Skip to main content

R-Trees – A Dynamic Index Structure for Spatial Searching

  • Reference work entry

Synonyms

R-tree

Definition

One of the most influential access methods in the area of Spatial Data Management is the R-tree structure proposed by Guttman in 1984 [8]. It is a hierarchical data structure based on B+-trees, used for the dynamic organization of a set of d-dimensional geometric objects. The original R-tree was designed for efficiently retrieving geometric objects contained within a given query range. Every object in the R-tree is represented by a minimum bounding d-dimensional rectangle (for simplicity, MBRs in the sequel). Data objects are grouped into larger MBRs forming the leaf nodes of the tree. Leaf nodes are grouped into larger internal nodes. The process continues recursively until the last group of nodes that form the root of the tree. The root represents an MBR that encloses all objects and nodes indexed by the tree, and each node corresponds to the MBR that bounds its children (cf. Fig. 1). A range query can be answered efficiently by traversing the tree...

This is a preview of subscription content, log in via an institution.

Recommended Reading

  1. Ang, C.-H., Tan, T.C.: New linear node splitting algorithm for r-trees. In: Proc. of Symposium on Advances in Spatial Databases (SSD), Berlin, Germany, 15–18 July 1997, pp. 339–349

    Google Scholar 

  2. Beckmann, N., Kriegel, H., Schneider, R., Seeger, B.: The R*-tree: An efficient and robust access method for points and rectangles. In: Proc. of ACM Management of Data (SIGMOD), New Jersey, USA, 23–25 May 1990, pp. 220–231

    Google Scholar 

  3. Brakatsoulas, S., Pfoser, D., Theodoridis, Y: Revisiting r-tree construction principles. In: Proc. of the East European Conference on Advances in Databases and Information Systems, Bratislava, Slovakia, 8–11 Sept 2002, pp. 149–162

    Google Scholar 

  4. Driscoll, J.R., Sarnak, N., Sleator, D.D., Tarjan, R.E.: Making data structures persistent. J. Comp. Syst. Sci. 38(1):86–124 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  5. Faloutsos, C., Kamel, I.: Beyond uniformity and independence: analysis of r-trees using the concept of fractal dimension. In: Proc. of ACM Symposium on Principles of Database Systems (PODS), Minnesota, USA, 24–26 May 1994, pp. 4–13

    Google Scholar 

  6. Faloutsos, C., Sellis, T., Roussopoulos, N.: Analysis of object oriented spatial access methods. SIGMOD Record 16(3):426–439 (1987)

    Article  Google Scholar 

  7. Garcia, Y.J., Lopez, M.A., Leutenegger, S.T.: On optimal node splitting for r-trees. In: Proc. of Very Large Data Bases (VLDB), New York, USA, 24–27 Aug 1998, pp. 334–344

    Google Scholar 

  8. Guttman, A.: R-trees: A dynamic index structure for spatial searching. In: Proc. of ACM Management of Data (SIGMOD), Massachusetts, USA, 18–21 June 1984, pp. 47–57

    Google Scholar 

  9. Hadjieleftheriou, M., Hoel, E., Tsotras, V.J.: Sail: A library for efficient application integration of spatial indices. In: Proc. of Scientific and Statistical Database Management (SSDBM), Santorini Island, Greece, 21–23 2004, pp. 135–138

    Google Scholar 

  10. Hadjieleftheriou, M., Kollios, G., Tsotras, V.J., Gunopulos, D.: Efficient indexing of spatiotemporal objects. In: Proc. of Extending Database Technology (EDBT), Prague, 24–28 Mar 2002, pp. 251–268

    Google Scholar 

  11. Huang, P.W., Lin, P.L., Lin, H.Y.: Optimizing storage utilization in r-tree dynamic index structure for spatial databases. J. Syst. Softw. 55(3):291–299 (2001)

    Article  Google Scholar 

  12. Kamel, I., Faloutsos, C.: On packing r-trees. In: Proc. of Conference on Information and Knowledge Management (CIKM), Washington DC, USA, 1–5 Nov 1993, pp. 490–499

    Google Scholar 

  13. Kamel, I., Faloutsos, C.: Hilbert r-tree: An improved r-tree using fractals. In: Proc. of Very Large Data Bases (VLDB), Santiago de Chile, Chile, 12–15 Sept 1994, pp. 500–509

    Google Scholar 

  14. Kollios, G., Tsotras, V.J., Gunopulos, D., Delis, A., Hadjieleftheriou, M.: Indexing animated objects using spatiotemporal access methods. IEEE Transactions Knowl. Data Eng. (TKDE) 13(5):758–777 (2001)

    Google Scholar 

  15. Kolovson, C., Stonebraker, M.: Segment Indexes: Dynamic indexing techniques for multi-dimensional interval data. In: Proc. of ACM Management of Data (SIGMOD),Colorado, USA, 29–31 May 1991, pp. 138–147

    Google Scholar 

  16. Kumar, A., Tsotras, V.J., Faloutsos, C.: Designing access methods for bitemporal databases. IEEE Transactions Knowl. Data Eng. (TKDE) 10(1):1–20 (1998)

    Article  Google Scholar 

  17. Leutenegger, S.T., Edgington, J.M., Lopez, M.A.: Str: A simple and efficient algorithm for r-tree packing. In: Proc. of International Conference on Data Engineering (ICDE), Birmingham, UK, 7–11 Apr 1997, pp. 497–506

    Google Scholar 

  18. Manolopoulos, Y., Nanopoulos, A., Papadopoulos, A.N., Theodoridis, Y.: Rtrees: Theory and Applications. Springer, Germany (2005)

    Google Scholar 

  19. Nanopoulos, A., Vassilakopoulos, M., Manolopoulos, Y.: Performance evaluation of lazy deletion methods in r-trees. GeoInformatica 7(4):337–354 (2003)

    Article  Google Scholar 

  20. Roussopoulos, N., Leifker, D.: Direct spatial search on pictorial databases using packed r-trees. SIGMOD Record 14(4):17–31 (1985)

    Article  Google Scholar 

  21. Saltenis, S., Jensen, C.S., Leutenegger, S.T., Lopez, M.A.: Indexing the positions of continuously moving objects. SIGMOD Record 29(2):331–342 (2000)

    Google Scholar 

  22. Schreck, T., Chen, Z.: Branch grafting method for r-tree implementation. J. Syst. Softw. 53(1):83–93 (2000)

    Article  Google Scholar 

  23. Sellis, T., Roussopoulos, N., Faloutsos, C: The r+-tree: A dynamic index for multi-dimensional objects. In: Proc. of Very Large Data Bases (VLDB), pp. 507–518 (1987)

    Google Scholar 

  24. Tao, Y., Papadias, D.: MV3R-Tree: A spatio-temporal access method for timestamp and interval queries. In: Proc. of Very Large Data Bases (VLDB), pp. 431–440 (2001)

    Google Scholar 

  25. Theodoridis, Y.: The R-tree-Portal. (2003)

    Google Scholar 

  26. Theodoridis, Y., Sellis, T.: A model for the prediction of r-tree performance. In: Proc. of ACM Symposium on Principles of Database Systems (PODS), pp. 161–171 (1996)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2008 Springer-Verlag

About this entry

Cite this entry

Hadjieleftheriou, M., Manolopoulos, Y., Theodoridis, Y., Tsotras, V. (2008). R-Trees – A Dynamic Index Structure for Spatial Searching. In: Shekhar, S., Xiong, H. (eds) Encyclopedia of GIS. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-35973-1_1151

Download citation

Publish with us

Policies and ethics