Improved approximation bounds for the group Steiner problem

Authors:
C. S. Helvig;G. Robins;A. Zelikovsky
Affiliations:
Department of Computer Science, University of Virginia, Charlottesville, Virginia;Department of Computer Science, University of Virginia, Charlottesville, Virginia;Department of Computer Science, UCLA, Los Angeles, California
Venue:
Proceedings of the conference on Design, automation and test in Europe
Year:
1998

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Abstract

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^e)-approximation algorithms for arbitrarily small values of e0, improving on the previously known O(k^0.5)-approximation. Our techniques also solve the graph Steiner arborescence problem with an O(k^e) 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.