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Randomly balanced binary trees

Abstract

A procedure to attach a new element to a binary tree at a predefined level is introduced; this insertion algorithm is performed in timeO (ln n), maintains all the properties of binary trees and can be seen as a generalization of the well known rotation technique. If the elements are inserted in the tree according to suitable distribution functions of the levels, the tree can be kept «balanced» even if the elements arrive in their proper order. Empirical evidence is given that the average searching time is of orderO (ln n) in this latter case. Finally, a brief comparison with existing methods is presented.

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References

  1. [1]

    Allen B., Munro I.,Self-organizing binary search trees. Journal A. C. M.,23,4 (1978), 526–535.

    MathSciNet  Google Scholar 

  2. [2]

    Baer J.-L.,Weight balanced trees. Proc. AFIPS 1975 NCC,44, AFIPS Press, Montvale, N. J., 467–472.

  3. [3]

    Baer J.-L., Schwab B.,A comparison of tree-balancing algorithms. Comm. ACM,20,5 (1977), 322–330.

    Article  Google Scholar 

  4. [4]

    Bentley J. L.,Multidimensional binary search trees used for associative searching. Comm. ACM,18, (1975), 505–517.

    Article  Google Scholar 

  5. [5]

    Guibas L. J.,A principle of independence for binary tree searching, Acta Informatica,4, (1975), 293–298.

    MATH  Article  MathSciNet  Google Scholar 

  6. [6]

    Jordan C,Calculus of Finite Differences. Chelsea Publ. Co. New York, N. Y., 1960.

    Google Scholar 

  7. [7]

    Knuth D. E.,The Art of Computer Programming,1–3 Addison Wesley, Reading, Mass., 1969–1973.

    MATH  Google Scholar 

  8. [8]

    Lynch W. C.,More combinatorial properties of certain trees. The Computer Journal,7, (1965), 299–302.

    MathSciNet  Google Scholar 

  9. [9]

    Nievergelt J.,Binary search trees and file organization. ACM Computing Surveys,6, (1974), 195–207.

    MATH  Article  Google Scholar 

  10. [10]

    Palmer E. M., Rahimi M. A., Robinson R. W.,Efficiency of a binary comparison storage technique. Journal A.C.M.,21, (1974), 376–384.

    MATH  MathSciNet  Google Scholar 

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Sprugnoli, R. Randomly balanced binary trees. Calcolo 17, 99–117 (1980). https://doi.org/10.1007/BF02576649

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Keywords

  • Binary Tree
  • Balance Tree
  • Binary Search Tree
  • Extra Space
  • Proper Order