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.SWAT.2022.19
URN: urn:nbn:de:0030-drops-161797
URL: https://drops.dagstuhl.de/opus/volltexte/2022/16179/
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Bose, Prosenjit ; Morin, Pat ; Odak, Saeed

An Optimal Algorithm for Product Structure in Planar Graphs

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LIPIcs-SWAT-2022-19.pdf (0.7 MB)


Abstract

The Product Structure Theorem for planar graphs (Dujmovińá et al. JACM, 67(4):22) states that any planar graph is contained in the strong product of a planar 3-tree, a path, and a 3-cycle. We give a simple linear-time algorithm for finding this decomposition as well as several related decompositions. This improves on the previous O(nlog n) time algorithm (Morin. Algorithmica, 85(5):1544-1558).

BibTeX - Entry

@InProceedings{bose_et_al:LIPIcs.SWAT.2022.19,
  author =	{Bose, Prosenjit and Morin, Pat and Odak, Saeed},
  title =	{{An Optimal Algorithm for Product Structure in Planar Graphs}},
  booktitle =	{18th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2022)},
  pages =	{19:1--19:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-236-5},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{227},
  editor =	{Czumaj, Artur and Xin, Qin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2022/16179},
  URN =		{urn:nbn:de:0030-drops-161797},
  doi =		{10.4230/LIPIcs.SWAT.2022.19},
  annote =	{Keywords: Planar graphs, product structure}
}

Keywords: Planar graphs, product structure
Collection: 18th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2022)
Issue Date: 2022
Date of publication: 22.06.2022


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