Constraint satisfaction over connected row-convex constraints

摘要

This paper studies constraint satisfaction over connected row-convex (CRC) constraints. It shows that CRC constraints are closed under composition, intersection, and transposition, the basic operations of path-consistency algorithms. This establishes that path consistency over CRC constraints produces a minimal and decomposable network and is thus a polynomial-time decision procedure for CRC networks. This paper also presents a new path-consistency algorithm for CRC constraints running in time O(n3d2) and space O(n2d), where n is the number of variables and d is the size of the largest domain, improving the traditional time and space complexity by orders of magnitude. The paper also shows how to construct CRC constraints by conjunction and disjunction of a set of basic CRC constraints, highlighting how CRC constraints generalize monotone constraints and presenting interesting subclasses of CRC constraints. Experimental results show that the algorithm behaves well in practice.