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Type: Conference paper
Title: On the shallow-light Steiner tree problem
Author: Guo, L.
Liao, K.
Shen, H.
Citation: Proceedings of the 15th Parallel and Distributed Computing, Applications and Technologies, 2015, vol.2015-July, pp.56-60
Publisher: IEEE
Issue Date: 2015
ISBN: 9781479983346
Conference Name: 15th International Conference on Parallel and Distributed Computing, Applications and Technologies (PDCAT) (9 Dec 2014 - 11 Dec 2014 : Hong Kong, China)
Statement of
Longkun Guo, Kewen Liao, Hong Shen
Abstract: Let G = (V, E) be a given graph with nonnegative integral edge cost and delay, S ⊆ V be a terminal set and +° ∈ S be the selected root. The shallow-light Steiner tree (SLST) problem is to compute a minimum cost tree spanning the terminals of S, such that the delay between r and every other terminal is bounded by a given delay constraint D ∈ Z+ ° . It is known that the SLST problem is NP-hard and unless NP ⊆ DTIME(nlog log n) there exists no approximation algorithm with ratio (1, γ log² n) for some fixed γ > 0 [12]. Nevertheless, under the same assumption it admits no approximation ratio better than (1, γ log |V |) for some fixed γ > 0 even when D = 2 [2]. This paper first gives an exact algorithm with time complexity O(3tnD + 2tn²D² + n³D³), where n and t are the numbers of vertices and terminals of the given graph respectively. This is a pseudo polynomial time parameterized algorithm with respect to the parameterization “number of terminals”. Later, this algorithm is improved to a parameterized approximation algorithm with a time complexity O(3t n2 + 2t n4 2 + n6 3 ) and a bifactor approximation ratio (1 + ∈ , 1). That is, for any small real number ∈ > 0, the algorithm computes a Steiner tree with delay and cost bounded by (1 + ∈ )D and the optimum cost respectively.
Keywords: Shallow light Steiner tree; parameterized approximation algorithm; exact algorithm; layer graph; pseudopolynomial time
Rights: © 2014 IEEE
DOI: 10.1109/PDCAT.2014.17
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