Advertisement

Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

On the costs of optimal and near-optimal binary search trees

  • 37 Accesses

  • 3 Citations

Summary

We show that the cost of an optimal binary search tree can vary substantially, depending only on the left-to-right order imposed on the probabilities. We also prove that the costs of some common classes of near-optimal trees cannot be bounded above by the cost of an optimal tree plus a constant.

This is a preview of subscription content, log in to check access.

References

  1. 1.

    Bayer, P.J.: Improved bounds on the costs of optimal and balanced binary search trees. Project MAC Technical Memorandum 69, M.I.T. Cambridge, MA., 1975

  2. 2.

    Fredman, M.L.: Two applications of a probabilistic search technique: sorting X + Y and building balanced search trees. Proc. 7th Ann. ACM Symp. Theor. Comput. 1975

  3. 3.

    Knuth, D.E.: Optimum binary search trees. Acta Informat. 1, 14–25 (1971)

  4. 4.

    Knuth, D.E.: The art of computer programming, Volume 3: Sorting and searching. Reading, MA.: Addison-Wesley 1973

  5. 5.

    Mehlhorn, K.: A best possible bound for the weighted path length of binary search trees. SIAM J. Comput. 6, 235–239 (1977)

Download references

Author information

Additional information

⋆ This work was supported by the National Research Council of Canada, while the author was at the University of Waterloo

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Allen, B. On the costs of optimal and near-optimal binary search trees. Acta Informatica 18, 255–263 (1982). https://doi.org/10.1007/BF00263193

Download citation

Keywords

  • Information System
  • Operating System
  • Data Structure
  • Communication Network
  • Information Theory