BIT Numerical Mathematics

, Volume 33, Issue 4, pp 561–579 | Cite as

Optimal dynamic multi-attribute hashing for range queries

  • Evan P. Harris
  • Kotagiri Ramamohanarao
Part I Computer Science

Abstract

This paper examines a partial match retrieval scheme which supports range queries for highly dynamic databases. The scheme relies on order preserving multi-attribute hashing. In general, designing optimal indexes is NP-hard. Greedy algorithms used to determine the optimal indexes for simple partial match queries are not directly applicable because there are a larger number of queries to consider in determining the optimal indexes. In this paper we present heuristic algorithms which provide near-optimal solutions. The optimisation scheme we propose can be used to design other dynamic file structures such as the grid file, BANG file and multilevel grid file to further enhance their retrieval performance taking into consideration the query distribution.

CR categories

D.4.3 E.2 E.5 F.2.2 H.3.2 H.3.3 

Keywords

partial-match retrieval multi-attribute hashing dynamic files range queries 

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References

  1. 1.
    A. V. Aho and J. D. Ullman:Optimal partial-match retrieval when fields are independently specified. ACM Transactions on Database Systems, 4(2): 168–179, June 1979.Google Scholar
  2. 2.
    J. L. Bentley:Multidimensional binary search trees used for associative searching. Communications of the ACM, 18(9): 509–517, September 1975.Google Scholar
  3. 3.
    J. L. Bentley:Multidimensional binary search trees in database applications. IEEE Transactions on Software Engineering, SE-5(4): 333–340, July 1979.Google Scholar
  4. 4.
    W. A. Burkhard:Interpolation-based index maintenance. BIT, 23: 274–294, 1983.Google Scholar
  5. 5.
    R. Cichelli:Minimal perfect hash functions made simple. Communications of the ACM, 23,(1): 17–19, January 1980.Google Scholar
  6. 6.
    R. Fagin, J. Nievergelt, and H. R. Strong:Extendible hashing — a fast access method for dynamic files. ACM Transactions on Database Systems, 4(3): 315–344, September 1979.Google Scholar
  7. 7.
    M. Freeston:The BANG file: a new kind of grid file. In U. Dayal and I. Traiger, editors, Proceedings of the 1987 ACM SIGMOD International Conference on the Management of Data, pages 260–269, San Francisco, California, USA, May 1987.Google Scholar
  8. 8.
    Y. Hsiao and A. L. Tharp:Adaptive hashing. Information Systems, 13(1): 111–127, 1988.Google Scholar
  9. 9.
    D. E. Knuth:Sorting and Searching, volume 3 ofThe Art of Computer Programming. Addison-Wesley, Reading, Massachusetts, USA, 1973.Google Scholar
  10. 10.
    H. Kriegel:Performance comparison of index structures for multi-key retrieval. In B. Yormark, editor, Proceedings of the 1984 ACM SIGMOD International Conference on the Management of Data, pages 186–196, Boston, MA, USA, June 1984.Google Scholar
  11. 11.
    H. Kriegel and B. Seeger:Multidimensional order preserving linear hashing with partial expansions. In G. Ausiello and P. Atzeni, editors, Proceedings of the International Conference on Database Theory, pages 203–220, Rome, Italy, September 1986. Also published as Lecture Notes in Computer Science 243 by Springer-Verlag.Google Scholar
  12. 12.
    P. Å. Larson:Linear hashing with partial expansions. In Proceedings of the Sixth International Conference on Very Large Data Bases, pages 224–232, Montreal, Canada, October 1980.Google Scholar
  13. 13.
    W. Litwin:Linear hashing: a new tool for file and table addressing. In Proceedings of the Sixth International Conference on Very Large Data Bases, pages 212–223, Montreal, Canada, October 1980.Google Scholar
  14. 14.
    J. W. Lloyd:Optimal partial-match retrieval. BIT, 20: 406–413, 1980.Google Scholar
  15. 15.
    J. W. Lloyd and K. Ramamohanarao:Partial-match retrieval for dynamic files. BIT, 22: 150–168, 1982.Google Scholar
  16. 16.
    S. Moran:On the complexity of designing optimal partial-match retrieval systems. ACM Transactions on Database Systems, 8(4): 543–551, December 1983.Google Scholar
  17. 17.
    S. Nahar, S. Sahni, and E. Shargowitz:Experiments with simulated annealing. In Proceedings of the 22nd Design Automation Conference, pages 748–752, 1985.Google Scholar
  18. 18.
    J. Nievergelt, H. Hinterberger, and K. C. Sevcik:The grid file: An adaptable symmetric multikey file structure. ACM Transactions on Database Systems, 9(1): 38–71, March 1984.Google Scholar
  19. 19.
    J. A. Orenstein:A dynamic hash file for random and sequential access. In M. Schkolnick and C. Thanos, editors, Proceedings of the Ninth International Conference on Very Large Data Bases, pages 132–141, Florence, Italy, November 1983.Google Scholar
  20. 20.
    K. Ramamohanarao and J. W. Lloyd:Dynamic hashing schemes. The Computer Journal, 25: 478–485, 1982.Google Scholar
  21. 21.
    K. Ramamohanarao and R. Sacks-Davis:Recursive linear hashing. ACM Transactions on Database Systems, 8(9): 369–391, September 1984.Google Scholar
  22. 22.
    K. Ramamohanarao, J. Shepherd, and R. Sacks-Davis:Multi-attribute hashing with multiple file copies for high performance partial-match retrieval. BIT, 30: 404–423, 1990.Google Scholar
  23. 23.
    R. L. Rivest:Partial-match retrieval algorithms. SIAM Journal on Computing, 5(1): 19–50, March 1976.Google Scholar
  24. 24.
    C. S. Roberts:Partial-match retrieval via the method of superimposed codes. Proceedings of the IEEE, 67(12): 1624–1642, December 1979.Google Scholar
  25. 25.
    J. T. Robinson:The k-d-B-tree: a search structure for large multidimensional dynamic indexes. In Proceedings of the SIGMOD Conference, pages 10–18, Ann Arbor, MI, USA, April 1981.Google Scholar
  26. 26.
    T. J. Sager:A polynomial time generator for minimal perfect hash functions. Communications of the ACM, 28(5): 523–532, May 1985.Google Scholar
  27. 27.
    K.-Y. Whang and R. Krishnamurthy:The multilevel grid file — a dynamic hierarchical multidimensional file structure. In International Symposium on Database Systems for Advanced Applications, pages 449–459, Tokyo, Japan, April 1991.Google Scholar

Copyright information

© the BIT Foundation 1993

Authors and Affiliations

  • Evan P. Harris
    • 1
  • Kotagiri Ramamohanarao
    • 1
  1. 1.Department of Computer ScienceThe University of MelbourneParkvilleAustralia

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