Abstract
For all 8192 combinations of Allen’s 13 relations between one task with origin \(o_i\) and fixed length \(\ell _i\) and another task with origin \(o_j\) and fixed length \(\ell _j\), this paper shows how to systematically derive a formula \(F(\underline{o_j}, \overline{o_j}, \ell _i, \ell _j)\), where \(\underline{o_j}\) and \(\overline{o_j}\) respectively denote the earliest and the latest origin of task j, evaluating to a set of integers which are infeasible for \(o_i\) for the given combination. Such forbidden regions allow maintaining range-consistency for an Allen constraint.
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Acknowledgment
The Nantes authors were partially supported both by the INRIA TASCMELB associated team and by the GRACeFUL project, which has received funding from the European Union’s Horizon 2020 research and innovation programme under grant agreement No 640954.
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Beldiceanu, N., Carlsson, M., Derrien, A., Prud’homme, C., Schutt, A., Stuckey, P.J. (2017). Range-Consistent Forbidden Regions of Allen’s Relations. In: Salvagnin, D., Lombardi, M. (eds) Integration of AI and OR Techniques in Constraint Programming. CPAIOR 2017. Lecture Notes in Computer Science(), vol 10335. Springer, Cham. https://doi.org/10.1007/978-3-319-59776-8_2
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