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.SoCG.2018.41
URN: urn:nbn:de:0030-drops-87542
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2018/8754/
Goaoc, Xavier ;
Paták, Pavel ;
Patáková, Zuzana ;
Tancer, Martin ;
Wagner, Uli
Shellability is NP-Complete
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}
}
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Keywords: |
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Shellability, simplicial complexes, NP-completeness, collapsibility |
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Collection: |
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34th International Symposium on Computational Geometry (SoCG 2018) |
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Issue Date: |
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2018 |
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Date of publication: |
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08.06.2018 |
