The full steiner tree problem

Authors:
Chin Lung Lu;Chuan Yi Tang;Richard Chia-Tung Lee
Affiliations:
Department of Biological Science and Technology, National Chiao Tung University, Hsinchu 300, Taiwan, ROC;Department of Computer Science, National Tsing Hua University, Hsinchu 300 Taiwan, ROC;Department of Computer Science and Information Engineering, National Chi-Nan University, Puli, Nantou Hsien 545, Taiwan, ROC
Venue:
Theoretical Computer Science
Year:
2003

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Abstract

Motivated by the reconstruction of phylogenetic tree in biology, we study the full Steiner tree problem in this paper. Given a complete graph G = (V,E) with a length function on E and a proper subset R ⊆ V, the problem is to find a full Steiner tree of minimum length in G, which is a kind of Steiner tree with all the vertices of R as its leaves. In this paper, we show that this problem is NP-complete and MAX SNP-hard, even when the lengths of the edges are restricted to either 1 or 2. For the instances with lengths either 1 or 2, we give a 8/5-approximation algorithm to find an approximate solution for the problem.