On the complexity of global scheduling constraints under structural restrictions

  • Authors:

  • Geoffrey Chu;Serge Gaspers;Nina Narodytska;Andreas Schutt;Toby Walsh

  • Affiliations:

  • Univ. of Melbourne, Melbourne, Australia;UNSW and NICTA, Sydney, Australia;UNSW and NICTA, Sydney, Australia;Univ. of Melbourne, Melbourne, Australia;NICTA and UNSW, Sydney, Australia

  • Venue:
  • IJCAI'13 Proceedings of the Twenty-Third international joint conference on Artificial Intelligence
  • Year:
  • 2013

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Abstract

We investigate the computational complexity of two global constraints, CUMULATIVE and INTERDISTANCE. These are key constraints in modeling and solving scheduling problems. Enforcing domain consistency on both is NP-hard. However, restricted versions of these constraints are often sufficient in practice. Some examples include scheduling problems with a large number of similar tasks, or tasks sparsely distributed over time. Another example is runway sequencing problems in air-traffic control, where landing periods have a regular pattern. Such cases can be characterized in terms of structural restrictions on the constraints. We identify a number of such structural restrictions and investigate how they impact the computational complexity of propagating these global constraints. In particular, we prove that such restrictions often make propagation tractable.