MAX-SNP hardness and approximation of selected-internal steiner trees

Authors:
Sun-Yuan Hsieh;Shih-Cheng Yang
Affiliations:
Department of Computer Science and Information Engineering, National Cheng Kung University, Tainan, Taiwan;Department of Computer Science and Information Engineering, National Cheng Kung University, Tainan, Taiwan
Venue:
COCOON'06 Proceedings of the 12th annual international conference on Computing and Combinatorics
Year:
2006

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Abstract

In this paper, we consider an interesting variant of the well-known Steiner tree problem: Given a complete graph G = (V,E) with a cost function c:E →R+ and two subsets R and R′ satisfying R′⊂R⊆V, a selected-internal Steiner tree is a Steiner tree which contains (or spans) all the vertices in R such that each vertex in R′ cannot be a leaf. The selected-internal Steiner tree problem is to find a selected-internal Steiner tree with the minimum cost. In this paper, we show that the problem is MAX SNP-hard even when the costs of all edges in the input graph are restricted to either 1 or 2. We also present an approximation algorithm for the problem.