Improved Approximation Bounds for the Group Steiner Problem
Christopher S. Helvig, Gabriel Robins, Alexander Zelikovsky · 1998
Given a weighted graph and a family of k disjoint groups of nodes, the Group Steiner Problem asks for a minimum-cost routing tree that contains at least one node from each group. We give polynomial-time O(k ffl )-approximation algorithms for arbitrarily small values of ffl ? 0, improving on the previously known O(k 1 2 )-approximation. Our techniques also solve the graph Steiner arborescence problem with an O(k ffl ) approximation bound. These results are directly applicable to a practical problem in VLSI layout, namely the routing of nets with multi-port terminals. Our Java implementation is available on the Web. 1 Introduction The classical Steiner problem can be formulated as follows: given an undirected weighted graph G = (V; E) and M ` V , find a minimum-cost tree that spans all of M . Nodes in V \\Gamma M (referred to as Steiner nodes) may be optionally included in order to reduce the total tree cost [11]. In this paper, we address a generalization of this problem, nam...