Polynomial-Time Approximation Scheme for Minimum Connected Dominating Set in Ad Hoc Wireless Networks

A connected dominating set in a graph is a subset of vertices such that every vertex is either in the subset or adjacent to a vertex in the subset and the subgraph induced by the subset is connected. The minimum connected dominating set is such a vertex subset with minimum cardinality. An application in ad hoc wireless networks requires the study of the minimum connected dominating set in unit-disk graphs. In this paper, we design $(1+1/s)$-approximation for the minimum connected dominating set in unit-disk graphs, running in time $n^{O((slog s)^2)}$