A Polynomial Time Approximation Scheme for Minimum Routing Cost Spanning Trees

Given an undirected graph with nonnegative costs on the edges, the routing cost of any of its spanning trees is the sum over all pairs of vertices of the cost of the path between the pair in the tree. Finding a spanning tree of minimum routing cost is NP-hard, even when the costs obey the triangle inequality. We show that the general case is in fact reducible to the metric case and present a polynomial-time approximation scheme valid for both versions of the problem. In particular, we show how to build a spanning tree of an n-vertex weighted graph with routing cost at most (1 + ) of the minimum in time O(nO( 1 ) ). Besides the obvious connection to network design, trees with small routing cost also find application in the construction of good multiple sequence alignments in computational biology. The communication cost spanning tree problem is a generalization of the minimum routing cost tree problem where the routing costs of different pairs are weighted by different requirement amoun...

• Type: Conference
• Year: 1998
• Where: SODA
• Authors: Bang Ye Wu, Giuseppe Lancia, Vineet Bafna, Kun-Mao Chao, R. Ravi, Chuan Yi Tang
• Keywords: Algorithms, Minimum Routing Cost, Routing Costs, SODA 1998, Spanning Trees