graphs where epsilon is any small positive number.