Lightweight MAC Algorithms

Arc-consistency algorithms are the workhorse of backtrackers that Maintain Arc-Consistency (MAC). This paper provides experimental evidence that, despite common belief to the contrary, it is not always necessary for a good arc-consistency algorithm to have an optimal worst case time-complexity. To sacrifice this optimality allows MAC solvers that (1) do not need additional data structures during search, (2) have an excellent average time-complexity, and (3) have a space-complexity that improves significantly on that of MAC solvers that do have optimal arc-consistency components. Results are presented from an experimental comparison between MAC-2001, MAC-3(d) and related algorithms. MAC-2001 has an arc-consistency component with an optimal worst case time-complexity, whereas MAC-3(d) has not. MAC-2001 requires additional data structures during search, whereas MAC-3d does not. MAC-3(d) has a space-complexity of O(e + nd), where n is the number of variables, d the maximum domain size, and e the number of constraints. We demonstrate that MAC-2001's space-complexity is O(ed min(n, d)). MAC-2001 required about 35% more average solution time than MAC-3(d) for easy and hard random problems and MAC-3(d) was the quickest algorithm to solve 23 out of 25 real-world problems, and was only marginally slower for the remaining 2. This indicates that lightweight algorithms like MAC-3(d) are promising, especially if checks are cheap and memory is scarce.