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.SoCG.2022.17
URN: urn:nbn:de:0030-drops-160253
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2022/16025/
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Black, Mitchell ; Blaser, Nello ; Nayyeri, Amir ; Vågset, Erlend Raa

ETH-Tight Algorithms for Finding Surfaces in Simplicial Complexes of Bounded Treewidth

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LIPIcs-SoCG-2022-17.pdf (1 MB)

Abstract

Given a simplicial complex with n simplices, we consider the Connected Subsurface Recognition (c-SR) problem of finding a subcomplex that is homeomorphic to a given connected surface with a fixed boundary. We also study the related Sum-of-Genus Subsurface Recognition (SoG) problem, where we instead search for a surface whose boundary, number of connected components, and total genus are given. For both of these problems, we give parameterized algorithms with respect to the treewidth k of the Hasse diagram that run in 2^{O(k log k)}n^{O(1)} time. For the SoG problem, we also prove that our algorithm is optimal assuming the exponential-time hypothesis. In fact, we prove the stronger result that our algorithm is ETH-tight even without restriction on the total genus.

BibTeX - Entry

@InProceedings{black_et_al:LIPIcs.SoCG.2022.17,
  author =	{Black, Mitchell and Blaser, Nello and Nayyeri, Amir and V\r{a}gset, Erlend Raa},
  title =	{{ETH-Tight Algorithms for Finding Surfaces in Simplicial Complexes of Bounded Treewidth}},
  booktitle =	{38th International Symposium on Computational Geometry (SoCG 2022)},
  pages =	{17:1--17:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-227-3},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{224},
  editor =	{Goaoc, Xavier and Kerber, Michael},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2022/16025},
  URN =		{urn:nbn:de:0030-drops-160253},
  doi =		{10.4230/LIPIcs.SoCG.2022.17},
  annote =	{Keywords: Computational Geometry, Surface Recognition, Treewidth, Hasse Diagram, Simplicial Complexes, Low-Dimensional Topology, Parameterized Complexity, Computational Complexity}
}

Keywords: Computational Geometry, Surface Recognition, Treewidth, Hasse Diagram, Simplicial Complexes, Low-Dimensional Topology, Parameterized Complexity, Computational Complexity
Collection: 38th International Symposium on Computational Geometry (SoCG 2022)
Issue Date: 2022
Date of publication: 01.06.2022

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