A Quadratic Edge-Finding Filtering Algorithm for Cumulative Resource Constraints
Abstract
The cumulative scheduling constraint, which enforces the sharing of a finite resource by several tasks, is widely used in constraint-based scheduling applications. Propagation of the cumulative constraint can be performed by several different filtering algorithms, often used in combination. One of the most important and successful of these filtering algorithms is edge-finding. Recent work by Vilím has resulted in a \(\mathcal{O}(kn \log n)\) algorithm for cumulative edge-finding, where n is the number of tasks and k is the number of distinct capacity requirements. In this paper, we present a sound \(\mathcal{O}(n^2)\) cumulative edge-finder. This algorithm reaches the same fixpoint as previous edge-finding algorithms, although it may take additional iterations to do so. While the complexity of this new algorithm does not strictly dominate Vilím’s for small k, experimental results on benchmarks from the Project Scheduling Problem Library suggest that it typically has a substantially reduced runtime. Furthermore, the results demonstrate that in practice the new algorithm rarely requires more propagations than previous edge-finders.
Keywords
Schedule Problem Release Date Outer Loop Project Schedule Problem Early Start TimePreview
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References
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