Reasoning about cardinal directions between extended objects: The NP-hardness result

  • Authors:

  • Weiming Liu;Sanjiang Li

  • Affiliations:

  • Centre for Quantum Computation and Intelligent Systems, Faculty of Engineering and Information Technology, University of Technology Sydney, Sydney, P.O. Box 123, Broadway, NSW 2007, Australia;Centre for Quantum Computation and Intelligent Systems, Faculty of Engineering and Information Technology, University of Technology Sydney, Sydney, P.O. Box 123, Broadway, NSW 2007, Australia

  • Venue:
  • Artificial Intelligence
  • Year:
  • 2011

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Abstract

The cardinal direction calculus (CDC) proposed by Goyal and Egenhofer is a very expressive qualitative calculus for directional information of extended objects. Early work has shown that consistency checking of complete networks of basic CDC constraints is tractable, while reasoning with the CDC in general is NP-hard. This paper shows, however, that if some constraints are unspecified, then consistency checking of incomplete networks of basic CDC constraints is already intractable. This draws a sharp boundary between the tractable and intractable subclasses of the CDC. The result is achieved by a reduction from the well-known 3-SAT problem.