Decomposition of geometric constraint graphs based on computing fundamental circuits. Correctness and complexity
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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.
CitationJoan-Arinyo, R.; Tarres, M.; Vila, S. Decomposition of geometric constraint graphs based on computing fundamental circuits. Correctness and complexity. "Computer Aided Design", 01 Juliol 2014, vol. 52, p. 1-16.