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.STACS.2022.23
URN: urn:nbn:de:0030-drops-158333
URL: https://drops.dagstuhl.de/opus/volltexte/2022/15833/
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Chiu, Yung-Chung ; Lu, Hsueh-I

Blazing a Trail via Matrix Multiplications: A Faster Algorithm for Non-Shortest Induced Paths

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LIPIcs-STACS-2022-23.pdf (0.9 MB)


Abstract

For vertices u and v of an n-vertex graph G, a uv-trail of G is an induced uv-path of G that is not a shortest uv-path of G. Berger, Seymour, and Spirkl [Discrete Mathematics 2021] gave the previously only known polynomial-time algorithm, running in O(n^{18}) time, to either output a uv-trail of G or ensure that G admits no uv-trail. We reduce the complexity to the time required to perform a poly-logarithmic number of multiplications of n²× n² Boolean matrices, leading to a largely improved O(n^{4.75})-time algorithm.

BibTeX - Entry

@InProceedings{chiu_et_al:LIPIcs.STACS.2022.23,
  author =	{Chiu, Yung-Chung and Lu, Hsueh-I},
  title =	{{Blazing a Trail via Matrix Multiplications: A Faster Algorithm for Non-Shortest Induced Paths}},
  booktitle =	{39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022)},
  pages =	{23:1--23:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-222-8},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{219},
  editor =	{Berenbrink, Petra and Monmege, Benjamin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2022/15833},
  URN =		{urn:nbn:de:0030-drops-158333},
  doi =		{10.4230/LIPIcs.STACS.2022.23},
  annote =	{Keywords: Induced subgraph, induced path, non-shortest path, dynamic data structure}
}

Keywords: Induced subgraph, induced path, non-shortest path, dynamic data structure
Collection: 39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022)
Issue Date: 2022
Date of publication: 09.03.2022


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