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On the max-entropy rule for a binary search tree

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Summary

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.

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References

  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)

  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 1977

  3. Knuth, D.: Fundamental Algorithms. (The Art of Computer Programming vol. 1), Addison-Wesley, 1968

  4. Knuth, D.: Sorting and Searching. (The Art of Computer Programming vol. 3), Addison-Wesley, 1973

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  6. Mehlhorn, K.: Nearly optimal binary search trees, Acta Informatica 5, 287–295 (1975)

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Authors and Affiliations

  1. Department of Information Sciences, Faculty of Engineering, Shizuoka University, Johoku 3-5-1, Hamamatsu, Japan

    Yasuichi Horibe

  2. Mathematical Institute of the Hungarian Academy of Sciences, Reáltanoda u. 13-15, 1053, Budapest, Hungary

    Tibor O. H. Nemetz

Authors
  1. Yasuichi Horibe
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  2. Tibor O. H. Nemetz
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Horibe, Y., Nemetz, T.O.H. On the max-entropy rule for a binary search tree. Acta Informatica 12, 63–72 (1979). https://doi.org/10.1007/BF00264017

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  • DOI: https://doi.org/10.1007/BF00264017

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