Geodetic Distance Queries on R-Trees for Indexing Geographic Data

  • Erich Schubert
  • Arthur Zimek
  • Hans-Peter Kriegel
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8098)


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.


Index Structure Range Query Query Point Geodetic Data Neighbor Query 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    Sinnott, R.: Virtues of the haversine. Sky and Telescope 68, 158–159 (1984)Google Scholar
  2. 2.
    Vincenty, T.: Direct and inverse solutions of geodesics on the ellipsoid with application of nested equations. Survey Review 23(176), 88–93 (1975)Google Scholar
  3. 3.
    Finkel, R.A., Bentley, J.L.: Quad trees. A data structure for retrieval on composite keys. Acta Informatica 4(1), 1–9 (1974)zbMATHCrossRefGoogle Scholar
  4. 4.
    Bentley, J.L.: Multidimensional binary search trees used for associative searching. Commun. ACM 18(9), 509–517 (1975)MathSciNetzbMATHCrossRefGoogle Scholar
  5. 5.
    Kunszt, P., Szalay, A., Thakar, A.: The hierarchical triangular mesh. Mining the Sky, 631–637 (2001)Google Scholar
  6. 6.
    Morton, G.M.: A computer oriented geodetic data base and a new technique in file sequencing. Technical report, International Business Machines Co. (1966)Google Scholar
  7. 7.
    Guttman, A.: R-Trees: A dynamic index structure for spatial searching. In: Proc. SIGMOD, pp. 47–57 (1984)Google Scholar
  8. 8.
    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)Google Scholar
  9. 9.
    White, D.A., Jain, R.: Similarity indexing with the SS-tree. In: Proc. ICDE, pp. 516–523 (1996)Google Scholar
  10. 10.
    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)Google Scholar
  11. 11.
    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)Google Scholar
  12. 12.
    Ciaccia, P., Patella, M.: Bulk loading the M-tree. In: Proc. ADC (1998)Google Scholar
  13. 13.
    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)CrossRefGoogle Scholar
  14. 14.
    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)Google Scholar
  15. 15.
    Katayama, N., Satoh, S.: The SR-tree: An index structure for high-dimensional nearest neighbor queries. In: Proc. SIGMOD, pp. 369–380 (1997)Google Scholar
  16. 16.
    Microsoft Corporation: Whitepaper New Spatial Features in SQL Server 2012 (2012)Google Scholar
  17. 17.
    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)Google Scholar
  18. 18.
    PostGIS project: Postgis 2.0 manual,
  19. 19.
    IBM Informix: IBM Informix Geodetic DataBlade Module User’s GuideGoogle Scholar
  20. 20.
    Lukatela, H.: Hipparchus geopositioning model: An overview. In: Proc. Auto. Cartography, vol. 8, pp. 87–96 (1987)Google Scholar
  21. 21.
    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)Google Scholar
  22. 22.
    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)CrossRefGoogle Scholar
  23. 23.
    Achtert, E., Kriegel, H.P., Schubert, E., Zimek, A.: Interactive data mining with 3d-parallel-coordinate-trees. In: Proc. SIGMOD (2013)Google Scholar
  24. 24.
    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)Google Scholar
  25. 25.
    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)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Erich Schubert
    • 1
  • Arthur Zimek
    • 1
  • Hans-Peter Kriegel
    • 1
  1. 1.Ludwig-Maximilians-Universität MünchenMünchenGermany

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