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. © 2012 Springer-Verlag.
CITATION STYLE
Liu, W., & Li, S. (2012). Solving minimal constraint networks in qualitative spatial and temporal reasoning. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 7514 LNCS, pp. 464–479). https://doi.org/10.1007/978-3-642-33558-7_35
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