Basic principles of mechanical theorem proving in elementary geometrics
Journal of Automated Reasoning
Enhancement schemes for constraint processing: backjumping, learning, and cutset decomposition
Artificial Intelligence
Using Graph Decomposition for Solving Continuous CSPs
CP '98 Proceedings of the 4th International Conference on Principles and Practice of Constraint Programming
A Constraint Programming Approach for Solving Rigid Geometric Systems
CP '02 Proceedings of the 6th International Conference on Principles and Practice of Constraint Programming
An Application of Automatic Theorem Proving in Computer Vision
ADG '98 Proceedings of the Second International Workshop on Automated Deduction in Geometry
Symbolic and numerical techniques for constraint solving
Symbolic and numerical techniques for constraint solving
Scene Modeling Based on Constraint System Decomposition Techniques
ICCV '03 Proceedings of the Ninth IEEE International Conference on Computer Vision - Volume 2
Consistency techniques for numeric CSPs
IJCAI'93 Proceedings of the 13th international joint conference on Artifical intelligence - Volume 1
Filtering numerical CSPs using well-constrained subsystems
CP'09 Proceedings of the 15th international conference on Principles and practice of constraint programming
When interval analysis helps inter-block backtracking
CP'06 Proceedings of the 12th international conference on Principles and Practice of Constraint Programming
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This paper details a technique, called inter-block backtracking (IBB), which improves interval solving of decomposed systems with non-linear equations over the reals. This technique, introduced in 1998 by Bliek et al., handles a system of equations previously decomposed into a set of (small) k × k sub-systems, called blocks. All solutions are obtained by combining the solutions computed in the different blocks. The approach seems particularly suitable for improving interval solving techniques. In this paper, we analyze into detail the different variants of IBB which differ in their backtracking and filtering strategies. We also introduce IBB-GBJ, a new variant based on Dechter's graph-based backjumping. An extensive comparison on a sample of eight CSPs allows us to better understand the behavior of IBB. It shows that the variants IBB-BT+ and IBB-GBJ are good compromises between simplicity and performance. Moreover, it clearly shows that limiting the scope of the filtering to the blocks is very useful. For all the tested instances, IBB gains several orders of magnitude as compared to a global solving.