A Bitwise GAC Algorithm for Alldifferent Constraints

The generalized arc consistency (GAC) algorithm is the prevailing solution for alldifferent constraint problems. The core part of GAC for alldifferent constraints is excavating and enumerating all the strongly connected components (SCCs) of the graph model. This causes a large amount of complex data structures to maintain the node information, leading to a large overhead both in time and memory space. More critically, the complexity of the data structures further precludes the coordination of different optimization schemes for GAC. To solve this problem, the key observation of this paper is that the GAC algorithm only cares whether a node of the graph model is in an SCC or not, rather than which SCCs it belongs to. Based on this observation, we propose AllDiffbit, which employs bitwise data structures and operations to efficiently determine if a node is in an SCC. This greatly reduces the corresponding overhead, and enhances the ability to incorporate existing optimizations to work in a synergistic way. Our experiments show that AllDiffbit outperforms the state-of-the-art GAC algorithms over 60%.