New length bounds for cycle bases

Michael Elkin, Christian Liebchen, Romeo Rizzi

Research output: Contribution to journalArticlepeer-review

15 Scopus citations

Abstract

Based on a recent work by Abraham, Bartal and Neiman (2007), we construct a strictly fundamental cycle basis of length O (n2) for any unweighted graph, whence proving the conjecture of Deo et al. (1982). For weighted graphs, we construct cycle bases of length O (W ṡ log n log log n), where W denotes the sum of the weights of the edges. This improves the upper bound that follows from the result of Elkin et al. (2005) by a logarithmic factor and, for comparison from below, some natural classes of large girth graphs are known to exhibit minimum cycle bases of length Ω (W ṡ log n). We achieve this bound for weighted graphs by not restricting ourselves to strictly fundamental cycle bases-as it is inherent to the approach of Elkin et al.-but rather also considering weakly fundamental cycle bases in our construction. This way we profit from some nice properties of Hierarchically Well-Separated Trees that were introduced by Bartal (1998).

Original languageEnglish
Pages (from-to)186-193
Number of pages8
JournalInformation Processing Letters
Volume104
Issue number5
DOIs
StatePublished - 30 Nov 2007

Keywords

  • Approximation algorithms
  • Cycle bases
  • Graph algorithms
  • Metric approximation

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Signal Processing
  • Information Systems
  • Computer Science Applications

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