On the partial terminal Steiner tree problem

Authors:
Sun-Yuan Hsieh;Huang-Ming Gao
Affiliations:
Department of Computer Science and Information Engineering, National Cheng Kung University, Tainan, Taiwan 701;Department of Computer Science and Information Engineering, National Cheng Kung University, Tainan, Taiwan 701
Venue:
The Journal of Supercomputing
Year:
2007

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Abstract

We investigate a practical variant of the well-known graph Steiner tree problem. For a complete graph G = ( V,E ) with length function l:E 驴 R + and two vertex subsets R 驴 V and R 驴驴 R, a partial terminal Steiner tree is a Steiner tree which contains all vertices in R such that all vertices in R 驴 R 驴 belong to the leaves of this Steiner tree. The partial terminal Steiner tree problem is to find a partial terminal Steiner tree T whose total lengths 驴 (u,v) 驴T l ( u,v ) is minimum. In this paper, we show that the problem is both NP-complete and MAX SNP-hard when the lengths of edges are restricted to either 1 or 2. We also provide an approximation algorithm for the problem.