Arc consistency for factorable relations

An optimal arc consistency algorithm AC-4 was given by Mohr and Henderson [8]. AC4 has cost 0(ea), and cost (na) for scene labelling. Although their algorithm is indeed optimal, under certain conditions a constraint satisfaction problem can be transformed into a less complex problem. In this paper, we present conditions and mechanisms for such transformations, and show how to factor relations into more manageable components. We describe how factorization can reduce AC-4's cost to O(ea), and apply this result to RETE match. Further, with our factorization, the cost of scene labelling is reduced to O(na).