A polynomial time approximation scheme for the two-source minimum routing cost spanning trees

Authors:
Bang Ye Wu
Affiliations:
Department of Computer Science and Information Engineering, Shu-Te University, YenChau, KaoShiung, Taiwan 824, ROC
Venue:
Journal of Algorithms
Year:
2002

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Abstract

Let G be an undirected graph with nonnegative edge lengths. Given two vertices as sources and all vertices as destinations, we investigated the problem how to construct a spanning tree of G such that the sum of distances from sources to destinations is minimum. In the paper, we show the NP-hardness of the problem and present a polynomial time approximation scheme. For any ε 0, the approximation scheme finds a (1 + ε)- approximation solution in O(n⌈1/ε+1⌈) time. We also generalize the approximation algorithm to the weighted case for distances that form a metric space.