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Reliability in computing: the role of interval methods in scientific computing
Algorithm 681: INTBIS, a portable interval Newton/bisection package
ACM Transactions on Mathematical Software (TOMS)
ILPS '94 Proceedings of the 1994 International Symposium on Logic programming
A branch and prune algorithm for the approximation of non-linear AE-solution sets
Proceedings of the 2006 ACM symposium on Applied computing
Handbook of Constraint Programming (Foundations of Artificial Intelligence)
Handbook of Constraint Programming (Foundations of Artificial Intelligence)
Consistency techniques for numeric CSPs
IJCAI'93 Proceedings of the 13th international joint conference on Artifical intelligence - Volume 1
Inner and outer approximations of existentially quantified equality constraints
CP'06 Proceedings of the 12th international conference on Principles and Practice of Constraint Programming
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This paper presents an interval-based method that follows the branch-and-prune scheme to compute a verified paving of a projection of the solution set of an under-constrained system. Benefits of this algorithm include anytime solving process, homogeneous verification of inner boxes, and applicability to generic problems, allowing any number of (possibly nonlinear) equality and inequality constraints. We present three key improvements of the algorithm dedicated to projection problems: (i) The verification process is enhanced in order to prove faster larger boxes in the projection space. (ii) Computational effort is saved by pruning redundant portions of the solution set that would project identically. (iii) A dedicated branching strategy allows reducing the number of treated boxes. Experimental results indicate that various applications can be modeled as projection problems and can be solved efficiently by the proposed method.