Note: Approximating the selected-internal Steiner tree

Authors:
Sun-Yuan Hsieh;Shih-Cheng Yang
Affiliations:
Department of Computer Science and Information Engineering, National Cheng Kung University, No. 1, University Road, Tainan 70101, Taiwan;Department of Computer Science and Information Engineering, National Cheng Kung University, No. 1, University Road, Tainan 70101, Taiwan
Venue:
Theoretical Computer Science
Year:
2007

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Abstract

In this paper, we consider a 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 present a 2@r-approximation algorithm for the problem, where @r is the best-known approximation ratio for the Steiner tree problem.