New upper bounds on the decomposability of planar graphs and fixed parameter algorithms

It is known that a planar graph on n vertices has branch-width/tree-width bounded by alphasqrt{n}. In many algorithmic applications it is useful to have a small bound on the constant alpha. We give a proof of the best, so far, upper bound for the constant alpha. In particular, for the case of tree-w...

Descripción completa

Detalles Bibliográficos
Autores: Fomin, Fedor V., Thilikos Touloupas, Dimitrios
Tipo de recurso: informe técnico
Fecha de publicación:2002
País:España
Institución:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2117/97430
Acceso en línea:https://hdl.handle.net/2117/97430
Access Level:acceso abierto
Palabra clave:Planar graphs
Decomposability
Fixed parameter algorithms
Tree-width
Branch-width
Separation theorems
Vertex cover
Dominating set
Àrees temàtiques de la UPC::Informàtica
id ES_57ef8fb27bd1dfd67286b2a0d2eb3abf
oai_identifier_str oai:upcommons.upc.edu:2117/97430
network_acronym_str ES
network_name_str España
repository_id_str
spelling New upper bounds on the decomposability of planar graphs and fixed parameter algorithmsFomin, Fedor V.Thilikos Touloupas, DimitriosPlanar graphsDecomposabilityFixed parameter algorithmsTree-widthBranch-widthSeparation theoremsVertex coverDominating setÀrees temàtiques de la UPC::InformàticaIt is known that a planar graph on n vertices has branch-width/tree-width bounded by alphasqrt{n}. In many algorithmic applications it is useful to have a small bound on the constant alpha. We give a proof of the best, so far, upper bound for the constant alpha. In particular, for the case of tree-width, alpha<3.182 and for the case of branch-width, alpha<2.122. Our proof is based on the planar separation theorem of Alon, Seymour & Thomas and some min-max theorem of the graph minors series. Based on these bounds we introduce a new method for solving different fixed parameter problems on planar graphs. We prove that our method provides the best so far exponential speed-up for fundamental problems on planar graphs like Vertex Cover, Dominating Set, Independent Set and many others.20022002-08-0120162016-11-29reporthttp://purl.org/coar/resource_type/c_93fcVoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/reportapplication/postscripthttps://hdl.handle.net/2117/97430reponame:UPCommons. Portal del coneixement obert de la UPCinstname:Universitat Politècnica de Catalunya (UPC)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2info:eu-repo/semantics/openAccessoai:upcommons.upc.edu:2117/974302026-05-27T15:37:01Z
dc.title.none.fl_str_mv New upper bounds on the decomposability of planar graphs and fixed parameter algorithms
title New upper bounds on the decomposability of planar graphs and fixed parameter algorithms
spellingShingle New upper bounds on the decomposability of planar graphs and fixed parameter algorithms
Fomin, Fedor V.
Planar graphs
Decomposability
Fixed parameter algorithms
Tree-width
Branch-width
Separation theorems
Vertex cover
Dominating set
Àrees temàtiques de la UPC::Informàtica
title_short New upper bounds on the decomposability of planar graphs and fixed parameter algorithms
title_full New upper bounds on the decomposability of planar graphs and fixed parameter algorithms
title_fullStr New upper bounds on the decomposability of planar graphs and fixed parameter algorithms
title_full_unstemmed New upper bounds on the decomposability of planar graphs and fixed parameter algorithms
title_sort New upper bounds on the decomposability of planar graphs and fixed parameter algorithms
dc.creator.none.fl_str_mv Fomin, Fedor V.
Thilikos Touloupas, Dimitrios
author Fomin, Fedor V.
author_facet Fomin, Fedor V.
Thilikos Touloupas, Dimitrios
author_role author
author2 Thilikos Touloupas, Dimitrios
author2_role author
dc.subject.none.fl_str_mv Planar graphs
Decomposability
Fixed parameter algorithms
Tree-width
Branch-width
Separation theorems
Vertex cover
Dominating set
Àrees temàtiques de la UPC::Informàtica
topic Planar graphs
Decomposability
Fixed parameter algorithms
Tree-width
Branch-width
Separation theorems
Vertex cover
Dominating set
Àrees temàtiques de la UPC::Informàtica
description It is known that a planar graph on n vertices has branch-width/tree-width bounded by alphasqrt{n}. In many algorithmic applications it is useful to have a small bound on the constant alpha. We give a proof of the best, so far, upper bound for the constant alpha. In particular, for the case of tree-width, alpha<3.182 and for the case of branch-width, alpha<2.122. Our proof is based on the planar separation theorem of Alon, Seymour & Thomas and some min-max theorem of the graph minors series. Based on these bounds we introduce a new method for solving different fixed parameter problems on planar graphs. We prove that our method provides the best so far exponential speed-up for fundamental problems on planar graphs like Vertex Cover, Dominating Set, Independent Set and many others.
publishDate 2002
dc.date.none.fl_str_mv 2002
2002-08-01
2016
2016-11-29
dc.type.none.fl_str_mv report
http://purl.org/coar/resource_type/c_93fc
VoR
http://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.openaire.fl_str_mv info:eu-repo/semantics/report
format report
dc.identifier.none.fl_str_mv https://hdl.handle.net/2117/97430
url https://hdl.handle.net/2117/97430
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/postscript
dc.source.none.fl_str_mv reponame:UPCommons. Portal del coneixement obert de la UPC
instname:Universitat Politècnica de Catalunya (UPC)
instname_str Universitat Politècnica de Catalunya (UPC)
reponame_str UPCommons. Portal del coneixement obert de la UPC
collection UPCommons. Portal del coneixement obert de la UPC
repository.name.fl_str_mv
repository.mail.fl_str_mv
_version_ 1869408488047771648
score 15,300724

Similares en LA Referencia