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Self-adjusting augmented search trees

  • Tony W. Lai
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 650)

Abstract

We consider the problem of maintaining a dynamic weighted binary search tree augmented with a secondary search structure. Although we show that partial rebuilding cannot simultaneously achieve optimal search and update times, we introduce a new technique related to partial building called weighted partial rebuilding, which supports optimal worst-case search times (within a constant factor) for primary keys, O(log n) amortized update times, and efficient amortized reweight times. We also give an example application.

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References

  1. 1.
    C. R. Aragon and R. G. Seidel. Randomized search trees. In Proceedings of the 30th Annual IEEE Symposium on Foundations of Computer Science, pages 540–545, 1989.Google Scholar
  2. 2.
    S. W. Bent, D. D. Sleator, and R. E. Tarjan. Biased search trees. SIAM Journal on Computing, 14:545–568, 1985.Google Scholar
  3. 3.
    V. Estivill-Castro and M. Sherk. Competitiveness and response time in on-line algorithms. In Proceedings of the 2nd International Symposium on Algorithms, pages 284–293, 1991.Google Scholar
  4. 4.
    G. Frederickson and S. Rodger. A new approach to the dynamic maintenance of maximal points in the plane. In Proceedings of the 25th Annual Allerton Conference on Communication, Control, and Computing, pages 879–888, 1987.Google Scholar
  5. 5.
    R. Klein, O. Nurmi, T. Ottmann, and D. Wood. A dynamic fixed windowing problem. Algorithmica, 4:535–550, 1989.MathSciNetGoogle Scholar
  6. 6.
    T. W. Lai and D. Wood. Adaptive heuristics for binary search trees and constant linkage cost. In Proceedings of the 2nd Annual ACM-SIAM Symposium on Discrete Algorithms, pages 72–77, 1991.Google Scholar
  7. 7.
    E. M. McCreight. Priority search trees. SIAM Journal on Computing, 14:257–276, 1985.MathSciNetGoogle Scholar
  8. 8.
    K. Mehlhorn. Dynamic binary search. SIAM Journal on Computing, 8:175–198, 1979.CrossRefGoogle Scholar
  9. 9.
    M. H. Overmars and J. van Leeuwen. Dynamic multi-dimensional data structures based on quad-and k-d trees. Acta Informatica, 17:267–285, 1982.CrossRefGoogle Scholar
  10. 10.
    N. Sarnak and R. E. Tarjan. Planar point location using persistant search trees. Communications of the ACM, 29:669–679, 1986.CrossRefGoogle Scholar
  11. 11.
    D. D. Sleator and R. E. Tarjan. Self-adjusting binary search trees. Journal of the ACM, 32:652–686, 1985.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1992

Authors and Affiliations

  • Tony W. Lai
    • 1
  1. 1.Department of Computer ScienceUniversity of TorontoTorontoCanada

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