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
Descrição
Resumo: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.