Journal article
Bounding component sizes of two-connected Steiner networks
Department of Computer Science, University of Copenhagen, Universitetsparken 1, DK-2100 Copenhagen Ø, Denmark
We consider the problem of constructing a shortest Euclidean 2-connected Steiner network in the plane (SMN) for a set of n terminals. This problem has natural applications in the design of survivable communication networks.In [P. Winter, M. Zachariasen, Two-connected Steiner networks: Structural properties, OR Letters 33 (2005) 395–402] we proved that all cycles in SMNs with Steiner points must have pairs of consecutive terminals of degree 2.
We use this result and the notion of reduced block-bridge trees suggested by Luebke [E.L. Luebke, k-connected Steiner network problems, PhD thesis, University of North Carolina, USA, 2002] to show that no full Steiner tree in a SMN spans more than ⌊n/3⌋+1 terminals.
Language: | English |
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Year: | 2007 |
Pages: | 159-163 |
ISSN: | 18726119 and 00200190 |
Types: | Journal article |
DOI: | 10.1016/j.ipl.2007.06.009 |
ORCIDs: | Winter, P. and Zachariasen, M. |