Please use this identifier to cite or link to this item: http://dx.doi.org/10.14279/depositonce-14368
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Main Title: The Zoo of Tree Spanner Problems
Author(s): Liebchen, Christian
Wünsch, Gregor
Type: Research Paper
URI: https://depositonce.tu-berlin.de/handle/11303/15595
http://dx.doi.org/10.14279/depositonce-14368
License: http://rightsstatements.org/vocab/InC/1.0/
Abstract: Tree spanner problems have important applications in network design, e.g. in the telecommunications industry. Mathematically, there have been considered quite a number of maxstretch tree spanner problems and of average stretch tree spanner problems. We propose a unified notation for 20 tree spanner problems, which we investigate for graphs with general positive weights, with metric weights, and with unit weights. This covers several prominent problems of combinatorial optimization. Having this notation at hand, we can clearly identify which problems coincide. In the case of unweighted graphs, the formally 20 problems collapse to only five different problems. Moreover, our systematic notation for tree spanner problems enables us to identify a tree spanner problem whose complexity status has not been solved so far. We are able to provide an NP-hardness proof. Furthermore, due to our new notation of tree spanner problems, we are able to detect that an inapproximability result that is due to Galbiati (2001, 2003) in fact applies to the classical max-stretch tree spanner problem. We conclude that the inapproximability factor for this problem thus is 2-ε, instead of only (1+sqrt(5))/2 ~ 1.618 according to Peleg and Reshef (1999).
Subject(s): tree spanner problems
maximum stretch tree spanners
average stretch tree spanners
minimum strictly fundamental cycle basis problem
min-max strictly fundamental cycle basis problem
combinatorial optimization
Issue Date: 2006
Date Available: 17-Dec-2021
Language Code: en
DDC Class: 510 Mathematik
Series: Preprint-Reihe des Instituts für Mathematik, Technische Universität Berlin
Series Number: 2006, 13
ISSN: 2197-8085
TU Affiliation(s): Fak. 2 Mathematik und Naturwissenschaften » Inst. Mathematik
Appears in Collections:Technische Universität Berlin » Publications

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