Improved Algorithms for Max-restricted Path Consistency

A binary constraints network consists of a set of n variables, defined on domains of size at most d, and a set of e binary constraints. The binary constraint satisfaction problem consists in finding a solution for a binary constraints network, that is an instantiation of all the variables which satisfies all the constraints. A value a in the domain of variable x is inconsistent if there is no solution which assigns a to x. Many filtering techniques have been proposed to filter out inconsistent values from the domains. Most of them are based on enforcing a given kind of local consistency. One of the most important such consistencies is max-restricted path consistency. The fastest algorithm to enforce maxrestricted path consistency has a O(end) time complexity and a O(end) space complexity. In this paper we present two improved algorithms for the same problem. The first still has a O(end) time complexity, but it reduces the space usage to O(ed). The second improves the time complexity to O(end), and has a O(end) space complexity.