A Faster Algorithm for the Inverse Spanning Tree Problem Ravindra
نویسنده
چکیده
In this paper, we consider the inverse spanning tree problem. Given an undirected graph Go = (Ni, AO) with n nodes, mn arcs, an arc cost vector c, and a spanning tree T, the inverse spanning tree problem is to perturb the arc cost vector c to a vector d so that T is a minimum spanning tree with respect to the cost vector d and the cost of perturbation given by Id c = L(l j) Aldij ciil is minimum. We show that the dual of the inverse spanning tree problem is a bipartite node weighted matching problem on a specially structured graph (which we call the path graph) that contains m nodes and as many as (m n + 1)(n 1) = O(nm) arcs. We first transform the bipartite node weighted matching problem into a specially structured minimum cost flow problem and use its special structure to develop an O(n3 ) algorithm. We next use its special structure more effectively and develop an O(n21log n) time algorithm. This improves the previous O(n3 ) time algorithm due to Sokkalingam et a. (1999, Oper. Res. 47, 291-298). © 2000 Academic Press
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