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 δ + 2 where δ 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.

Authors

• Lu Ruan
• Hongwei Du
• Xiaohua Jia
• Weili Wu
• Yingshu Li University of Sydney
• Ker-I Ko

Keywords

• Connected dominating set
• Greedy approximation