(6+epsilon)-Approximation for Minimum Weight Dominating Set in Unit Disk Graphs

It was a long-standing open problem whether the minimum weightdominating set in unit disk graphs has a polynomial-timeconstant-approximation. In 2006, Ambuhl et alsolvedthis problem by presenting a 72-approximation for the minimumweight dominating set and also a 89-approximation for the minimumweight connected dominating set in unit disk graphs. In this paper,we improve their results by giving a (6 +e)-approximation for the minimum weight dominatingset and a (10 + e)-approximation for the minimumweight connected dominating set in unit disk graphs whereeis any small positive number.