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Optimizing spatial Min/Max aggregations

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Abstract.

Aggregate computation over a collection of spatial objects appears in many real-life applications. Aggregates are computed on values (weights) associated with spatial objects, for example, the temperature or rainfall over the area covered by the object. In this paper we concentrate on MIN/MAX aggregations: “given a query rectangle, find the minimum/maximum weight among all objects intersecting the query rectangle.” Traditionally such queries have been performed as range searches. Assuming that objects are indexed by a spatial access method (SAM), the MIN/MAX is computed while retrieving those objects intersecting the query interval. This requires effort proportional to the number of objects satisfying the query, which may be large. A better approach is to maintain aggregate information among the index nodes of the spatial access method; then various index paths can be eliminated during the range search. Yet another approach is to build a specialized index that maintains the aggregate incrementally. We propose four novel optimizations for improving the performance of MIN/MAX queries when an index structure (traditional or specialized) is present. Moreover, we introduce the MR-tree, an R-tree-like dynamic specialized index that incorporates all four optimizations. Our experiments show that the MR-tree offers drastic performance improvement over previous solutions. As a byproduct of this work we present an optimized version of the MSB-tree, an index that has been proposed for the MIN/MAX computation over 1D interval objects.

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References

  1. Agarwal P, Erickson J (1998) Geometric range searching and its relatives. In: Chazelle B, Goodman E, Pollack R (eds) Advances in discrete and computational geometry. American Mathematical Society, Providence, RI

  2. Aoki PM (1999) How to avoid building datablades that know the value of everything and the cost of nothing. In: Proceedings of the international conference on scientific and statistical database management (SSDBM), pp 122-133

  3. Aref WG, Samet H (1990) Efficient processing of window queries in the pyramid data structure. In: ACM international symposium on principles of database systems (PODS), pp 265-272

  4. Bentley JL (1980) Multidimensional divide-and-conquer. Commun ACM 23(4):214-229

    Google Scholar 

  5. Beckmann N, Kriegel HP, Schneider R, Seeger B (1990) The R*-tree: an efficient and robust access method for points and rectangles. In: Proceedings of the ACM/SIGMOD annual conference on management of data (SIGMOD), pp 322-331

  6. Chung C, Chun S, Lee J, Lee S (2001) Dynamic update cube for range-sum queries. In: Proceedings of the international conference on very large data bases (VLDB), pp 521-530

  7. Chan C, Ioannidis YE (1999) Hierarchical prefix cubes for range-sum queries. In: Proceedings of the international conference on very large data bases (VLDB), pp 675-686

  8. Geffner S, Agrawal D, El Abbadi A (2000) The dynamic data cube. In: Proceedings of the international conference on extending database technology (EDBT), pp 237-253

  9. Geffner S, Agrawal D, El Abbadi A, Smith T (1999) Relative prefix sums: an efficient approach for querying dynamic OLAP data cubes. In: Proceedings of the international conference on data engineering (ICDE), pp 328-335

  10. Gray J, Bosworth A, Layman A, Piramish H (1996) Data cube: a relational aggregation operator generalizing group-by, cross-tab, and sub-totals. In: Proceedings of the international conference on data engineering (ICDE), pp 152-159

  11. Guttman A (1984) R-trees: a dynamic index structure for spatial searching. In: Proceedings of the ACM/SIGMOD annual conference on management of data (SIGMOD), pp 47-57

  12. Ho C, Agrawal R, Megiddo N, Srikant R (1997) Range queries in OLAP data cubes. In: Proceedings of the ACM/SIGMOD annual conference on management of data (SIGMOD), pp 73-88

  13. Ho CT, Agrawal R, Megiddo N, Tsay JJ (1997) Techniques for speeding up range-max queries in OLAP data cubes. IBM Research Report

  14. International Research Institute for Climate Prediction (2003) NOAA NCEP CPC merged analysis monthly December 2003 release (version 1). URL=http://iridl.ldeo.columbia.edu/SOURCES/.NOAA/ .NCEP/.CPC/.Merged\_Analysis/.monthly/.v0312/

  15. Jürgens M, Lenz HJ (1998) The R a *-tree: an improved R-tree with materialized data for supporting range queries on OLAP-data. In: International workshop on database and expert systems applications (DEXAW)

  16. Jürgens M, Lenz HJ (1999) PISA: Performance models for index structures with and without aggregated data. In: Proceedings of the international conference on scientific and statistical database management (SSDBM), pp 78-87

  17. Lazaridis I, Mehrotra S (2001) Progressive approximate aggregate queries with a multi-resolution tree structure. In: Proceedings of the ACM/SIGMOD annual conference on management of data (SIGMOD), pp 401-412

  18. Matousek J (1994) Geometric range searching. ACM Comput Surv 26(4):421-461

    Google Scholar 

  19. Mehlhorn K (1984) Multi-dimensional searching and computational geometry. Data Structures and Algorithms 3: Multi-Dimensional Searching and Computational Geometry. Springer, New York, ISBN 0387136428

    Google Scholar 

  20. Papadias D, Kalnis P, Zhang J, Tao Y (2001) Efficient OLAP operations in spatial data warehouses. In: Proceedings of the symposium on spatial and temporal databases (SSTD), pp 443-459

  21. Preparata F, Shamos M (1985) Computational geometry: an introduction. Springer, Berlin Heidelberg New York

    Google Scholar 

  22. Papadias D, Tao Y, Kalnis P, Zhang J (2002) Indexing spatio-temporal data warehouses. In: Proceedings of international conference on data engineering (ICDE), pp 166-175

  23. Roussopoulos N, Kotidis Y, Roussopoulos M (1997) Cubetree: organization of and bulk incremental updates on the data cube. In: Proceedings of the ACM/SIGMOD annual conference on management of data (SIGMOD), pp 89-99

  24. Sellis TK, Roussopoulos N, Faloutsos C (1987) The R+-tree: a dynamic index for multi-dimensional objects. In: Proceedings of the international conference on very large data bases (VLDB), pp 507-518

  25. Yang J, Widom J (2000) Temporal view self-maintenance. In: Proceedings of the international conference on extending database technology (EDBT), pp 395-412

  26. Yang J, Widom J (2001) Incremental computation and maintenance of temporal aggregates. In: Proceedings of the international conference on data engineering (ICDE), pp 51-60

  27. Zhang D, Markowetz A, Tsotras VJ, Gunopulos D, Seeger B (2001) Efficient computation of temporal aggregates with range predicates. In: ACM international symposium on principles of database systems (PODS), pp 237-245

  28. Zhang D, Tsotras VJ (2001) Improving Min/Max aggregation over spatial objects. In: ACM international symposium on advances in geographic information systems (GIS), pp 88-93

  29. Zhang D, Tsotras VJ, Gunopulos D (2002) Efficient aggregation over objects with extent. In: ACM international symposium on principles of database systems (PODS), pp 121-132

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Authors and Affiliations

  1. College of Computer and Information Science, Northeastern University, 360 Huntington Ab., #202WVH, MA 02115, Boston, USA

    Donghui Zhang

  2. Department of Computer Science and Engineering, University of California, CA 92521, Riverside, USA

    Vassilis J. Tsotras

Authors
  1. Donghui Zhang
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  2. Vassilis J. Tsotras
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Corresponding author

Correspondence to Donghui Zhang.

Additional information

Received: 5 September 2003, Published online: 24 February 2005

Edited by: T. Özsu

Vassilis J. Tsotras: This research was supported by NSF Grants IIS-9907477, EIA-9983445, and IIS-0070135 and by the Department of Defense.

Correspondence to: D. Zhang

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Zhang, D., Tsotras, V.J. Optimizing spatial Min/Max aggregations. The VLDB Journal 14, 170–181 (2005). https://doi.org/10.1007/s00778-004-0142-4

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  • DOI: https://doi.org/10.1007/s00778-004-0142-4

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