TY - JOUR

T1 - On the partial terminal Steiner tree problem

AU - Hsieh, Sun-Yuan

AU - Gao, Huang Ming

PY - 2007/7/1

Y1 - 2007/7/1

N2 - 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 → R + and two vertex subsets R ⊂ V and R' ⊆ R, a partial terminal Steiner tree is a Steiner tree which contains all vertices in R such that all vertices in R \ R' 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 ∑(u,v)∈Tl(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.

AB - 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 → R + and two vertex subsets R ⊂ V and R' ⊆ R, a partial terminal Steiner tree is a Steiner tree which contains all vertices in R such that all vertices in R \ R' 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 ∑(u,v)∈Tl(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.

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U2 - 10.1007/s11227-007-0102-z

DO - 10.1007/s11227-007-0102-z

M3 - Article

AN - SCOPUS:34248163983

VL - 41

SP - 41

EP - 52

JO - Journal of Supercomputing

JF - Journal of Supercomputing

SN - 0920-8542

IS - 1

ER -