Efficient Polygon Amalgamation Methods for Spatial OLAP and Spatial Data Mining

  • Xiaofang Zhou
  • David Truffet
  • Jiawei Han
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1651)


The polygon amalgamation operation computes the boundary of the union of a set of polygons. This is an important operation for spatial on-line analytical processing and spatial data mining, where polygons representing different spatial objects often need to be amalgamated by varying criteria when the user wants to aggregate or reclassify these objects. The processing cost of this operation can be very high for a large number of polygons. Based on the observation that not all polygons to be amalgamated contribute to the boundary, we investigate in this paper efficient polygon amalgamation methods by excluding those internal polygons without retrieving them from the database. Two novel algorithms, adjacency-based and occupancy-based, are proposed. While both algorithms can reduce the amalgamation cost significantly, the occupancy-based algorithm is particularly attractive because: 1) it retrieves a smaller amount of data than the adjacency-based algorithm; 2) it is based on a simple extension to a commonly used spatial indexing mechanism; and 3) it can handle fuzzy amalgamation.


spatial databases polygon amalgamation on-line analytical processing (OLAP) spatial indexing 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    D.J. Abel. SIRO-DBMS: A database toolkit for geographical information systems. Int. J. Geographical Information Systems, 4(3):443–464, 1989.Google Scholar
  2. [2]
    D.J. Abel and J.L. Smith. A data structure and algorithm based on a linear key for a rectangle retrieval problem. Computer Vision, Graphics and Image Processing, 24(1):1–13, 1983.CrossRefGoogle Scholar
  3. [3]
    T. Brinkho, H.P. Kriegel, and B. Seeger. Efficient processing of spatial joins using R-trees. In Proc. ACM SIGMOD Int. Conf. on Management of Data, pages 237–246, Washington, D. C., 1993.Google Scholar
  4. [4]
    S. Chaudhuri and U. Dayal. An overview of data warehousing and olap technology. SIGMOD Record, 26(1), 1997.Google Scholar
  5. [5]
    D.J. DeWitt and R.H. Gerber. Multiprocessor hash-based join algorithms. In Proc. 1985 Int. Conf. on Very Large Data Bases, pages 151–164, Austin, Texas, 1985.Google Scholar
  6. [6]
    M.J. Egenhofer. Reasoning about binary topological relationships. In LNCS 552: Proceedings of 2nd Int. Symp. on Spatial Databases (SSD’91), pages 143–160. Springer-Verlag, 1991.Google Scholar
  7. [7]
    M. Ester, H.-P. Kriegel, and J. Sander. Spatial data mining: A database approach. In LNCS 1262: Proceedings of the 5th Int. Symp. on Spatial Databases (SSD’97), pages 47–66, Berlin, Germany, 1997. Springer-Verlag.Google Scholar
  8. [8]
    M. Ester, H.-P. Kriegel, J. Sander, and X. XU. Density-connected sets and their application for trend detection in spatial databases. In Proc. 3rd Int. Conf. Knowledge Discovery and Data Mining (KDD’97), pages 10–15, Newport Beach, California, 1997.Google Scholar
  9. [9]
    V. Gaede. Optimal redundancy in spatial database systems. In M. J. Egenhofer and J. R. Herring, editors, LNCS 951: Proc. 4th Int. Symp. on Spatial Databases (SSD’95), pages 96–116, Portland, Maine, 1995. Springer-Verlag.Google Scholar
  10. [10]
    V. Gaede and O. Günther. Multidimensional access methods. ACM Computing Surveys, 30(2):170–231, 1998.CrossRefGoogle Scholar
  11. [11]
    O. Günther. Efficient computation of spatial joins. In Proceedings of 9th International Conference on Data Engineering, pages 50–59, Vienna, Austria, 1993.Google Scholar
  12. [12]
    R.H. Güting. An introduction to spatial database systems. /LDB Journal, 3(4):357–399, 1994.Google Scholar
  13. [13]
    A. Guttman. R-trees: A dynamic index structure for spatial searching. In Proc. ACM SIGMOD Int. Conf. on Management of Data, pages 47–54, Boston, Massachusetts, 1984.Google Scholar
  14. [14]
    J. Han, K. Koperski, and N. Stefanovic. GeoMiner: A system prototype for spatial data mining. In Proc. ACM SIGMOD Int. Conf. on Management of Data, pages 560–563, Tucson, Arizona, 1997.Google Scholar
  15. [15]
    J. Han, N. Stefanovic, and K. Koperski. Selective materialization: An efficient method for spatial data cube construction. In Proc. Pacific-Asia Conf. on Knowledge Discovery and Data Mining, pages 144–158, Melbourne, Australia, 1998.Google Scholar
  16. [16]
    V. Harinarayan, A. Rajaraman, and J.D. Ullman. Implementing data cubes efficiently. In Proc. 1996 ACM SIGMOD Int. Conf. on Management of Data, pages 206–216, Montreal, Canada, 1996.Google Scholar
  17. [17]
    W. Lu, J. Han, and B.C. Ooi. Knowledge discovery in large spatial databases. In Proc. Far East Workshop Geographic Information Systems, pages 275–289, Singapore, 1993.Google Scholar
  18. [18]
    R. Ng and J. Han. Efficient and efective clustering method for spatial data mining. In Proceedings of 1994 International Conference on Very Large Data Bases, pages 144–155, Santiago, Chile, 1994.Google Scholar
  19. [19]
    J. Orenstein. Redundancy in spatial databases. In Proc. ACM SIGMOD Int. Conf. on Management of Data, pages 294–305, Portland, Oregon, 1989.Google Scholar
  20. [20]
    J. Orenstein and F.A. Manola. Probe spatial data modeling and query processing in an image database application. IEEE Trans. on Software Eng., 14(5):611–629, 1988.CrossRefGoogle Scholar
  21. [21]
    J.M. Patel and D.J. DeWitt. Partition based spatial-merge join. In Proc. ACM SIGMOD Int. Conf. on Management of Data, pages 259–270, Montreal, Canada, 1996.Google Scholar
  22. [22]
    F.P. Preparata and M.I. Shamos. Computational Geometry: an introduction. Springer-Verlag, 1985.Google Scholar
  23. [23]
    H. Samet. Applications of Spatial Data Structures. Addison-Wesley, 1990.Google Scholar
  24. [24]
    T. Sellis, N. Roussopoulos, and C. Faloutsos. The R+-tree: a dynamic index for multi-dimensional objects. In Proc. 13th Int. Conf. on Very Large Data Bases, pages 3–11, Brighton, England, 1987.Google Scholar
  25. [25]
    D. Truffet and M.E. Orlowska. Two phase query processing with fuzzy approximations. In Proc. 4th ACM International Workshop on Advances in Geographic Information Systems (ACM-GIS’96), Rockville, USA, 1996.Google Scholar
  26. [26]
    X. Zhou, D.J. Abel, and D. Truffet. Data partitioning for parallel spatial join processing. In LNCS 1262: Proc. 5th Int. Symp. on Spatial Databases (SSD’97), pages 178–196, Berlin, Germany, 1997. Springer-Verlag.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Xiaofang Zhou
    • 1
  • David Truffet
    • 2
  • Jiawei Han
    • 3
  1. 1.Department of Computer Science and Electrical EngineeringUniversity of QueenslandBrisbaneAustralia
  2. 2.CSIRO Mathematical and Information SciencesCanberraAustralia
  3. 3.School of Computing SciencesSimon Fraser UniversityBurnanyCanada

Personalised recommendations