Complexity and algorithms for Euler characteristic of simplicial complexes

We consider the problem of computing the Euler characteristic of an abstract simplicial complex given by its vertices and facets. We show that this problem is #P-complete and present two new practical algorithms for computing Euler characteristic. The two new algorithms are derived using combinatori...

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Detalhes bibliográficos
Autores: Roune, B.H., Sáenz-de-Cabezón, E. [0000-0002-5615-4194]
Formato: artículo
Estado:Versión publicada
Fecha de publicación:2013
País:España
Recursos:Universidad de La Rioja (UR)
Repositorio:RIUR. Repositorio Institucional de la Universidad de La Rioja
OAI Identifier:oai:portal.dialnet.es:doc/5bbc68b0b750603269e80daa
Acesso em linha:https://investigacion.unirioja.es/documentos/5bbc68b0b750603269e80daa
Access Level:acceso abierto
Palavra-chave:#P-complete
Algorithms
Computational complexity
Euler characteristic
Monomial ideal
Simplicial complex
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spelling Complexity and algorithms for Euler characteristic of simplicial complexesRoune, B.H.Sáenz-de-Cabezón, E. [0000-0002-5615-4194]#P-completeAlgorithmsComputational complexityEuler characteristicMonomial idealSimplicial complexWe consider the problem of computing the Euler characteristic of an abstract simplicial complex given by its vertices and facets. We show that this problem is #P-complete and present two new practical algorithms for computing Euler characteristic. The two new algorithms are derived using combinatorial commutative algebra and we also give a second description of them that requires no algebra. We present experiments showing that the two new algorithms can be implemented to be faster than previous Euler characteristic implementations by a large margin. © 2012 Elsevier B.V.2013info:eu-repo/semantics/articleSubtype: Articleinfo:eu-repo/semantics/publishedVersionapplication/pdfhttps://investigacion.unirioja.es/documentos/5bbc68b0b750603269e80daareponame:RIUR. Repositorio Institucional de la Universidad de La Riojainstname:Universidad de La Rioja (UR)Inglésinfo:eu-repo/semantics/altIdentifier/doi/10.1016/J.JSC.2012.07.003info:eu-repo/semantics/altIdentifier/wos/WOS:000312574000009info:eu-repo/semantics/altIdentifier/pissn/0747-7171Complexity and algorithms for Euler characteristic of simplicial complexes, 2013, vol. 50, pág. 170-196info:eu-repo/semantics/openAccessoai:portal.dialnet.es:doc/5bbc68b0b750603269e80daa2026-06-14T12:47:17Z
dc.title.none.fl_str_mv Complexity and algorithms for Euler characteristic of simplicial complexes
title Complexity and algorithms for Euler characteristic of simplicial complexes
spellingShingle Complexity and algorithms for Euler characteristic of simplicial complexes
Roune, B.H.
#P-complete
Algorithms
Computational complexity
Euler characteristic
Monomial ideal
Simplicial complex
title_short Complexity and algorithms for Euler characteristic of simplicial complexes
title_full Complexity and algorithms for Euler characteristic of simplicial complexes
title_fullStr Complexity and algorithms for Euler characteristic of simplicial complexes
title_full_unstemmed Complexity and algorithms for Euler characteristic of simplicial complexes
title_sort Complexity and algorithms for Euler characteristic of simplicial complexes
dc.creator.none.fl_str_mv Roune, B.H.
Sáenz-de-Cabezón, E. [0000-0002-5615-4194]
author Roune, B.H.
author_facet Roune, B.H.
Sáenz-de-Cabezón, E. [0000-0002-5615-4194]
author_role author
author2 Sáenz-de-Cabezón, E. [0000-0002-5615-4194]
author2_role author
dc.subject.none.fl_str_mv #P-complete
Algorithms
Computational complexity
Euler characteristic
Monomial ideal
Simplicial complex
topic #P-complete
Algorithms
Computational complexity
Euler characteristic
Monomial ideal
Simplicial complex
description We consider the problem of computing the Euler characteristic of an abstract simplicial complex given by its vertices and facets. We show that this problem is #P-complete and present two new practical algorithms for computing Euler characteristic. The two new algorithms are derived using combinatorial commutative algebra and we also give a second description of them that requires no algebra. We present experiments showing that the two new algorithms can be implemented to be faster than previous Euler characteristic implementations by a large margin. © 2012 Elsevier B.V.
publishDate 2013
dc.date.none.fl_str_mv 2013
dc.type.none.fl_str_mv info:eu-repo/semantics/article
Subtype: Article
info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv https://investigacion.unirioja.es/documentos/5bbc68b0b750603269e80daa
url https://investigacion.unirioja.es/documentos/5bbc68b0b750603269e80daa
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1016/J.JSC.2012.07.003
info:eu-repo/semantics/altIdentifier/wos/WOS:000312574000009
info:eu-repo/semantics/altIdentifier/pissn/0747-7171
Complexity and algorithms for Euler characteristic of simplicial complexes, 2013, vol. 50, pág. 170-196
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:RIUR. Repositorio Institucional de la Universidad de La Rioja
instname:Universidad de La Rioja (UR)
instname_str Universidad de La Rioja (UR)
reponame_str RIUR. Repositorio Institucional de la Universidad de La Rioja
collection RIUR. Repositorio Institucional de la Universidad de La Rioja
repository.name.fl_str_mv
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