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.
Ruan et al. REF presented one one-step greedy approximation with performance ratio ln ∆+2, where is the maximum node degree.
A greedy approximation for minimum connected dominating sets
Theor. Comput. Sci.
Theor. Comput. Sci.
Mathematics Computer Science