Hybrid tractable CSPs which generalize tree structure

  • Authors:

  • Martin C. Cooper;Peter G. Jeavons;András Z. Salamon

  • Affiliations:

  • IRIT, University of Toulouse III, 31062 Toulouse, France, email: cooper@irit.fr;Computing Laboratory, University of Oxford, Oxford, OX1 3QD, UK, email: Peter.Jeavons@comlab.ox.ac.uk, Andras.Salamon@comlab.ox.ac.uk;Computing Laboratory, University of Oxford, Oxford, OX1 3QD, UK, email: Peter.Jeavons@comlab.ox.ac.uk, Andras.Salamon@comlab.ox.ac.uk and The Oxford-Man Institute of Quantitative Finance, 9 Alfred ...

  • Venue:
  • Proceedings of the 2008 conference on ECAI 2008: 18th European Conference on Artificial Intelligence
  • Year:
  • 2008

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Abstract

The constraint satisfaction problem (CSP) is a central generic problem in artificial intelligence. Considerable progress has been made in identifying properties which ensure tractability in such problems, such as the property of being tree-structured. In this paper we introduce the broken-triangle property, which allows us to define a hybrid tractable class for this problem which significantly generalizes the class of problems with tree structure. We show that the broken-triangle property is conservative (i.e., it is preserved under domain reduction and hence under arc consistency operations) and that there is a polynomial-time algorithm to determine an ordering of the variables for which the broken-triangle property holds (or to determine that no such ordering exists). We also present a non-conservative extension of the broken-triangle property which is also sufficient to ensure tractability and can be detected in polynomial time.