Title:
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Decomposition of geometric constraint graphs based on computing fundamental circuits. Correctness and complexity
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Author:
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Joan Arinyo, Robert; Tarres Puertas, Marta Isabel; Vila Marta, Sebastià
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Other authors:
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Universitat Politècnica de Catalunya. Departament de Ciències de la Computació; Universitat Politècnica de Catalunya. Departament de Disseny i Programació de Sistemes Electrònics; Universitat Politècnica de Catalunya. GIE - Grup d'Informàtica a l'Enginyeria |
Abstract:
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In geometric constraint solving, Decomposition Recombination solvers (DR-solvers) refer to a general solving approach where the problem is divided into a set of sub-problems, each sub-problem is recursively divided until reaching basic problems which are solved by a dedicated equational solver. Then the solution to the starting problem is computed by merging the solutions to the sub-problems.; Triangle- or tree-decomposition is one of the most widely used approaches in the decomposition step in DR-solvers. It may be seen as decomposing a graph into three subgraphs such that subgraphs pairwise share one graph vertex. Shared vertices are called hinges. Then a merging step places the geometry in each sub-problem with respect to the other two.; In this work we report on a new algorithm to decompose biconnected geometric constraint graphs by searching for hinges in fundamental circuits of a specific planar embedding of the constraint graph. We prove that the algorithm is correct. (C) 2014 Elsevier Ltd. All rights reserved. |
Subject(s):
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-Àrees temàtiques de la UPC::Matemàtiques i estadística::Geometria::Geometria computacional -Computational geometry -Geometric constraint solving -Graph decomposition -Fundamental circuits -Bridges -Planar embeddings -CONSTRUCTIVE APPROACH -SYSTEMS -SOLVER -ALGORITHM -DESIGN -PLANS -Geometria computacional |
Rights:
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Document type:
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Article - Published version Article |
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