Graphs & digraphs (2nd ed.)
A k-tree generalization that characterized consistency of dimensioned engineering drawings
SIAM Journal on Discrete Mathematics
Algebraic solution for geometry from dimensional constraints
SMA '91 Proceedings of the first ACM symposium on Solid modeling foundations and CAD/CAM applications
The deductive foundations of computer programming: a one-volume version of “the logical basis for computer programming”
A graph-constructive approach to solving systems of geometric constraints
ACM Transactions on Graphics (TOG)
Combining constructive and equational geometric constraint-solving techniques
ACM Transactions on Graphics (TOG)
The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
On the Domain of Constructive Geometric Constraint Solving Techniques
SCCG '01 Proceedings of the 17th Spring conference on Computer graphics
Constraint solving for computer-aided design
Constraint solving for computer-aided design
Symbolic and numerical techniques for constraint solving
Symbolic and numerical techniques for constraint solving
Transforming an under-constrained geometric constraint problem into a well-constrained one
SM '03 Proceedings of the eighth ACM symposium on Solid modeling and applications
Geometric constraint solving via C-tree decomposition
SM '03 Proceedings of the eighth ACM symposium on Solid modeling and applications
Spatial geometric constraint solving based on k-connected graph decomposition
Proceedings of the 2006 ACM symposium on Applied computing
Geometric constraint solving: The witness configuration method
Computer-Aided Design
Proceedings of the 2011 ACM Symposium on Applied Computing
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Geometric problems defined by constraints can be represented by geometric constraint graphs whose nodes are geometric elements and whose arcs represent geometric constraints. Reduction and decomposition are techniques commonly used to analyze geometric constraint graphs in geometric constraint solving. In this paper we first introduce the concept of deficit of a constraint graph. Then we give a new formalization of the decomposition algorithm due to Owen. This new formalization is based on preserving the deficit rather than on computing triconnected components of the graph and is simpler. Finally we apply tree decompositions to prove that the class of problems solved by the formalizations studied here and other formalizations reported in the literature is the same.