Abstract
Energetic reasoning is a strong filtering technique for the Cumulative constraint. However, the best algorithms process \(O(n^2)\) time intervals to perform the satisfiability check which makes it too costly to use in practice. We present how to apply the energetic reasoning by processing only \(O(n \log n)\) intervals. We show how to compute the energy in an interval in \(O(\log n)\) time. This allows us to propose a \(O(n \log ^2 n)\) checker and a filtering algorithm for the energetic reasoning with \(O(n^2 \log n)\) average time complexity. Experiments show that these two algorithms outperform their state of the art counterparts.
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Acknowledgment
In memory of Alejandro López-Ortiz (1967–2017) who introduced me to research, algorithm design, and even Monge matrices. – C.-G. Q
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Ouellet, Y., Quimper, CG. (2018). A \(O(n \log ^2 n)\) Checker and \(O(n^2 \log n)\) Filtering Algorithm for the Energetic Reasoning. In: van Hoeve, WJ. (eds) Integration of Constraint Programming, Artificial Intelligence, and Operations Research. CPAIOR 2018. Lecture Notes in Computer Science(), vol 10848. Springer, Cham. https://doi.org/10.1007/978-3-319-93031-2_34
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