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Linear-time filtering algorithms for the disjunctive constraint and a quadratic filtering algorithm for the cumulative not-first not-last

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We present new filtering algorithms for Disjunctive and Cumulative constraints, each of which improves the complexity of the state-of-the-art algorithms by a factor of log n. We show how to perform Time-Tabling and Detectable Precedences in linear time on the Disjunctive constraint. Furthermore, we present a linear-time Overload Checking for the Disjunctive and Cumulative constraints. Finally, we show how the rule of Not-first/Not-last can be enforced in quadratic time for the Cumulative constraint. These algorithms rely on the union find data structure, from which we take advantage to introduce a new data structure that we call it time line. This data structure provides constant time operations that were previously implemented in logarithmic time by the Θ-tree data structure. Experiments show that these new algorithms are competitive even for a small number of tasks and outperform existing algorithms as the number of tasks increases. We also show that the time line can be used to solve specific scheduling problems.

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Authors and Affiliations

  1. Université Laval, Québec, QC, Canada

    Hamed Fahimi, Yanick Ouellet & Claude-Guy Quimper

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  1. Hamed Fahimi
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  2. Yanick Ouellet
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  3. Claude-Guy Quimper
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Correspondence to Hamed Fahimi.

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A preliminary version of this paper appears as [8]

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Fahimi, H., Ouellet, Y. & Quimper, CG. Linear-time filtering algorithms for the disjunctive constraint and a quadratic filtering algorithm for the cumulative not-first not-last. Constraints 23, 272–293 (2018). https://doi.org/10.1007/s10601-018-9282-9

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  • DOI: https://doi.org/10.1007/s10601-018-9282-9

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