A greedy approximation for minimum connected dominating sets

Given a graph, a connected dominating set 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.A minimum connected dominating set is such a vertex subset with minimum cardinality. In this paper, we present a new one-step greedy approximation with performance ratio ln + 2 where is the maximum degree in the input graph. The interesting aspect is that the greedy potential function of this algorithm is not supmodular while all previously known one-step greedy algorithms with similar performance have supmodular potential functions. © 2004 Elsevier B.V. All rights reserved.