Algorithm 681: INTBIS, a portable interval Newton/bisection package
ACM Transactions on Mathematical Software (TOMS)
A filtering algorithm for constraints of difference in CSPs
AAAI '94 Proceedings of the twelfth national conference on Artificial intelligence (vol. 1)
Revising hull and box consistency
Proceedings of the 1999 international conference on Logic programming
Efficient and Safe Global Constraints for Handling Numerical Constraint Systems
SIAM Journal on Numerical Analysis
Artificial Intelligence
Consistency techniques for numeric CSPs
IJCAI'93 Proceedings of the 13th international joint conference on Artifical intelligence - Volume 1
Constructive interval disjunction
CP'07 Proceedings of the 13th 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
Inter-block backtracking: exploiting the structure in continuous CSPs
COCOS'03 Proceedings of the Second international conference on Global Optimization and Constraint Satisfaction
Sweeping with continuous domains
CP'10 Proceedings of the 16th international conference on Principles and practice of constraint programming
A safe and flexible CP-based approach for velocity tuning problems
CP'10 Proceedings of the 16th international conference on Principles and practice of constraint programming
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When interval methods handle systems of equations over the reals, two main types of filtering/contraction algorithms are used to reduce the search space. When the system is well-constrained, interval Newton algorithms behave like a global constraint over the whole n × n system. Also, filtering algorithms issued from constraint programming perform an AC3-like propagation loop, where the constraints are iteratively handled one by one by a revise procedure. Applying a revise procedure amounts in contracting a 1 × 1 subsystem. This paper investigates the possibility of defining contracting well-constrained subsystems of size k (1 ≤ k ≤ n). We theoretically define the Box-k-consistency as a generalization of the state-of-the-art Box-consistency. Well-constrained subsystems act as global constraints that can bring additional filtering w.r.t. interval Newton and 1 × 1 standard subsystems. Also, the filtering performed inside a subsystem allows the solving process to learn interesting multi-dimensional branching points, i.e., to bisect several variable domains simultaneously. Experiments highlight gains in CPU time w.r.t. state-of-the-art algorithms on decomposed and structured systems.