Approximation Algorithms for Connected Dominating Sets

The dominatingset problemin graphs asks for a minimumsize subset of vertices with the followingproperty: each vertex is required to either be in the dominating set, or adjacent to somenode in the dominatingset. We focus on the question of nding a connected dominating set of minimum size, where the graph induced by vertices in the dominating set is required to be connected as well. This problem arises in network testing, as well as in wireless communication. Two polynomial time algorithms that achieve approximation factors of OH
 are presented, where
is the maximum degree, and H is the harmonic function. This question also arises in relation to the traveling tourist problem, where one is looking for the shortest tour such that each vertex is either visited, or has at least one of its neighbors visited. We study a generalization of the problem when the vertices have weights, and give an algorithm which achieves a performance ratio of 3lnn. We also consider the more general problem...

• Type: Journal
• Year: 1998
• Where: ALGORITHMICA
• Authors: Sudipto Guha, Samir Khuller
• Keywords: ALGORITHMICA 1998, Approximation Factor, Connected Dominating Set, Dominatingset Problemin Graphs