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...
| Autores: | , |
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| 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 |
| 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. |
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