Abstract
Geographic data have become abundantly available in the recent years due to the widespread deployment of GPS devices for example in mobile phones. At the same time, the data covered are no longer restricted to the local area of a single application, but often span the whole world. However, we do still use very rough approximations when indexing these data, which are usually stored and indexed using an equirectangular projection. When distances are measured using Euclidean distance in this projection, a non-neglibile error may occur. Databases are lacking good support for accelerated nearest neighbor queries and range queries in such datasets for the much more appropriate geodetic (great-circle) distance. In this article, we will show two approaches how a widely known spatial index structure – the R-tree – can be easily used for nearest neighbor queries with the geodetic distance, with no changes to the actual index structure. This allows existing database indexes immediately to be used with low distortion and highly efficient nearest neighbor queries and radius queries as well as window queries.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Sinnott, R.: Virtues of the haversine. Sky and Telescope 68, 158–159 (1984)
Vincenty, T.: Direct and inverse solutions of geodesics on the ellipsoid with application of nested equations. Survey Review 23(176), 88–93 (1975)
Finkel, R.A., Bentley, J.L.: Quad trees. A data structure for retrieval on composite keys. Acta Informatica 4(1), 1–9 (1974)
Bentley, J.L.: Multidimensional binary search trees used for associative searching. Commun. ACM 18(9), 509–517 (1975)
Kunszt, P., Szalay, A., Thakar, A.: The hierarchical triangular mesh. Mining the Sky, 631–637 (2001)
Morton, G.M.: A computer oriented geodetic data base and a new technique in file sequencing. Technical report, International Business Machines Co. (1966)
Guttman, A.: R-Trees: A dynamic index structure for spatial searching. In: Proc. SIGMOD, pp. 47–57 (1984)
Beckmann, N., Kriegel, H.P., Schneider, R., Seeger, B.: The R*-Tree: An efficient and robust access method for points and rectangles. In: Proc. SIGMOD, pp. 322–331 (1990)
White, D.A., Jain, R.: Similarity indexing with the SS-tree. In: Proc. ICDE, pp. 516–523 (1996)
Ciaccia, P., Patella, M., Zezula, P.: M-Tree: an efficient access method for similarity search in metric spaces. In: Proc. VLDB, pp. 426–435 (1997)
Kurniawati, R., Jin, J.S., Shepherd, J.A.: The SS+-tree: An improved index structure for similarity searches in a high-dimensional feature space. In: Proc. SPIE, vol. 3022, pp. 110–120 (1997)
Ciaccia, P., Patella, M.: Bulk loading the M-tree. In: Proc. ADC (1998)
Traina Jr., C., Traina, A., Seeger, B., Faloutsos, C.: Slim-trees: High performance metric trees minimizing overlap between nodes. In: Zaniolo, C., Grust, T., Scholl, M.H., Lockemann, P.C. (eds.) EDBT 2000. LNCS, vol. 1777, pp. 51–65. Springer, Heidelberg (2000)
Traina Jr, C., Traina, A., Faloutsos, C., Seeger, B.: Fast indexing and visualization of metric data sets using slim-trees. IEEE TKDE 14(2), 244–260 (2002)
Katayama, N., Satoh, S.: The SR-tree: An index structure for high-dimensional nearest neighbor queries. In: Proc. SIGMOD, pp. 369–380 (1997)
Microsoft Corporation: Whitepaper New Spatial Features in SQL Server 2012 (2012)
Fang, Y., Friedman, M., Nair, G., Rys, M., Schmid, A.E.: Spatial indexing in microsoft sql server 2008. In: Proc. SIGMOD, pp. 1207–1216 (2008)
PostGIS project: Postgis 2.0 manual, http://postgis.net/docs/manual-2.0/
IBM Informix: IBM Informix Geodetic DataBlade Module User’s Guide
Lukatela, H.: Hipparchus geopositioning model: An overview. In: Proc. Auto. Cartography, vol. 8, pp. 87–96 (1987)
Kothuri, R.K.V., Ravada, S., Abugov, D.: Quadtree and R-tree indexes in oracle spatial: a comparison using GIS data. In: Proc. SIGMOD, pp. 546–557 (2002)
Hu, Y., Ravada, S., Anderson, R.: Geodetic point-in-polygon query processing in oracle spatial. In: Pfoser, D., Tao, Y., Mouratidis, K., Nascimento, M.A., Mokbel, M., Shekhar, S., Huang, Y. (eds.) SSTD 2011. LNCS, vol. 6849, pp. 297–312. Springer, Heidelberg (2011)
Achtert, E., Kriegel, H.P., Schubert, E., Zimek, A.: Interactive data mining with 3d-parallel-coordinate-trees. In: Proc. SIGMOD (2013)
Hu, Y., Ravada, S., Anderson, R., Bamba, B.: Topological relationship query processing for complex regions in oracle spatial. In: Proc. ACM GIS, pp. 3–12 (2012)
Weber, R., Schek, H.J., Blott, S.: A quantitative analysis and performance study for similarity-search methods in high-dimensional spaces. In: Proc. VLDB, pp. 194–205 (1998)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Schubert, E., Zimek, A., Kriegel, HP. (2013). Geodetic Distance Queries on R-Trees for Indexing Geographic Data. In: Nascimento, M.A., et al. Advances in Spatial and Temporal Databases. SSTD 2013. Lecture Notes in Computer Science, vol 8098. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40235-7_9
Download citation
DOI: https://doi.org/10.1007/978-3-642-40235-7_9
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-40234-0
Online ISBN: 978-3-642-40235-7
eBook Packages: Computer ScienceComputer Science (R0)