Constraint satisfaction problems: convexity makes all different constraints tractable

  • Authors:

  • Michael Fellows;Tobias Friedrich;Danny Hermelin;Nina Narodytska;Frances Rosamond

  • Affiliations:

  • Charles Darwin University, Darwin, Northern Territory, Australia;Max-Planck-Institut für Informatik, Saarbrücken, Germany;Max-Planck-Institut für Informatik, Saarbrücken, Germany;NICTA and University of New South Wales, Sydney, Australia;Charles Darwin University, Darwin, Northern Territory, Australia

  • Venue:
  • IJCAI'11 Proceedings of the Twenty-Second international joint conference on Artificial Intelligence - Volume Volume One
  • Year:
  • 2011

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Abstract

We examine the complexity of constraint satisfaction problems that consist of a set of AllDiff constraints. Such CSPs naturally model a wide range of real-world and combinatorial problems, like scheduling, frequency allocations and graph coloring problems. As this problem is known to be NP-complete, we investigate under which further assumptions it becomes tractable. We observe that a crucial property seems to be the convexity of the variable domains and constraints. Our main contribution is an extensive study of the complexity of Multiple AllDiff CSPs for a set of natural parameters, like maximum domain size and maximum size of the constraint scopes. We show that, depending on the parameter, convexity can make the problem tractable while it is provably intractable in general