On exact solutions to the Euclidean bottleneck Steiner tree problem

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We study the Euclidean bottleneck Steiner tree problem: given a set P of n points in the Euclidean plane and a positive integer k, find a Steiner tree with at most k Steiner points such that the length of the longest edge in the tree is minimized. This problem is known to be NP-hard even to approximate within ratio root 2 and there was no known exact algorithm even for k = 1 prior to this work. In this paper, we focus on finding exact solutions to the problem for a small constant k. Based on geometric properties of optimal location of Steiner points, we present an optimal Theta(n log n)-time exact algorithm for k = 1 and an O(n(2))-time algorithm for k = 2. Also, we present an optimal Theta(n log n)-time exact algorithm for any constant k for a special case where there is no edge between Steiner points. (C) 2010 Elsevier B.V. All rights reserved.
Publisher
ELSEVIER SCIENCE BV
Issue Date
2010-07
Language
English
Article Type
Article
Keywords

APPROXIMATION ALGORITHM; PLANE

Citation

INFORMATION PROCESSING LETTERS, v.110, no.16, pp.672 - 678

ISSN
0020-0190
DOI
10.1016/j.ipl.2010.05.014
URI
http://hdl.handle.net/10203/22084
Appears in Collection
CS-Journal Papers(저널논문)
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