Box-set consistency for interval-based constraint problems

As opposed to finite domain CSPs, arc consistency cannot be enforced, in general, on CSPs over the reals, including very simple instances. In contrast, a stronger property, the so-called box-set consistency, that requires a no-split condition in addition to arc consistency, can be obtained on a much larger number of problems. To obtain this property, we devise a lazy algorithm that combines hull consistency filtering, interval union projection, and intelligent domain splitting. It can be applied to any numerical CSP, and achieves box-set consistency if constraints are redundancy-free in terms of variables. This holds even if the problem is not intervalconvex. The main contribution of our approach lies in the way we bypass the non-convexity issue, which so far was a synonym for either a loss of accuracy or an unbounded growth of label size. We prove the correctness of our algorithm and through experimental results, we show that, as compared to a strategy based on a standard bisection...

• Type: Conference
• Year: 2005
• Where: SAC
• Authors: Gilles Chabert, Gilles Trombettoni, Bertrand Neveu
• Keywords: Applied Computing, Arc Consistency, Box-set Consistency, SAC 2005, So-called Box-set Consistency