• search hit 6 of 12
Back to Result List

Classes of Cycle Bases

Please always quote using this URN:urn:nbn:de:0296-matheon-2662
  • In the last years, new variants of the minimum cycle basis (MCB) problem and new classes of cycle bases have been introduced, as motivated by several applications from disparate areas of scientific and technological inquiries. At present, the complexity status of the MCB problem has been settled only for undirected, directed, and strictly fundamental cycle bases. In this paper, we over an unitary classification accommodating these 3 classes and further including the following 4 relevant classes: 2-bases (or planar bases), weakly fundamental cycle bases, totally unimodular cycle bases, and integral cycle bases. The classification is complete in that, for each ordered pair (A;B) of classes considered, we either prove that A ? B holds for every graph or provide a counterexample graph for which A ? B. The seven notions of cycle bases are distinct (either A ? B or B ? A is exhibited for each pair (A;B)). All counterexamples proposed have been designed to be ultimately effective in separating the various algorithmic variants of the MCB problem naturally associated to each one of these seven classes. We even provide a linear time algorithm for computing a minimum 2-basis of a graph. Finally, notice that the resolution of the complexity status of some of the remaining three classes would have an immediate impact on practical applications, as for instance in periodic railway timetabling, only integral cycle bases are of direct use.

Download full text files

Export metadata

Additional Services

Share in Twitter Search Google Scholar
Metadaten
Author:Christian Liebchen, Romeo Rizzi
URN:urn:nbn:de:0296-matheon-2662
Referee:Rolf H. Möhring
Document Type:Preprint, Research Center Matheon
Language:English
Date of first Publication:2005/11/14
Release Date:2005/09/08
Preprint Number:287
Verstanden ✔
Diese Webseite verwendet technisch erforderliche Session-Cookies. Durch die weitere Nutzung der Webseite stimmen Sie diesem zu. Unsere Datenschutzerklärung finden Sie hier.