Global Consistency for Continuous Constraints

This paper provides a technique for solving general constraint satisfaction problems (CSPs) with continuous variables. Constraints are represented by a hierarchical binary decomposition of the space of feasible values. We propose algorithms for pathand higher degrees of consistency based on logical operations defined on this representation and demonstrate that the algorithms terminate in polynomial time. We show that, in analogy to convex temporal problems and discrete row-convex problems, convexity properties of the solution spaces can be exploited to compute minimal and decomposablenetworks using path consistency algorithms. Based on these properties, we also show that a certain class of non binary CSPs can be solved using strong 5-consistency.