Solving non-binary convex CSPs in continuous domains

Abstract

A globally consistent labeling is a compact representation of the complete solution space for a constraint satisfaction problem (CSP). Constraint satisfaction is NP-complete and so is the construction of globally consistent labelings for general problems. However, for binary constraints, it is known that when constraints are convex, path-consistency is sufficient to ensure global consistency and can be computed in polynomial time. We show how in continuous domains, this result can be generalized to ternary and in fact arbitrary n-ary constraints using the concept of (3,2)-relational consistency. This leads to polynomial-time algorithms for computing globally consistent labelings for a large class of numerical constraint satisfaction problems.