A gentle introduction to NUMERICA
Artificial Intelligence - Special issue: artificial intelligence 40 years later
On the Representation of Timed Polyhedra
ICALP '00 Proceedings of the 27th International Colloquium on Automata, Languages and Programming
Orthogonal Polyhedra: Representation and Computation
HSCC '99 Proceedings of the Second International Workshop on Hybrid Systems: Computation and Control
Search Techniques for Non-linear Constraint Satisfaction Problems with Inequalities
AI '01 Proceedings of the 14th Biennial Conference of the Canadian Society on Computational Studies of Intelligence: Advances in Artificial Intelligence
Universally Quantified Interval Constraints
CP '02 Proceedings of the 6th International Conference on Principles and Practice of Constraint Programming
Consistency techniques for numeric CSPs
IJCAI'93 Proceedings of the 13th international joint conference on Artifical intelligence - Volume 1
Extending consistent domains of numeric CSP
IJCAI'99 Proceedings of the 16th international joint conference on Artifical intelligence - Volume 1
Algorithm 852: RealPaver: an interval solver using constraint satisfaction techniques
ACM Transactions on Mathematical Software (TOMS)
An efficient algorithm for a sharp approximation of universally quantified inequalities
Proceedings of the 2008 ACM symposium on Applied computing
Search heuristics for constraint-aided embodiment design
Artificial Intelligence for Engineering Design, Analysis and Manufacturing
Generalized interval projection: a new technique for consistent domain extension
IJCAI'07 Proceedings of the 20th international joint conference on Artifical intelligence
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Most of the working solvers for numerical constraint satisfaction problems (NCSPs) are designed to delivering point-wise solutions with an arbitrary accuracy. When there is a continuum of feasible points this might lead to prohibitively verbose representations of the output. In many practical applications, such large sets of solutions express equally relevant alternatives which need to be identified as completely as possible. The goal of this paper is to show that by using appropriate approximation techniques, explicit representations of the solution sets, preserving both accuracy and completeness, can still be proposed for NCSPs with continuum of solutions. We present a technique for constructing concise inner and outer approximations as unions of interval boxes. The proposed technique combines a new splitting strategy with the extreme vertex representation of orthogonal polyhedra [1,2,3], as defined in computational geometry. This allows for compacting the representation of the approximations and improves efficiency.