Arc Consistency Revisited

Abstract

Binary constraints are a general representation for constraints and is used in Constraint Satisfaction Problems (CSPs). However, many problems are more easily modelled with non-binary constraints (constraints with arity >2). Several well-known binary encoding methods can be used to transform non-binary CSPs to binary CSPs. Historically, work on constraint satisfaction began with binary CSPs with many algorithms proposed to maintain Arc Consistency (AC) on binary constraints. In more recent times, research has focused on non-binary constraints and efficient Generalized Arc Consistency (GAC) algorithms for non-binary constraints. Existing results and “folklore” suggest that AC algorithms on the binary encoding of a non-binary CSP do not compete with GAC algorithms on the original problem. We propose new algorithms to enforce AC on binary encoded instances. Preliminary experiments show that our AC algorithm on the binary encoded instances is competitive to state-of-the-art GAC algorithms on the original non-binary instances and faster in some instances. This result is surprising and is contrary to the “folklore” on AC versus GAC algorithms. We believe our results can lead to a revival of AC algorithms as binary constraints and resulting algorithms are simpler than the non-binary ones.