Range-Consistent Forbidden Regions of Allen’s Relations

  • Nicolas Beldiceanu
  • Mats CarlssonEmail author
  • Alban Derrien
  • Charles Prud’homme
  • Andreas Schutt
  • Peter J. Stuckey
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10335)


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.



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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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.TASC (LS2N-CNRS)IMT AtlantiqueNantesFrance
  2. 2.RISE SICSKistaSweden
  3. 3.Data61CSIROCanberraAustralia
  4. 4.University of MelbourneMelbourneAustralia
  5. 5.Lab-STICC UMR 6285 – CNRSUniversité de Bretagne-SudLorientFrance

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