Date of Original Version

7-1996

Type

Conference Proceeding

Abstract or Description

Given an undirected graph with two different nonnegative costs associated with every edge e (say, we for the weight and l e for the length of edge e) and a budget L, consider the problem of finding a spanning tree of total edge length at most L and minimum total weight under this restriction. This constrained minimum spanning tree problem is weakly NP-hard. We present a polynomial-time approximation scheme for this problem. This algorithm always produces a spanning tree of total length at most (1 + ε)L and of total weight at most that of any spanning tree of total length at most L, for any fixed ε >0. The algorithm uses Lagrangean relaxation, and exploits adjacency relations for matroids.

DOI

10.1007/3-540-61422-2_121

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Published In

Proc. of the Scandinavian Workshop on Algorithmic Theory (SWAT), LNCS 1097, 66-75.