A Simple, Compact and Dynamic Partition Scheme Based on Co-centric Spheres

  • Dimitris G. Kapopoulos
  • Michael Hatzopoulos
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2563)


This paper describes the MB-tree, a symmetric data structure for the organization of multidimensional points. The proposed structure is based on a new partition scheme that divides the data space into cocentric partitions in an ‘onion’-like manner and ensures that partitions that are spatially successive in a multidimensional space are also successive in terms of their storage. Each partition is characterized from a distance from a fixed point and the resultant structure is k-d-cut, adaptable and brickwall. It has very efficient point search and adapts nicely to dynamic data spaces with high frequency of insertions and deletions and to non-uniformly distributed data. The organization is an extension of B-trees in order to index multidimensional data when the data space is metric. The indexing mechanism is organized as a B+-tree and compared to similar approaches the size of the index is minimum. Although the MB-tree has a simple structure, its performance compares to the one of other more complex indexes. We present the partition scheme and the index, describe its dynamic behavior, examine algorithms for several types of queries and provide experimental results.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Boehm C., Berchtold S. and Keim D.A.: “Searching in High-Dimensional Spaces: Index Structures for Improving the Performance of Multimedia Data-bases”, ACM Computing Surveys, Vol.33, No.3, pp. 322–373, 2001.CrossRefGoogle Scholar
  2. [2]
    Ciaccia P., Patella M. and Zezula P.: “M-tree: an Efficient Access Method for Similarity Search in Metric Spaces”, Proceedings 23rd VLDB Conference, pp. 426–435, 1997.Google Scholar
  3. [3]
    Dandamundi S. and Sorenson P.: “An empirical performance comparison of some variations of the k-d-tree and BD-tree”, International Journal of Computer and Information Sciences, Vol.14, pp. 135–159, 1985.CrossRefGoogle Scholar
  4. [4]
    Dandamundi S. and Sorenson P.: “Algorithms for BD-trees”, Software Practice and Experience, Vol. 16, No.12, pp. 1077–1096, 1986.CrossRefGoogle Scholar
  5. [5]
    Faloutsos C.: “Searching Multimedia Databases by Content”, Kluwer, Boston, 1996.Google Scholar
  6. [6]
    Freeston M.: “The BANG file: a New Kind of Grid File”, Proceedings 1987 ACM SIGMOD Conference, pp. 260–269, 1987.Google Scholar
  7. [7]
    Gaede V. and Gunther O.: “Multidimensional Access Methods”, ACM Computing Surveys, Vol. 30, No.2, pp. 170–231, 1998.CrossRefGoogle Scholar
  8. [8]
    Kapopoulos D.G. and Hatzopoulos M.: “The Gr-Tree: the Use of Active Regions in G-Trees”, Proceedings 3rd ADBIS Conference, pp. 141–155, 1999.Google Scholar
  9. [9]
    Kapopoulos D.G. and Hatzopoulos M.: “The Arc-Tree: a Novel Symmetric Access Method for Multidimensional Data”, Proceedings 5th ADBIS Conference, pp. 294–307, 2001.Google Scholar
  10. [10]
    Kumar A.: “G-Tree: A New Data Structure for Organizing Multidimensional Data”, IEEE Transactions on Knowledge and Data Engineering, Vol.6, No.2, pp. 341–347, 1994.CrossRefGoogle Scholar
  11. [11]
    Lang C. and Singh A.: “A Framework for Accelerating High-dimensional NN-queries”, Technical Report TRCS01-04, University of California, Santa Bar-bara, 2002.Google Scholar
  12. [12]
    Nievergelt J., Hintenberger H. and Sevcik K.C.: “The Grid File: an Adaptable, Symmetric Multikey File Structure”, ACM Transactions Database Systems, Vol. 9, No.1, pp. 38–71, 1984.CrossRefGoogle Scholar
  13. [13]
    Orenstein J. and Merrett T.: “A Class of Data Structures for Associative Searching”, Proceedings 3rd ACM PODS Symposium, pp. 181–190, 1984.Google Scholar
  14. [14]
    Orenstein J.: “Spatial Query Processing in an Object-Oriented Database System”, Proceedings 1986 ACM SIGMOD Conference, pp. 326–336, 1986.Google Scholar
  15. [15]
    Robinson J.T.: “The K-D-B-tree: A Search Structure for Large Multidimensional Dynamic Indexes”, Proceedings 1981 ACM SIGMOD Conference, pp. 10–18, 1981.Google Scholar
  16. [16]
    Samet H.: “Spatial Databases”, Proceedings 23rd VLDB Conference, pp. 63–129, 1997.Google Scholar
  17. [17]
    Manolopoulos Y., Theodoridis Y. and Tsotras V. J.: “Advanced Database Indexing”, Kluwer, Boston, 1999.Google Scholar
  18. [18]
    Traina C., Traina A., Seeger B. and Faloutsos C.: “Slim-Trees: High Performance Metric Trees Minimizing Overlap Between Nodes”, Proceedings 7th EDBT Conference, 2000.Google Scholar
  19. [19]
    White D. and Jain R.: “Similarity Indexing with the SS-tree”, Proceedings 12th ICDE Conference, pp. 516–523, 1996.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Dimitris G. Kapopoulos
    • 1
  • Michael Hatzopoulos
    • 1
  1. 1.Department of Informatics and TelecommunicationsUniversity of AthensAthensGreece

Personalised recommendations