Solving minimal constraint networks in qualitative spatial and temporal reasoning

Authors:
Weiming Liu;Sanjiang Li
Affiliations:
Centre for Quantum Computation and Intelligent Systems, Faculty of Engineering and Information Technology, University of Technology Sydney, Australia;Centre for Quantum Computation and Intelligent Systems, Faculty of Engineering and Information Technology, University of Technology Sydney, Australia
Venue:
CP'12 Proceedings of the 18th international conference on Principles and Practice of Constraint Programming
Year:
2012

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Abstract

The minimal label problem (MLP) (also known as the deductive closure problem) is a fundamental problem in qualitative spatial and temporal reasoning (QSTR). Given a qualitative constraint network Γ, the minimal network of Γ relates each pair of variables (x,y) by the minimal label of (x,y), which is the minimal relation between x,y that is entailed by network Γ. It is well-known that MLP is equivalent to the corresponding consistency problem with respect to polynomial Turing-reductions. This paper further shows, for several qualitative calculi including Interval Algebra and RCC-8 algebra, that deciding the minimality of qualitative constraint networks and computing a solution of a minimal constraint network are both NP-hard problems.