Acta Informatica

, Volume 12, Issue 1, pp 63–72 | Cite as

On the max-entropy rule for a binary search tree

  • Yasuichi Horibe
  • Tibor O. H. Nemetz


A modified max-entropy rule is proposed for constructing nearly optimum binary search tree in the case of ordered keys with given probabilities. The average cost of the trees obtained by this rule is shown to be bounded by the entropy of the probability distribution plus a constant not larger than one. An algorithm for implementing this rule is then suggested and its complexity is investigated in a probabilistic setting.


Information System Probability Distribution Operating System Data Structure Communication Network 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    Güttler, R., Mehlhorn, K., Schneider, W.: Binary Search Trees: Average and Worst Case Behavior, submitted to Acta Informatica. (a preliminary version appeared in Informatik-Fachberichte vol. 5, 301–317, Springer-Verlag, 1976)Google Scholar
  2. 2.
    Horibe, Y.: Entropy and Balance in Binary Trees, Colloque International du C.N.R.S. held at E.N.S.E.T., Cachan, France, July 1977Google Scholar
  3. 3.
    Knuth, D.: Fundamental Algorithms. (The Art of Computer Programming vol. 1), Addison-Wesley, 1968Google Scholar
  4. 4.
    Knuth, D.: Sorting and Searching. (The Art of Computer Programming vol. 3), Addison-Wesley, 1973Google Scholar
  5. 5.
    Mehlhorn, K.: Private communication (to Y. Horibe)Google Scholar
  6. 6.
    Mehlhorn, K.: Nearly optimal binary search trees, Acta Informatica 5, 287–295 (1975)CrossRefzbMATHMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag 1979

Authors and Affiliations

  • Yasuichi Horibe
    • 1
  • Tibor O. H. Nemetz
    • 2
  1. 1.Department of Information Sciences, Faculty of EngineeringShizuoka UniversityHamamatsuJapan
  2. 2.Mathematical Institute of the Hungarian Academy of SciencesBudapestHungary

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