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Hardness and Approximation of the Selected-Leaf-Terminal Steiner Tree Problem

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2 Author(s)
Sun-yuan Hsieh ; National Cheng Kung University, Taiwan ; Huang-ming Gao

For a complete graph G = (V, E) with length function l : E rarr R+ and two vertex subsets R sub V and R' sube R, a selected-leaf-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 selected-leaf-terminal Steiner tree problem is to find a selected-leaf-terminal Steiner tree T whose total lengths Sigma (u, v)epsiT 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

Published in:

2006 Seventh International Conference on Parallel and Distributed Computing, Applications and Technologies (PDCAT'06)

Date of Conference:

Dec. 2006