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

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 VNi ∩ VNj = for i ≠ j. 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.