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VLSI Design
Volume 4, Issue 1, Pages 53-57
http://dx.doi.org/10.1155/1996/43738

Minimum-Cost Node-Disjoint Steiner Trees in Series-Parallel Networks

1MEDS, J. L. Kellogg Graduate School of Management, Northwestern University, Evanston 60208, IL, USA
2USAir, Operations Research Department, 2345 Crystal Drive, Arlington 22227, VA, USA

Received 22 February 1994; Revised 3 February 1995

Copyright © 1996 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The routing problem in VLSI-layout can be modeled as a problem of packing node-disjoint Steiner trees in a graph. The problem is as follows: Given an undirected network G = (V, E) and a net list Ψ {Ni,i=1,...,r} , a family ΓG={TNi=(VNi,ENi),i=1,...,r} is a node-disjoint family of Steiner trees spanning Ψ if TNi , is a Steiner tree spanning Ni for i = 1, ..., r and VNiVNj = for ij. The edge-disjoint version of this problem is known to be NP-hard for t. series-parallel graphs (see Rlchey and Parker [5]). In this paper we give a O(n5) algorithm for finding a minimum-cost node-disjoint family of Steiner trees in series-parallel networks. Our algorithm can be extended to k-trees and is polynomial for fixed k.