License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ISAAC.2022.13
URN: urn:nbn:de:0030-drops-172982
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2022/17298/
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Fox, Kyle ; Stanley, Thomas

Computation of Cycle Bases in Surface Embedded Graphs

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LIPIcs-ISAAC-2022-13.pdf (0.7 MB)

Abstract

We present an O(n³ g²log g + m) + Õ(n^{ω + 1}) time deterministic algorithm to find the minimum cycle basis of a directed graph embedded on an orientable surface of genus g. This result improves upon the previous fastest known running time of O(m³n + m²n² log n) applicable to general directed graphs.
While an O(n^ω + 2^{2g}n² + m) time deterministic algorithm was known for undirected graphs, the use of the underlying field ℚ in the directed case (as opposed to ℤ₂ for the undirected case) presents extra challenges. It turns out that some of our new observations are useful for both variants of the problem, so we present an O(n^ω + n² g² log g + m) time deterministic algorithm for undirected graphs as well.

BibTeX - Entry

@InProceedings{fox_et_al:LIPIcs.ISAAC.2022.13,
  author =	{Fox, Kyle and Stanley, Thomas},
  title =	{{Computation of Cycle Bases in Surface Embedded Graphs}},
  booktitle =	{33rd International Symposium on Algorithms and Computation (ISAAC 2022)},
  pages =	{13:1--13:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-258-7},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{248},
  editor =	{Bae, Sang Won and Park, Heejin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2022/17298},
  URN =		{urn:nbn:de:0030-drops-172982},
  doi =		{10.4230/LIPIcs.ISAAC.2022.13},
  annote =	{Keywords: cycle basis, surface embedded graphs, homology}
}

Keywords: cycle basis, surface embedded graphs, homology
Collection: 33rd International Symposium on Algorithms and Computation (ISAAC 2022)
Issue Date: 2022
Date of publication: 14.12.2022

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