Computational aspects of the Helly property: a survey

Detalhes bibliográficos
Autor(a) principal: Dourado,Mitre C.
Data de Publicação: 2006
Outros Autores: Protti,Fabio, Szwarcfiter,Jayme L.
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Journal of the Brazilian Computer Society
Texto Completo: http://old.scielo.br/scielo.php?script=sci_arttext&pid=S0104-65002006000200002
Resumo: In 1923, Eduard Helly published his celebrated theorem, which originated the well known Helly property. Say that a family of subsets has the Helly property when every subfamily of it, formed by pairwise intersecting subsets, contains a common element. There are many generalizations of this property which are relevant to some parts of mathematics and several applications in computer science. In this work, we survey computational aspects of the Helly property. The main focus is algorithmic. That is, we describe algorithms for solving different problems arising from the basic Helly property. We also discuss the complexity of these problems, some of them leading to NP-hardness results.
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spelling Computational aspects of the Helly property: a surveyComputational ComplexityHelly propertyNP-complete problemsIn 1923, Eduard Helly published his celebrated theorem, which originated the well known Helly property. Say that a family of subsets has the Helly property when every subfamily of it, formed by pairwise intersecting subsets, contains a common element. There are many generalizations of this property which are relevant to some parts of mathematics and several applications in computer science. In this work, we survey computational aspects of the Helly property. The main focus is algorithmic. That is, we describe algorithms for solving different problems arising from the basic Helly property. We also discuss the complexity of these problems, some of them leading to NP-hardness results.Sociedade Brasileira de Computação2006-06-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersiontext/htmlhttp://old.scielo.br/scielo.php?script=sci_arttext&pid=S0104-65002006000200002Journal of the Brazilian Computer Society v.12 n.1 2006reponame:Journal of the Brazilian Computer Societyinstname:Sociedade Brasileira de Computação (SBC)instacron:UFRGS10.1007/BF03192384info:eu-repo/semantics/openAccessDourado,Mitre C.Protti,FabioSzwarcfiter,Jayme L.eng2010-05-24T00:00:00Zoai:scielo:S0104-65002006000200002Revistahttps://journal-bcs.springeropen.com/PUBhttps://old.scielo.br/oai/scielo-oai.phpjbcs@icmc.sc.usp.br1678-48040104-6500opendoar:2010-05-24T00:00Journal of the Brazilian Computer Society - Sociedade Brasileira de Computação (SBC)false
dc.title.none.fl_str_mv Computational aspects of the Helly property: a survey
title Computational aspects of the Helly property: a survey
spellingShingle Computational aspects of the Helly property: a survey
Dourado,Mitre C.
Computational Complexity
Helly property
NP-complete problems
title_short Computational aspects of the Helly property: a survey
title_full Computational aspects of the Helly property: a survey
title_fullStr Computational aspects of the Helly property: a survey
title_full_unstemmed Computational aspects of the Helly property: a survey
title_sort Computational aspects of the Helly property: a survey
author Dourado,Mitre C.
author_facet Dourado,Mitre C.
Protti,Fabio
Szwarcfiter,Jayme L.
author_role author
author2 Protti,Fabio
Szwarcfiter,Jayme L.
author2_role author
author
dc.contributor.author.fl_str_mv Dourado,Mitre C.
Protti,Fabio
Szwarcfiter,Jayme L.
dc.subject.por.fl_str_mv Computational Complexity
Helly property
NP-complete problems
topic Computational Complexity
Helly property
NP-complete problems
description In 1923, Eduard Helly published his celebrated theorem, which originated the well known Helly property. Say that a family of subsets has the Helly property when every subfamily of it, formed by pairwise intersecting subsets, contains a common element. There are many generalizations of this property which are relevant to some parts of mathematics and several applications in computer science. In this work, we survey computational aspects of the Helly property. The main focus is algorithmic. That is, we describe algorithms for solving different problems arising from the basic Helly property. We also discuss the complexity of these problems, some of them leading to NP-hardness results.
publishDate 2006
dc.date.none.fl_str_mv 2006-06-01
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
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status_str publishedVersion
dc.identifier.uri.fl_str_mv http://old.scielo.br/scielo.php?script=sci_arttext&pid=S0104-65002006000200002
url http://old.scielo.br/scielo.php?script=sci_arttext&pid=S0104-65002006000200002
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 10.1007/BF03192384
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv text/html
dc.publisher.none.fl_str_mv Sociedade Brasileira de Computação
publisher.none.fl_str_mv Sociedade Brasileira de Computação
dc.source.none.fl_str_mv Journal of the Brazilian Computer Society v.12 n.1 2006
reponame:Journal of the Brazilian Computer Society
instname:Sociedade Brasileira de Computação (SBC)
instacron:UFRGS
instname_str Sociedade Brasileira de Computação (SBC)
instacron_str UFRGS
institution UFRGS
reponame_str Journal of the Brazilian Computer Society
collection Journal of the Brazilian Computer Society
repository.name.fl_str_mv Journal of the Brazilian Computer Society - Sociedade Brasileira de Computação (SBC)
repository.mail.fl_str_mv jbcs@icmc.sc.usp.br
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