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Título: | Spatial reasoning with rectangular cardinal relations: the convex tractable subalgebra |
Fecha de publicación: | 3-ene-2013 |
Editorial: | Springer |
Cita bibliográfica: | Annals of Mathematics and Artificial Intelligence, Vol. 67, 2013, pp. 31-70 |
ISSN: | Print: 1012-2443 Electronic: 1573-7470 |
Palabras clave: | Qualitative spatial reasoning Cardinal direction relations Rectangle algebra Interval Algebra Qualitative constraint networks Constraint satisfaction problems |
Resumen: | Qualitative spatial representation and reasoning plays a important role in various spatial applications. In this paper we introduce a new formalism, we name RCD calculus, for qualitative spatial reasoning with cardinal direction relations between regions of the plane approximated by rectangles. We believe this calculus leads to an attractive balance between efficiency, simplicity and expressive power, which makes it adequate for spatial applications. We define a constraint algebra and we identify a convex tractable subalgebra allowing efficient reasoning with definite and imprecise knowledge about spatial configurations specified by qualitative constraint networks. For such tractable fragment, we propose several polynomial algorithms based on constraint satisfaction to solve the consistency and minimality problems. Some of them rely on a translation of qualitative networks of the RCD calculus to qualitative networks of the Interval or Rectangle Algebra, and back. We show that the consistency problem for convex networks can also be solved inside the RCD calculus, by applying a suitable adaptation of the path-consistency algorithm. However, path consistency can not be applied to obtain the minimal network, contrary to what happens in the convex fragment of the Rectangle Algebra. Finally, we partially analyze the complexity of the consistency problem when adding non-convex relations, showing that it becomes NP-complete in the cases considered. This analysis may contribute to find a maximal tractable subclass of the RCD calculus and of the Rectangle Algebra, which remains an open problem. |
Autor/es principal/es: | Navarrete, Isabel Morales, Antonio Sciavicco, Guido Cárdenas Viedma, María Antonia |
Facultad/Departamentos/Servicios: | Facultades, Departamentos, Servicios y Escuelas::Departamentos de la UMU::Ingeniería de la Información y las Comunicaciones |
Versión del editor: | https://link.springer.com/article/10.1007/s10472-012-9327-5#citeas |
URI: | http://hdl.handle.net/10201/141736 |
DOI: | https://doi.org/10.1007/s10472-012-9327-5 |
Tipo de documento: | info:eu-repo/semantics/article |
Número páginas / Extensión: | 42 |
Derechos: | info:eu-repo/semantics/embargoedAccess |
Descripción: | © Springer 2012. This document is the Published version of a Published Work that appeared in final form in Annals of Mathematics and Artificial Intelligence. To access the final edited and published work see https://doi.org/10.1007/s10472-012-9327-5 |
Aparece en las colecciones: | Artículos: Ingeniería de la Información y las Comunicaciones |
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