Filtering Numerical CSPs Using Well-Constrained Subsystems

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 Boxk-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-dimen...

• Type: Conference
• Year: 2009
• Where: CP
• Authors: Ignacio Araya, Gilles Trombettoni, Bertrand Neveu
• Keywords: CP 2009, Interval Methods, Programming Languages, Revise Procedure Amounts, State-of-the-art Algorithms