Diameter-constrained steiner tree

Authors:
Wei Ding;Guohui Lin;Guoliang Xue
Affiliations:
Zhejiang Water Conservancy and Hydropower College, Hangzhou, Zhejiang, China;Department of Computing Science, University of Alberta, Edmonton, Alberta, Canada;Department of Computer Science and Engineering, Arizona State University, Tempe, AZ
Venue:
COCOA'10 Proceedings of the 4th international conference on Combinatorial optimization and applications - Volume Part II
Year:
2010

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Abstract

Given an edge-weighted undirected graph G = (V, E, c, w), where each edge e ε E has a cost c(e) and a weight w(e), a set S ⊆ V of terminals and a positive constant D0, we seek a minimum cost Steiner tree where all terminals appear as leaves and its diameter is bounded by D0. Note that the diameter of a tree represents the maximum weight of path connecting two different leaves in the tree. Such problem is called the minimum cost diameter-constrained Steiner tree problem. This problem is NP-hard even when the topology of Steiner tree is fixed. In present paper we focus on this restricted version and present a fully polynomial time approximation scheme (FPTAS) for computing a minimum cost diameter-constrained Steiner tree under a fixed topology.