Aggregate Processing of Planar Points

  • Yufei Tao
  • Dimitris Papadias
  • Jun Zhang
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2287)


Aggregate window queries return summarized information about objects that fall inside a query rectangle (e.g., the number of objects instead of their concrete ids). Traditional approaches for processing such queries usually retrieve considerable extra information, thus compromising the processing cost. The paper addresses this problem for planar points from both theoretical and practical points of view. We show that, an aggregate window query can be answered in logarithmic worst-case time by an indexing structure called the aPtree. Next we study the practical behavior of the aP-tree and propose efficient cost models that predict the structure size and actual query cost. Extensive experiments show that the aP-tree, while involving more space consumption, accelerates query processing by up to an order of magnitude compared to a specialized method based on R-trees. Furthermore, our cost models are accurate and can be employed for the selection of the most appropriate method, balancing the space and query time tradeoff.


Query Processing Query Performance Planar Point Node Access Minimum Bound Rectangle 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [BGO+96]
    Becker, B., Gschwind, S., Ohler, T., Seeger, B., Widmayer, P. An Asymptotically Optimal Multiversion B-Tree. VLDB Journal, Vol. 5(4), pp. 264–275, 1996.CrossRefGoogle Scholar
  2. [BKS+90]
    Beckmann, B., Kriegel, H.P., Schneider, R, Seeger, B. The R*-tree: An Efficient and Robust Access Method. ACM SIGMOD, 1990.Google Scholar
  3. [BS96]
    Bercken van den, J., Seeger, B. Query Processing Techniques for Multiversion Access Methods. VLDB, 1996.Google Scholar
  4. [JL98]
    Jurgens, M., Lenz, H. The Ra*-tree: An Improved R-tree with Materialized Data for Supporting Range Queries on OLAP-Data. DEXA Workshop, 1998.Google Scholar
  5. [KF93]
    Kamel, I., Faloutsos, C. On Packing R-trees. CIKM, 1993.Google Scholar
  6. [KGT+]
    Kollios, G., Gunopulos, D., Tsotras, V., Dellis, A., Hadjieleftheriou, M. Indexing Animated Objects Using Spatiotemporal Access Methods. To appear in IEEE TKDE.Google Scholar
  7. [KKK99]
    Kim, J., Kang, S., Kim, M. Effective Temporal Aggregation using Pointbased Trees. DEXA, 1999.Google Scholar
  8. [KS95]
    Kline, N., Snodgrass, R. Computing Temporal Aggregates. IEEE ICDE, 1995.Google Scholar
  9. [KTF98]
    Kumar, A, Tsotras, V., Faloutsos, C. Design Access Methods for Bitemporal Databases. IEEE TKDE 10(1): 1–20, 1998.Google Scholar
  10. [LM01]
    Lazaridis, I., Mehrotra, S. Progressive Approximate Aggregate Queries with a Multi-Resolution Tree Structure. ACM SIGMOD, 2001.Google Scholar
  11. [PKZ+01]
    Papadias, D., Kalnis, P., Zhang, J., Tao, Y. Efficient OLAP Operations in Spatial Data Warehouses. SSTD, 2001.Google Scholar
  12. [PT01]
    Pedersen, T., Tryfona, N. Pre-aggregation in Spatial Data Warehouses. SSTD, 2001.Google Scholar
  13. [PTK+02]
    Papadias, D., Tao, Y., Kalnis, P., Zhang, J. Indexing Spatio-temporal Data Warehouses. IEEE ICDE, 2002.Google Scholar
  14. [ST97]
    Salzberg, B., Tsotras, V. A Comparison of Access Methods for Temporal Data. ACM Computing Surveys, 31(2): 158–221, 1997.CrossRefGoogle Scholar
  15. [TP01]
    Tao, Y., Papadias, D. The MV3R-tree: A Spatio-Temporal Access Method for Timestamp and Interval Queries. VLDB, 2001.Google Scholar
  16. [TPZ02]
    Tao, Y., Papadias, D., Zhang, J. Efficient Cost Models for Overlapping and Multi-Version Structures. IEEE ICDE, 2002.Google Scholar
  17. [TS96]
    Theodoridis, Y., Sellis, T. A Model for the Prediction of R-tree Performance. ACM PODS, 1996.Google Scholar
  18. [TSN99]
    Theodoridis, Y., Silva, J. Nascimento, M. On the Generation of Spatiotemporal Datasets. SSD, 1999.Google Scholar
  19. [VV97]
    Varman, P., Verma, R. An Efficient Multiversion Access Structure. IEEE TKDE, Vol. 9, No. 3, pp. 391–409, 1997.Google Scholar
  20. [Yao78]
    Yao, A. Random 2-3 Trees. Acta Informatica, Vol. 2(9), 159–179, 1978.CrossRefGoogle Scholar
  21. [YW01]
    Yang, J., Widom, J. Incremental Computation and Maintenance of Temporal Aggregates. IEEE ICDE, 2001.Google Scholar
  22. [ZMT+01]
    Zhang, D., Markowetz, A., Tsotras, V., Gunopulos, D., Seeger, B. Efficient Computation of Temporal Aggregates with Range Predicates. ACM PODS, 2001.Google Scholar
  23. [ZTS02]
    Zhang, D., Tsotras, V., Seeger, B. Efficient Temporal Join Processing Using Indices. IEEE ICDE, 2002.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Yufei Tao
    • 1
  • Dimitris Papadias
    • 1
  • Jun Zhang
    • 1
  1. 1.Department of Computer ScienceHong Kong University of Science and TechnologyHong Kong

Personalised recommendations