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dc.creatorGonzález Lorenzo, Aldoes
dc.creatorBac, Alexandraes
dc.creatorMari, Jean-Luces
dc.creatorReal Jurado, Pedroes
dc.date.accessioned2021-09-16T08:03:57Z
dc.date.available2021-09-16T08:03:57Z
dc.date.issued2017
dc.identifier.citationGonzález Lorenzo, A., Bac, A., Mari, J. y Real Jurado, P. (2017). Allowing cycles in discrete Morse theory. Topology and its Applications, 228 (September 2017), 1-35.
dc.identifier.issn0166-8641es
dc.identifier.urihttps://hdl.handle.net/11441/125876
dc.description.abstractDiscrete gradient vector fields are combinatorial structures that can be used for accelerating the homology computation of CW complexes, such as simplicial or cubical complexes, by reducing their number of cells. Consequently, they provide a bound for the Betti numbers (the most basic homological information). A discrete gradient vector field can eventually reduce the complex to its minimal form, having as many cells of each dimension as its corresponding Betti number, but this is not guaranteed. Moreover, finding an optimal discrete gradient vector field is an NP-hard problem. We describe here a generalization, which we call Homological Discrete Vector Field (HDVF), which can overcome these limitations by allowing cycles under a certain algebraic condition. In this work we define the HDVF and its associated reduction, we study how to efficiently compute a HDVF, we establish the relation between the HDVF and other concepts in computational homology and we estimate the average complexity of its computation. We also introduce five basic operations for modifying a HDVF, which can also be applied to discrete gradient vector fields.es
dc.formatapplication/pdfes
dc.format.extent35es
dc.language.isoenges
dc.publisherElsevieres
dc.relation.ispartofTopology and its Applications, 228 (September 2017), 1-35.
dc.rightsAttribution-NonCommercial-NoDerivatives 4.0 Internacional*
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/4.0/*
dc.subjectComputational topologyes
dc.subjectHomologyes
dc.subjectCW complexes
dc.subjectDiscrete Morse theoryes
dc.subjectHomological discrete vector fieldes
dc.titleAllowing cycles in discrete Morse theoryes
dc.typeinfo:eu-repo/semantics/articlees
dcterms.identifierhttps://ror.org/03yxnpp24
dc.type.versioninfo:eu-repo/semantics/publishedVersiones
dc.rights.accessRightsinfo:eu-repo/semantics/openAccesses
dc.contributor.affiliationUniversidad de Sevilla. Departamento de Matemática Aplicada I (ETSII)es
dc.relation.publisherversion0166-8641es
dc.identifier.doi10.1016/j.topol.2017.05.008es
dc.journaltitleTopology and its Applicationses
dc.publication.volumen228es
dc.publication.issueSeptember 2017es
dc.publication.initialPage1es
dc.publication.endPage35es
dc.identifier.sisius21237022es

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