On Multi-Way Spatial Joins with Direction Predicates

  • Hongjun Zhu
  • Jianwen Su
  • Oscar H. Ibarra
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2121)

Abstract

Spatial joins are fundamental in spatial databases. Over the last decade, the primary focus of research has been on joins with the predicate “region intersection.” In modern database applications involving geospatial data such as GIS, efficient evaluation of joins with other spatial predicates is yet to be fully explored. In addition, most existing join algorithms were developed for two-way joins. Traditionally, a multi-way join is treated as a sequence of two-way joins. The goal of this paper is to study evaluation of multi-way spatial joins with direction predicates: complexity bounds and efficient algorithms. We first give I/O efficient plane sweeping based algorithms for 2-way direction joins and show that by combining the plane sweeping technique with external priority search trees, a 2-way direction join of N-tuple relations can be evaluated in O(Nlogb N/M + k) I/Os in the worst case, where M is the size of the memory, b is the page size and k is the result size. The algorithms are then extended to perform a subclass of multi-way direction joins called “star joins”. We show that the I/O complexity of evaluating an way star join of N-tuple relations is O(mN logb MN +K + k), where mN 2 is the size of the intermediate result, M, b and k (= N m) are the same as above. We also apply the algorithm for star joins to evaluate a more general case of multi-way joins, which are star connections of star joins and show that this can be done in polynomial time. In the general case, we show that testing emptiness of a multi-way direction join is NP-complete. This lower bound holds even when in the join predicate (1) only one attribute for each relation is involved, and (2) each spatial attribute occurs a bounded number of times. It implies that join evaluation in these cases is NP-hard.

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References

  1. [APR+98]
    L. Arge, O Procopiuc, S. Ramaswamy, T. Suel, and J. Vitter. Scalable sweeping-based spatial join. In Proc. Int. Conf. on Very Large Data Bases, 1998.Google Scholar
  2. [Arg95]
    L. Arge. The buffer tree: A new technique for optimal I/O-algorithms. In Proc. Workshop on Algorithms and Data structures, 1995.Google Scholar
  3. [ASV99]
    L. Arge, V. Samoladas, and J. S. Vitter. On two-dimensional indexibility and optimal range search indexing. In Proc. ACM Symp. on Principles of Database Systems, 1999.Google Scholar
  4. [AV96]
    L. Arge and J. S. Vitter. Optimal dynamic interval management in external memory. In Proc. IEEE Symp. on Foundations of Computer Science, 1996.Google Scholar
  5. [BHF93]
    L. Becker, K. Hinriches, and U. Finke. A new algorithm for computing joins with grid files. In Proc. Int. Conf. on Data Engineering, pages 190–197, 1993.Google Scholar
  6. [BKS93]
    T. Brinkhoff, H-P. Kriegel, and B. Seeger. Efficient processing of spatial join using R-trees. In Proc. ACM SIGMOD Int. Conf. on Management of Data, 1993.Google Scholar
  7. [BKSS94]
    T. Brinkhoff, H-P. Kriegel, R. Schneider, and B. Seeger. Multi-step processing of spatial joins. In Proc. ACM SIGMOD Int. Conf. on Management of Data, 1994.Google Scholar
  8. [Dut89]
    S. Dutta. Qualitative spatial reasoning: a semi-qualitative approach using fuzzy logic. In Proc. Symp. on Large Spatial Databases, 1989.Google Scholar
  9. [Fra92]
    A. U. Frank. Qualitative spatial reasoning about distances and directions in geographic space. Journal of Visual Languages and Computing, 3:343–371, 1992.CrossRefGoogle Scholar
  10. [GTVV93]
    M. T. Goodrich, J.-J. Tsay, D. E. Vengroff, and J. S. Vitter. External-memory computational geometry. In Proc. IEEE Symp. on Foundations of Computer Science, pages 714–723, 1993.Google Scholar
  11. [Gün93]
    O. Günther. Efficient computation of spatial joins. In Proc. Int. Conf. on Data Engineering, pages 50–59, 1993.Google Scholar
  12. [Her93]
    D. Hernandez. Mantaining qualitative spatial knowledge. In Proceedings of the European Conference on Spatial Information Theory, 1993.Google Scholar
  13. [HJR97]
    Y.-W. Huang, N. Jing, and E. A. Rundensteiner. Spatial joins using R-trees: Breadth-first traversal with global optimizations. In Proc. Int. Conf. on Very Large Data Bases, 1997.Google Scholar
  14. [HS98]
    G. R. Hjaltason and H. Samet. Incremental distance join algorithms for spatial databases. In Proc. ACM SIGMOD Int. Conf. on Management of Data, pages 237–248, 1998.Google Scholar
  15. [LR96]
    M-L. Lo and C. V. Ravishankar. Spatial hash-joins. In Proc. ACM SIGMOD Int. Conf. on Management of Data, 1996.Google Scholar
  16. [McC85]
    E. M. McCreight. Priority search trees. SIAM Journal of COmputing, 14:257–276, 1985.MATHCrossRefMathSciNetGoogle Scholar
  17. [MP98]
    N. Mamoulis and D. Papadias. Constraint-based algorithms for computing clique intersection joins. In Proc. ACM Symp. on Advances in Geographic Information Systems, 1998.Google Scholar
  18. [MP99]
    N. Mamoulis and D. Papadias. Integration of spatial join algorithms for processing multiple inputs. In Proc. ACM SIGMOD Int. Conf. on Management of Data, 1999.Google Scholar
  19. [PD96]
    J. M. Patel and D. J. DeWitt. Partition based spatial-merge join. In Proc. ACM SIGMOD Int. Conf. on Management of Data, 1996.Google Scholar
  20. [PMT99]
    D. Papadias, N. Mamoulis, and Y. Theodoridis. Processing and optimization of multiway spatial joins using R-trees. In Proc. ACM Symp. on Principles of Database Systems, 1999.Google Scholar
  21. [PRS99]
    A. Papadopoulos, P. Rigaux, and M. Scholl. A performance evaluation of spatial join processing strategies. In Proc. Symp. on Large Spatial Databases, pages 286–307, 1999.Google Scholar
  22. [PS93]
    D. Papadias and T. Sellis. The semantics of relations in 2D space using represectative points: spatial indexes. In Proceedings of the European Conference on Spatial Information Theory, 1993.Google Scholar
  23. [PTS94]
    D. Papadias, Y. Theodoridis, and T. Sellis. The retrieval of direction relations using r-trees. In Proc. 5th Int. Conf. Database and Expert Systems Applications, pages 173–182, 1994.Google Scholar
  24. [Rot91]
    D. Rotem. Spatial join indices. In Proc. Int. Conf. on Data Engineering, pages 500–509, 1991.Google Scholar
  25. [SA97]
    J. C. Shafer and R. Agrawal. Parallel algorithms for high dimensional similarity joins for data mining applications. In Proc. Int. Conf. on Very Large Data Bases, pages 176–185, 1997.Google Scholar
  26. [SH76]
    M. I. Shamos and D. Hoey. Geometric intersection problems. In Proc. IEEE Symp. on Foundations of Computer Science, pages 208–215, 1976.Google Scholar
  27. [Vit98]
    J. Vitter. External memory algorithms: Dealing with massive data. In Proc. ACM Symp. on Principles of Database Systems, pages 233–243, 1998.Google Scholar
  28. [ZS98]
    G. Zimbrao and J. M. Souza. A raster approximation for processing of spatial joins. In Proc. Int. Conf. on Very Large Data Bases, pages 558–569, 1998.Google Scholar
  29. [ZSI99]
    H. Zhu, J. Su, and O.H. Ibarra. An index structure for spatial joins in linear constraint databases. In Proc. Int. Conf. on Data Engineering, 1999.Google Scholar
  30. [ZSI00a]
    H. Zhu, J. Su, and O. H. Ibarra. Extending rectangle join algorithms for rectilinear polygons. In Proc. Int. Conf. on WebInformation Management, 2000.Google Scholar
  31. [ZSI00b]
    H. Zhu, J. Su, and O. H. Ibarra. Towards spatial joins for polygons. In Proc. Int. Conf. on Statistical and Scientific Database Management, 2000.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Hongjun Zhu
    • 1
  • Jianwen Su
    • 1
  • Oscar H. Ibarra
    • 1
  1. 1.Department of Computer ScienceUniversity of CaliforniaSanta BarbaraUSA

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