Filtering numerical CSPs using well-constrained subsystems

Ignacio Araya, Gilles Trombettoni, Bertrand Neveu

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

3 Scopus citations


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.

Original languageEnglish
Title of host publicationPrinciples and Practice of Constraint Programming - CP 2009 - 15th International Conference, CP 2009, Proceedings
Number of pages15
StatePublished - 2009
Externally publishedYes
Event15th International Conference on Principles and Practice of Constraint Programming, CP 2009 - Lisbon, Portugal
Duration: 20 Sep 200924 Sep 2009

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume5732 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference15th International Conference on Principles and Practice of Constraint Programming, CP 2009


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