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.MFCS.2022.25
URN: urn:nbn:de:0030-drops-168233
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2022/16823/
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Brückner, Guido ; Rutter, Ignaz ; Stumpf, Peter

Extending Partial Representations of Circle Graphs in Near-Linear Time

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Abstract

The partial representation extension problem generalizes the recognition problem for geometric intersection graphs. The input consists of a graph G, a subgraph H ⊆ G and a representation H of H. The question is whether G admits a representation G whose restriction to H is H. We study this question for circle graphs, which are intersection graphs of chords of a circle. Their representations are called chord diagrams.
We show that for a graph with n vertices and m edges the partial representation extension problem can be solved in O((n + m) α(n + m)) time, where α is the inverse Ackermann function. This improves over an O(n³)-time algorithm by Chaplick, Fulek and Klavík [2019]. The main technical contributions are a canonical way of orienting chord diagrams and a novel compact representation of the set of all canonically oriented chord diagrams that represent a given circle graph G, which is of independent interest.

BibTeX - Entry

@InProceedings{bruckner_et_al:LIPIcs.MFCS.2022.25,
  author =	{Br\"{u}ckner, Guido and Rutter, Ignaz and Stumpf, Peter},
  title =	{{Extending Partial Representations of Circle Graphs in Near-Linear Time}},
  booktitle =	{47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022)},
  pages =	{25:1--25:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-256-3},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{241},
  editor =	{Szeider, Stefan and Ganian, Robert and Silva, Alexandra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2022/16823},
  URN =		{urn:nbn:de:0030-drops-168233},
  doi =		{10.4230/LIPIcs.MFCS.2022.25},
  annote =	{Keywords: circle graphs, partial representation extension, split decomposition tree, recognition algorithm}
}

Keywords: circle graphs, partial representation extension, split decomposition tree, recognition algorithm
Collection: 47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022)
Issue Date: 2022
Date of publication: 22.08.2022

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