An Approximation Algorithm for the Generalized Minimum Spanning Tree Problem with Bounded Cluster Size

Abstract

Given a complete undirected graph with the nodes partitioned into m node sets called clusters, the Generalized Minimum Spanning Tree problem denoted by GMST is to find a minimum-cost tree which includes exactly one node from each cluster. It is known that the GMST problem is NP-hard and even finding a near optimal solution is NP-hard. We give an approximation algorithm for the Generalized Minimum Spanning Tree problem in the case when the cluster size is bounded by ρ. In this case, the GMST problem can be approximated to within 2ρ.

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