Maintaining Singleton Arc-Consistency

Singleton Arc-Consistency (SAC) [7] is a simple and strong level of consistency but is costly to enforce. To date, research has focused on improving the performance of algorithms that achieve SAC, and comparing algorithms as a preprocessing step before actually solving a problem. Here, we show for the first time how a basic SAC algorithm can be readily incorporated into an open source constraint programming toolkit and then used within the search process i.e. the search process maintains SAC. We also present three new levels of SAC: BoundSAC where the first and last values in domains are SAC, First-SAC where only the first value is SAC, and Existential-SAC where some value in the domain is SAC. Again, we show how these levels of SAC can be maintained by the search process, and present the first empirical study of their behaviours. This leads us to the point where we can investigate the effect of maintaining different levels of consistency on different sets of variables within a problem, i.e. maintaining mixed-consistency [9]. We show that maintaining mixed-consistency can result in significant performance improvements.