Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik GmbH Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik GmbH scholarly article en Goaoc, Xavier; Paták, Pavel; Patáková, Zuzana; Tancer, Martin; Wagner, Uli http://www.dagstuhl.de/lipics License
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URN: urn:nbn:de:0030-drops-87542
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Shellability is NP-Complete

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Abstract

We prove that for every d >= 2, deciding if a pure, d-dimensional, simplicial complex is shellable is NP-hard, hence NP-complete. This resolves a question raised, e.g., by Danaraj and Klee in 1978. Our reduction also yields that for every d >= 2 and k >= 0, deciding if a pure, d-dimensional, simplicial complex is k-decomposable is NP-hard. For d >= 3, both problems remain NP-hard when restricted to contractible pure d-dimensional complexes.

BibTeX - Entry

@InProceedings{goaoc_et_al:LIPIcs:2018:8754,
  author =	{Xavier Goaoc and Pavel Pat{\'a}k and Zuzana Pat{\'a}kov{\'a} and Martin Tancer and Uli Wagner},
  title =	{{Shellability is NP-Complete}},
  booktitle =	{34th International Symposium on Computational Geometry (SoCG 2018)},
  pages =	{41:1--41:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-066-8},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{99},
  editor =	{Bettina Speckmann and Csaba D. T{\'o}th},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2018/8754},
  URN =		{urn:nbn:de:0030-drops-87542},
  doi =		{10.4230/LIPIcs.SoCG.2018.41},
  annote =	{Keywords: Shellability, simplicial complexes, NP-completeness, collapsibility}
}

Keywords: Shellability, simplicial complexes, NP-completeness, collapsibility
Seminar: 34th International Symposium on Computational Geometry (SoCG 2018)
Issue date: 2018
Date of publication: 2018


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