Light-Weight versus Heavy-Weight Algorithms for SAC and Neighbourhood SAC

This paper compares different forms of singleton arc consistency (SAC) algorithms with respect to: (i) their relative efficiency as a function of the increase in problem size and/or difficulty, (ii) the effectiveness with which they can be transformed into algorithms for establishing neighbourhood singleton arc consistency (NSAC) In such comparisons, it was found useful to distinguish two classes of SAC algorithm with the terms “light-weight” and “heavy-weight”. The difference turns on the complexity of data structures required; this complexity is much greater for the heavyweight than the light-weight algorithms. The present work shows that this difference is reflected in scalability. In general, light-weight algorithms scale better than heavy-weight algorithms on both random and structured problems, although in the latter case the heavyweight algorithm SAC-3 is able to compensate for its extra overhead. In addition, it is shown that modifying heavy-weight algorithms to produce NSAC algorithms is problematic because the logic underlying their improvements, while suited to SAC, requires major revisions when carried over to neighbourhood SAC. As a result, even for problems where heavy-weight SAC algorithms are competitive with light-weight algorithms, the efficiency of the corresponding NSAC algorithms is seriously compromised. In contrast, light-weight SAC algorithms can be easily converted to efficient NSAC algorithms. These results show that heavy-weight algorithms for SAC cannot be considered as unconditional improvements on light-weight algorithms, and more importantly that more attention should be paid to the basic tradeoff between reducing the number of dominant operations (constraint checks) and minimizing extra overhead in local consistency algorithms.