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Edge-finding, extended edge-finding, not-first/not-last and energetic reasoning are well-known filtering rules used in constraint-based scheduling problems for propagating constraints over disjunctive and cumulative resources. In practice, these filtering algorithms frequently form part of a sequence to form a more powerful propagator, thereby helping to reduce search tree size. In this paper, we propose a sound O(n2) extended edge-finding algorithm for cumulative resources, where n is the number of tasks sharing the resource. This algorithm uses the notion of minimum slack to detect when extended edge-finding justifies a strengthening of a domain, and it is more efficacious when executed on a domain already at the fix point of standard edge-finding. Previously, the best known complexity for filtering extended edge-finding on cumulative resources was O(kn2) (where k is the number of distinct capacity requirements). Experimental results on resource constrained scheduling benchmarks confirm that the new algorithm outperforms previous extended edge-finding algorithms, and sometimes results in better performance than standard edge-finding alone. Furthermore, we show that our method is competitive with the current state-of-the-art in edge-finding-based algorithms.

A quadratic extended edge-finding filtering algorithm for cumulative resource constraints