Enhancement schemes for constraint processing: backjumping, learning, and cutset decomposition
Artificial Intelligence
Revising hull and box consistency
Proceedings of the 1999 international conference on Logic programming
Scene Modeling Based on Constraint System Decomposition Techniques
ICCV '03 Proceedings of the Ninth IEEE International Conference on Computer Vision - Volume 2
Efficient and Safe Global Constraints for Handling Numerical Constraint Systems
SIAM Journal on Numerical Analysis
Algorithm 852: RealPaver: an interval solver using constraint satisfaction techniques
ACM Transactions on Mathematical Software (TOMS)
Artificial Intelligence
Consistency techniques for numeric CSPs
IJCAI'93 Proceedings of the 13th international joint conference on Artifical intelligence - Volume 1
Algorithms for identifying rigid subsystems in geometric constraint systems
IJCAI'03 Proceedings of the 18th international joint conference on Artificial intelligence
Constructive interval disjunction
CP'07 Proceedings of the 13th international conference on Principles and practice of constraint programming
Inter-block backtracking: exploiting the structure in continuous CSPs
COCOS'03 Proceedings of the Second international conference on Global Optimization and Constraint Satisfaction
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Inter-block backtracking (IBB) computes all the solutions of sparse systems of nonlinear equations over the reals. This algorithm, introduced by Bliek et al. (1998) handles a system of equations previously decomposed into a set of (small) k 脳k sub-systems, called blocks. Partial solutions are computed in the different blocks in a certain order and combined together to obtain the set of global solutions. When solutions inside blocks are computed with interval-based techniques, IBB can be viewed as a new interval-based algorithm for solving decomposed systems of nonlinear equations. Previous implementations used Ilog Solver and its IlcInterval library as a black box, which implied several strong limitations. New versions come from the integration of IBB with the interval-based library Ibex. IBB is now reliable (no solution is lost) while still gaining at least one order of magnitude w.r.t. solving the entire system. On a sample of benchmarks, we have compared several variants of IBB that differ in the way the contraction/filtering is performed inside blocks and is shared between blocks. We have observed that the use of interval Newton inside blocks has the most positive impact on the robustness and performance of IBB. This modifies the influence of other features, such as intelligent backtracking. Also, an incremental variant of inter-block filtering makes this feature more often fruitful.