License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ESA.2019.13
URN: urn:nbn:de:0030-drops-111346
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2019/11134/
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Bauer, Ulrich ; Rathod, Abhishek ; Spreer, Jonathan

Parametrized Complexity of Expansion Height

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Abstract

Deciding whether two simplicial complexes are homotopy equivalent is a fundamental problem in topology, which is famously undecidable. There exists a combinatorial refinement of this concept, called simple-homotopy equivalence: two simplicial complexes are of the same simple-homotopy type if they can be transformed into each other by a sequence of two basic homotopy equivalences, an elementary collapse and its inverse, an elementary expansion. In this article we consider the following related problem: given a 2-dimensional simplicial complex, is there a simple-homotopy equivalence to a 1-dimensional simplicial complex using at most p expansions? We show that the problem, which we call the erasability expansion height, is W[P]-complete in the natural parameter p.

BibTeX - Entry

@InProceedings{bauer_et_al:LIPIcs:2019:11134,
  author =	{Ulrich Bauer and Abhishek Rathod and Jonathan Spreer},
  title =	{{Parametrized Complexity of Expansion Height}},
  booktitle =	{27th Annual European Symposium on Algorithms (ESA 2019)},
  pages =	{13:1--13:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-124-5},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{144},
  editor =	{Michael A. Bender and Ola Svensson and Grzegorz Herman},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2019/11134},
  URN =		{urn:nbn:de:0030-drops-111346},
  doi =		{10.4230/LIPIcs.ESA.2019.13},
  annote =	{Keywords: Simple-homotopy theory, simple-homotopy type, parametrized complexity theory, simplicial complexes, (modified) dunce hat}
}

Keywords: Simple-homotopy theory, simple-homotopy type, parametrized complexity theory, simplicial complexes, (modified) dunce hat
Collection: 27th Annual European Symposium on Algorithms (ESA 2019)
Issue Date: 2019
Date of publication: 06.09.2019

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