Advertisement

Path balance heuristic for self-adjusting binary search trees

  • R. Balasubramanian
  • Venkatesh Raman
Algorithms
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1026)

Abstract

In (A. Subramanian, An Explanation of Splaying, Proceedings of the 14th Foundations of Software Technology and Theoretical Computer Science, LNCS Springer Verlag 880 354–365), D. Sleator suggested the following heuristic for self adjusting binary search trees: Every time an access is made, restructure the entire path from the root of the search tree to the accessed node into a balanced binary search tree on those nodes, and place all other subtrees rooted at the children of the nodes in the access path in their proper positions. We show that the method has an O(log n log log n/ log log log n) amortized complexity.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    B. Allen and I. Munro, Self-organizing Search Trees, Journal of the ACM 25 (1978) 526–535.Google Scholar
  2. 2.
    J. R. Bitner, Heuristics that dynamically organize data structures, SIAM Journal of Computing 8 (1979) 82–110.Google Scholar
  3. 3.
    T. H. Cormen, C. E. Leiserson, and R. L. Rivest, Introduction to Algorithms, The MIT Press, Cambridge, Massachusetts (1990).Google Scholar
  4. 4.
    M. L. Fredman, R. Sedgewick, D. D. Sleator and R. E. Tarjan, The Pairing Heap: A New Form of Self-Adjusting Heap, Algorithmica 1 (1986) 111–129.Google Scholar
  5. 5.
    D. E. Knuth, The Art of Computer Programming, Vol 3: Sorting and Searching, Addison-Wesley, Reading, Massachusettes (1973).Google Scholar
  6. 6.
    D. D. Sleator, R. E. Tarjan, and Thurston, Rotation distance, triangulations and hyperbolic geometry, Proceedings of the 18th ACM Symposium on Theory of Computing (1986) 122–135.Google Scholar
  7. 7.
    D. D. Sleator and R. E. Tarjan, Self-adjusting Binary Search Trees, Journal of the ACM 32 (1985) 652–686.Google Scholar
  8. 8.
    A. Subramanian, An Explanation of Splaying, Proceedings of the 14th Foundations of Software Technology and Theoretical Computer Science, LNCS Springer Verlag 880 354–365.Google Scholar
  9. 9.
    R. E. Tarjan, Amortized Computational Complexity, SIAM Journal of Algebraic and Discrete Mathematics, 6 (2) (1985) 306–318.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • R. Balasubramanian
    • 1
  • Venkatesh Raman
    • 1
  1. 1.The Institute of Mathematical SciencesMadras

Personalised recommendations