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The Euclidean Bottleneck Full Steiner Tree Problem.
- Source :
-
Algorithmica . Jan2015, Vol. 71 Issue 1, p139-151. 13p. - Publication Year :
- 2015
-
Abstract
- Given two sets in the plane, R of n (terminal) points and S of m (Steiner) points, a full Steiner tree is a Steiner tree in which all points of R are leaves. In the bottleneck full Steiner tree (BFST) problem, one has to find a full Steiner tree T (with any number of Steiner points from S), such that the length of the longest edge in T is minimized, and, in the k-BFST problem, has to find a full Steiner tree T with at most k≤ m Steiner points from S such that the length of the longest edge in T is minimized. The problems are motivated by wireless network design. In this paper, we present an exact algorithm of ${{{\mathcal {O}}}}((n+m)\log^{2}{m})$ time to solve the BFST problem. Moreover, we show that the k-BFST problem is NP-hard and that there exists a polynomial-time approximation algorithm for the problem with performance ratio 4. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 01784617
- Volume :
- 71
- Issue :
- 1
- Database :
- Academic Search Index
- Journal :
- Algorithmica
- Publication Type :
- Academic Journal
- Accession number :
- 100524861
- Full Text :
- https://doi.org/10.1007/s00453-013-9788-x