NDLI: Spatial Reasoning About Points in a Multidimensional Setting

Content Provider	Springer Nature Link
Author	Balbiani, Philippe Condotta, Jean François
Copyright Year	2002
Abstract	For n ≥ 1, we consider the possible relations between two points of the Euclidean space of dimension n. We define the n-point algebra on the pattern of the point algebra and the cardinal algebra. Generalizing the concept of convexity just as the one of preconvexity, we prove that the consistency problem of convex n-point networks is polynomial for n ≥ 1, whereas the consistency problem of preconvex n-point networks is NP-complete for n ≥ 3. We characterize a subset of the set of all preconvex relations: the set of all strongly preconvex relations, which contains the set of all convex relations. We demonstrate that the consistency problem of strongly preconvex n-point networks can be decided in polynomial time by means of the weak path-consistency method for all n ≥ 1. For n = 3 the set of all strongly preconvex relations is a maximal tractable subclass of the set of all n-point relations. Finally, we prove that the concept of strong preconvexity corresponds to the one of ORD-Horn representability.
Starting Page	221
Ending Page	238
Page Count	18
File Format	PDF
ISSN	0924669X
Journal	Applied Intelligence
Volume Number	17
Issue Number	3
e-ISSN	15737497
Language	English
Publisher	Kluwer Academic Publishers
Publisher Date	2002-01-01
Publisher Place	Boston
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Artificial Intelligence (incl. Robotics) Mechanical Engineering Manufacturing, Machines, Tools
Content Type	Text
Resource Type	Article
Subject	Artificial Intelligence

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