Linear orderings of random geometric graphs (extended abstract)

In random geometric graphs, vertices are randomly distributed on [0,1]^2 and pairs of vertices are connected by edges whenever they are sufficiently close together. Layout problems seek a linear ordering of the vertices of a graph such that a certain measure is minimized. In this paper, we study sev...

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Detalhes bibliográficos
Autores: Díaz Cort, Josep|||0000-0003-4422-0067, Penrose, Matthew, Petit Silvestre, Jordi|||0000-0001-8331-8126, Serna Iglesias, María José|||0000-0001-9729-8648
Formato: informe técnico
Fecha de publicación:1999
País:España
Recursos:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2117/93009
Acesso em linha:https://hdl.handle.net/2117/93009
Access Level:acceso abierto
Palavra-chave:Random geometric graphs
Layout problems
Àrees temàtiques de la UPC::Informàtica::Informàtica teòrica
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oai_identifier_str oai:upcommons.upc.edu:2117/93009
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repository_id_str
spelling Linear orderings of random geometric graphs (extended abstract)Díaz Cort, Josep|||0000-0003-4422-0067Penrose, MatthewPetit Silvestre, Jordi|||0000-0001-8331-8126Serna Iglesias, María José|||0000-0001-9729-8648Random geometric graphsLayout problemsÀrees temàtiques de la UPC::Informàtica::Informàtica teòricaIn random geometric graphs, vertices are randomly distributed on [0,1]^2 and pairs of vertices are connected by edges whenever they are sufficiently close together. Layout problems seek a linear ordering of the vertices of a graph such that a certain measure is minimized. In this paper, we study several layout problems on random geometric graphs: Bandwidth, Minimum Linear Arrangement, Minimum Cut, Minimum Sum Cut, Vertex Separation and Bisection. We first prove that some of these problems remain \NP-complete even for geometric graphs. Afterwards, we compute lower bounds that hold with high probability on random geometric graphs. Finally, we characterize the probabilistic behavior of the lexicographic ordering for our layout problems on the class of random geometric graphs.19991999-04-0120162016-11-07reporthttp://purl.org/coar/resource_type/c_93fcVoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/reportapplication/pdfhttps://hdl.handle.net/2117/93009reponame: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:2117/930092026-05-27T15:37:01Z
dc.title.none.fl_str_mv Linear orderings of random geometric graphs (extended abstract)
title Linear orderings of random geometric graphs (extended abstract)
spellingShingle Linear orderings of random geometric graphs (extended abstract)
Díaz Cort, Josep|||0000-0003-4422-0067
Random geometric graphs
Layout problems
Àrees temàtiques de la UPC::Informàtica::Informàtica teòrica
title_short Linear orderings of random geometric graphs (extended abstract)
title_full Linear orderings of random geometric graphs (extended abstract)
title_fullStr Linear orderings of random geometric graphs (extended abstract)
title_full_unstemmed Linear orderings of random geometric graphs (extended abstract)
title_sort Linear orderings of random geometric graphs (extended abstract)
dc.creator.none.fl_str_mv Díaz Cort, Josep|||0000-0003-4422-0067
Penrose, Matthew
Petit Silvestre, Jordi|||0000-0001-8331-8126
Serna Iglesias, María José|||0000-0001-9729-8648
author Díaz Cort, Josep|||0000-0003-4422-0067
author_facet Díaz Cort, Josep|||0000-0003-4422-0067
Penrose, Matthew
Petit Silvestre, Jordi|||0000-0001-8331-8126
Serna Iglesias, María José|||0000-0001-9729-8648
author_role author
author2 Penrose, Matthew
Petit Silvestre, Jordi|||0000-0001-8331-8126
Serna Iglesias, María José|||0000-0001-9729-8648
author2_role author
author
author
dc.subject.none.fl_str_mv Random geometric graphs
Layout problems
Àrees temàtiques de la UPC::Informàtica::Informàtica teòrica
topic Random geometric graphs
Layout problems
Àrees temàtiques de la UPC::Informàtica::Informàtica teòrica
description In random geometric graphs, vertices are randomly distributed on [0,1]^2 and pairs of vertices are connected by edges whenever they are sufficiently close together. Layout problems seek a linear ordering of the vertices of a graph such that a certain measure is minimized. In this paper, we study several layout problems on random geometric graphs: Bandwidth, Minimum Linear Arrangement, Minimum Cut, Minimum Sum Cut, Vertex Separation and Bisection. We first prove that some of these problems remain \NP-complete even for geometric graphs. Afterwards, we compute lower bounds that hold with high probability on random geometric graphs. Finally, we characterize the probabilistic behavior of the lexicographic ordering for our layout problems on the class of random geometric graphs.
publishDate 1999
dc.date.none.fl_str_mv 1999
1999-04-01
2016
2016-11-07
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/2117/93009
url https://hdl.handle.net/2117/93009
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/pdf
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
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score 15,300719

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