Bimodal Depth-First Search for Scalable GAC for AllDifferent

We propose a version of DFS designed for Constraint Programming, called bimodal DFS, that scales to both sparse and dense graphs. It runs in O(n + ~m) time, where ~m is the sum, for each vertex v, of the minimum between the numbers of successors and non-successors of v. Integrating it into Régin’s GAC algorithm for the AllDifferent constraint results in faster performance as the problem size increases, outperforming a GPU-accelerated version. In the vast majority of our tests, GAC now performs similarly to BC in terms of speed, but is able to solve more problems.