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

In geometric constraint solving, 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...

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Detalles Bibliográficos
Autores: Hidalgo Garcia, Marta, Joan Arinyo, Robert|||0000-0002-1896-2940
Tipo de recurso: informe técnico
Fecha de publicación:2014
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:2117/99483
Acceso en línea:https://hdl.handle.net/2117/99483
Access Level:acceso abierto
Palabra clave:Parametric solid modeling
Geometric constraint solving
Constraint graphs
Tree-decompositions
Construction steps dependencies
Parameter ranges
Àrees temàtiques de la UPC::Informàtica::Infografia
Descripción
Sumario:In geometric constraint solving, 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 other steps 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.