Two New Lightweight Arc Consistency Algorithms

Coarse-grained arc consistency algorithms like AC-3, AC-3d, and AC-2001, are efficient when it comes to transforming a Constraint Satisfaction Problem (CSP) to its arc consistent equivalent. These algorithms repeatedly carry out revisions to remove unsupported values from the domains of the variables. The order of these revisions is determined by so-called revision ordering heuristics. In this paper, we classify revision ordering heuristics into three different categories: arc based, variable based, and reverse variable based revision ordering heuristics. We point out advantages of using reverse variable based revision ordering heuristics and propose two new lightweight arc consistency algorithms AC-3dl and AC-3ds, which exploit these advantages. Both algorithms are equipped with domain heuristics which are inspired by AC-3d’s double support heuristic. AC-3dl uses a lazy version of a double support heuristic while AC-3ds uses AC-3d’s double support heuristic with a minor change. We experimentally compare MAC-3, MAC-3d, MAC-3dl and MAC-3ds. MAC-3ds is the best in saving checks. MAC-3dl is good in saving time and checks on average. Experimental results demonstrate that lightweight algorithms based on reverse variable based revision ordering heuristics are good in saving checks as well as time.