## On the Complexity of Qualitative Spatial Reasoning: A Maximal Tractable Fragment of the Region Connection Calculus (1997)

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Venue: | Artificial Intelligence |

Citations: | 108 - 22 self |

### BibTeX

@ARTICLE{Renz97onthe,

author = {Jochen Renz and Bernhard Nebel},

title = {On the Complexity of Qualitative Spatial Reasoning: A Maximal Tractable Fragment of the Region Connection Calculus},

journal = {Artificial Intelligence},

year = {1997},

volume = {108},

pages = {69--123}

}

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### Abstract

The computational properties of qualitative spatial reasoning have been investigated to some degree. However, the question for the boundary between polynomial and NP-hard reasoning problems has not been addressed yet. In this paper we explore this boundary in the "Region Connection Calculus" RCC-8. We extend Bennett's encoding of RCC-8 in modal logic. Based on this encoding, we prove that reasoning is NPcomplete in general and identify a maximal tractable subset of the relations in RCC-8 that contains all base relations. Further, we show that for this subset path-consistency is sufficient for deciding consistency. 1 Introduction When describing a spatial configuration or when reasoning about such a configuration, often it is not possible or desirable to obtain precise, quantitative data. In these cases, qualitative reasoning about spatial configurations may be used. One particular approach in this context has been developed by Randell, Cui, and Cohn [20], the so-called Region Connecti...