The Full Steiner Tree Problem in Phylogeny

Authors:
Chin Lung Lu;Chuan Yi Tang;Richard Chia-Tung Lee
Affiliations:
-;-;-
Venue:
COCOON '02 Proceedings of the 8th Annual International Conference on Computing and Combinatorics
Year:
2002

Citing 4
Cited 1

The steiner problem with edge lengths 1 and 2,

Information Processing Letters
Proof verification and the hardness of approximation problems

Journal of the ACM (JACM)
Complexity and Approximation: Combinatorial Optimization Problems and Their Approximability Properties

Complexity and Approximation: Combinatorial Optimization Problems and Their Approximability Properties
Computers and Intractability: A Guide to the Theory of NP-Completeness

Computers and Intractability: A Guide to the Theory of NP-Completeness

A Survey of Parallel and Distributed Algorithms for the Steiner Tree Problem

International Journal of Parallel Programming

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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 驴 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 5/3-approximation algorithm to find an approximate solution for the problem.