Abstract
R-trees and related structures, like R+-trees and R*-trees, have been used to answer queries involving topological information about objects represented by their minimum bounding rectangles (MBRs). This paper describes how the R-tree method can be used for the storage and retrieval of direction relations. Direction relations deal with order in space, as for instance, left, above, north, southeast etc. In this paper we define direction relations between points and extend the definitions to relations between objects. Then we present our tests regarding the retrieval of direction relations between objects using R-trees and discuss the representational properties of MBR approximations with respect to directions in 2D space.
This research is supported by the Esprit II Basic Research Program EP 688I (Amusing) and by a research grant from the General Secretariat of Research and Technology of Greece (PENED 91).
Preview
Unable to display preview. Download preview PDF.
References
Allen, J.F. (1983) Maintaining Knowledge About Temporal Intervals. CACM 26 (11), 832–843.
Beckmann, N., Kriegel, H.P. Schneider, V., Seeger, B. (1990) The R*-tree: an Efficient and Robust Access Method for Points and Rectangles. In the Proceedings of ACM-SIGMOD Conference.
Chang, S.K, Jungert, E., Li, Y. (1989) The Design of Pictorial Database upon the Theory of Symbolic Projections. In the Proceedings of the First Symposium on the Design and Implementation of Large Spatial Databases (SSD). Springer-Verlag.
Dutta, S. (1989) Qualitative Spatial Reasoning. A Semi-Qualitative Approach using Fuzzy Logic. In the Proceedings of the First Symposium on the Design and Implementation of Large Spatial Databases (SSD). Springer-Verlag.
Egenhofer, M., Herring, J. (1990) A Mathematical Framework for the Definitions of Topological Relationships. In the Proceedings of the 4th International Symposium on Spatial Data Handling (SDH).
Frank, A. U., (1992) Qualitative Spatial Reasoning about Distances and Directions in Geographic Space. Journal of Visual Languages and Computing, 3, pp 343–371.
Freksa, C. (1991) Qualitative Spatial Reasoning. In Mark, D.M. and Frank, A.U (eds.) Cognitive and Linguistic Aspects of Geographic Space. Kluwer, Dordrecht
Guttman, A. (1984) R-trees: a Dynamic Index Structure for Spatial Searching. In the Proceedings of ACM-SIGMOD Conference.
Hernandez, D. (1993) Maintaining Qualitative Spatial Knowledge. In Frank, A.U., Campari, I. (eds.) Proceedings of the European Conference on Spatial Information Theory (COSIT). Springer-Verlag.
Papadias, D., Sellis, T. (1993) The Semantics of Relations in 2D Space Using Representative Points: Spatial Indexes. In Frank, A.U., Campari, I. (eds.) Proceedings of the European Conference on Spatial Information Theory (COSIT). Springer-Verlag.
Papadias, D., Sellis, T. (1994) On the Qualitative Representation of Spatial Knowledge in Two-Dimensional Space. To appear in the Very Large Data Bases Journal, Special Issue on Spatial Databases.
Randell, D. A., Cui, Z., Cohn, A., (1992) A Spatial Logic Based on Regions and Connection. In the Proceedings of the 3rd International Conferrence on Principles of Knowledge Representation and Reasoning (KR). Morgan Kaufman.
Sellis, T., Roussopoulos, N., Faloutsos, C. (1987) The R+-tree: A Dynamic Index for Multi-Dimensional Objects. In the Proceedings of the 13th VLDB conference.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1994 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Papadias, D., Theodoridis, Y., Sellis, T. (1994). The retrieval of direction relations using R-trees. In: Karagiannis, D. (eds) Database and Expert Systems Applications. DEXA 1994. Lecture Notes in Computer Science, vol 856. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-58435-8_182
Download citation
DOI: https://doi.org/10.1007/3-540-58435-8_182
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-58435-3
Online ISBN: 978-3-540-48796-8
eBook Packages: Springer Book Archive