h-graphs : a new representation for tree decompositions of graphs

In geometric constraint solving, 2D well constrained geometric problems can be abstracted as Laman graphs. If the graph is tree decomposable, the constraint-based geometric problem can be solved by a Decomposition-Recombination planner based solver. In general decomposition and recombination steps c...

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Detalles Bibliográficos
Autores: Hidalgo Garcia, Marta, Joan Arinyo, Robert|||0000-0002-1896-2940
Tipo de recurso: artículo
Fecha de publicación:2015
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:2117/78683
Acceso en línea:https://hdl.handle.net/2117/78683
https://dx.doi.org/10.1016/j.cad.2015.05.003
Access Level:acceso abierto
Palabra clave:Trees (Graph Theory)
Computational geometry
Constraint programming (Computer science)
Parametric solid modeling
Geometric constraint solving
Constraint graphs
Tree-decompositions
Construction steps dependencies
Parameter ranges
GEOMETRIC CONSTRAINT SYSTEMS
PARAMETER RANGES
PLANS
CAD
Arbres (Grafs, Teoria de)
Geometria computacional
Programació per restriccions (Informàtica)
Àrees temàtiques de la UPC::Informàtica
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spelling h-graphs : a new representation for tree decompositions of graphsHidalgo Garcia, MartaJoan Arinyo, Robert|||0000-0002-1896-2940Trees (Graph Theory)Computational geometryConstraint programming (Computer science)Parametric solid modelingGeometric constraint solvingConstraint graphsTree-decompositionsConstruction steps dependenciesParameter rangesGEOMETRIC CONSTRAINT SYSTEMSPARAMETER RANGESPLANSCADArbres (Grafs, Teoria de)Geometria computacionalProgramació per restriccions (Informàtica)Àrees temàtiques de la UPC::InformàticaIn geometric constraint solving, 2D well constrained geometric problems can be abstracted as Laman graphs. If the graph is tree decomposable, the constraint-based geometric problem can be solved by a Decomposition-Recombination planner based solver. In general decomposition and recombination steps can be completed only when steps on which they are dependent have already been completed. This fact naturally defines a hierarchy in the decomposition-recombination steps that traditional tree decomposition representations do not capture explicitly.; In this work we introduce h-graphs, a new representation for decompositions of tree decomposable Laman graphs, which captures dependence relations between different tree decomposition steps. We show how h-graphs help in efficiently computing parameter ranges for which solution instances to well constrained, tree decomposable geometric constraint problems with one degree of freedom can actually be constructed. (C) 2015 Elsevier Ltd. All rights reserved.20152015-10-0120152015-11-02journal articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/2117/78683https://dx.doi.org/10.1016/j.cad.2015.05.003reponame:UPCommons. Portal del coneixement obert de la UPCinstname:Universitat Politècnica de Catalunya (UPC)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2http://creativecommons.org/licenses/by-nc-nd/3.0/es/info:eu-repo/semantics/openAccessoai:upcommons.upc.edu:2117/786832026-05-27T15:37:01Z
dc.title.none.fl_str_mv h-graphs : a new representation for tree decompositions of graphs
title h-graphs : a new representation for tree decompositions of graphs
spellingShingle h-graphs : a new representation for tree decompositions of graphs
Hidalgo Garcia, Marta
Trees (Graph Theory)
Computational geometry
Constraint programming (Computer science)
Parametric solid modeling
Geometric constraint solving
Constraint graphs
Tree-decompositions
Construction steps dependencies
Parameter ranges
GEOMETRIC CONSTRAINT SYSTEMS
PARAMETER RANGES
PLANS
CAD
Arbres (Grafs, Teoria de)
Geometria computacional
Programació per restriccions (Informàtica)
Àrees temàtiques de la UPC::Informàtica
title_short h-graphs : a new representation for tree decompositions of graphs
title_full h-graphs : a new representation for tree decompositions of graphs
title_fullStr h-graphs : a new representation for tree decompositions of graphs
title_full_unstemmed h-graphs : a new representation for tree decompositions of graphs
title_sort h-graphs : a new representation for tree decompositions of graphs
dc.creator.none.fl_str_mv Hidalgo Garcia, Marta
Joan Arinyo, Robert|||0000-0002-1896-2940
author Hidalgo Garcia, Marta
author_facet Hidalgo Garcia, Marta
Joan Arinyo, Robert|||0000-0002-1896-2940
author_role author
author2 Joan Arinyo, Robert|||0000-0002-1896-2940
author2_role author
dc.subject.none.fl_str_mv Trees (Graph Theory)
Computational geometry
Constraint programming (Computer science)
Parametric solid modeling
Geometric constraint solving
Constraint graphs
Tree-decompositions
Construction steps dependencies
Parameter ranges
GEOMETRIC CONSTRAINT SYSTEMS
PARAMETER RANGES
PLANS
CAD
Arbres (Grafs, Teoria de)
Geometria computacional
Programació per restriccions (Informàtica)
Àrees temàtiques de la UPC::Informàtica
topic Trees (Graph Theory)
Computational geometry
Constraint programming (Computer science)
Parametric solid modeling
Geometric constraint solving
Constraint graphs
Tree-decompositions
Construction steps dependencies
Parameter ranges
GEOMETRIC CONSTRAINT SYSTEMS
PARAMETER RANGES
PLANS
CAD
Arbres (Grafs, Teoria de)
Geometria computacional
Programació per restriccions (Informàtica)
Àrees temàtiques de la UPC::Informàtica
description In geometric constraint solving, 2D well constrained geometric problems can be abstracted as Laman graphs. If the graph is tree decomposable, the constraint-based geometric problem can be solved by a Decomposition-Recombination planner based solver. In general decomposition and recombination steps can be completed only when steps on which they are dependent have already been completed. This fact naturally defines a hierarchy in the decomposition-recombination steps that traditional tree decomposition representations do not capture explicitly.; In this work we introduce h-graphs, a new representation for decompositions of tree decomposable Laman graphs, which captures dependence relations between different tree decomposition steps. We show how h-graphs help in efficiently computing parameter ranges for which solution instances to well constrained, tree decomposable geometric constraint problems with one degree of freedom can actually be constructed. (C) 2015 Elsevier Ltd. All rights reserved.
publishDate 2015
dc.date.none.fl_str_mv 2015
2015-10-01
2015
2015-11-02
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
VoR
http://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/2117/78683
https://dx.doi.org/10.1016/j.cad.2015.05.003
url https://hdl.handle.net/2117/78683
https://dx.doi.org/10.1016/j.cad.2015.05.003
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

http://creativecommons.org/licenses/by-nc-nd/3.0/es/
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

http://creativecommons.org/licenses/by-nc-nd/3.0/es/
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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