Almost Optimal Dynamic 2–3 trees

  • Li Wanxue 


This paper presents a principle to create Almost Optimal Dynamical 2–3 trees based on the theory of Milleret al.,[4] and gives a searching algorithm, an insertion algorithm and a deletion algorithm for these 2–3 trees. Experimental result given in this paper indicates that these 2–3 trees have very good performance at node-visit cost. We discuss asymptotic property of the 2–3 trees asN→∞, and evaluate its approximate height,h=log2.45(N+1), whereN is the number of nodes of a 2–3 tree. Finally, this paper analyses the time complexities of the algorithms, which areO(log2.45(N+1)).


Leaf Node Insertion Algorithm Father Node Approximate Height Deletion Algorithm 
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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    D. E. Knuth, The art of computer programming, Vol. 3: Sorting and Searching, Addison-Wesley, 1973.Google Scholar
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    A. chi-chih Yao, On random 2–3 tree,Acta Informatica,9(1978), 159–170.MATHCrossRefGoogle Scholar
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    R. Miller, N. Pippenger, A. Rosenberg and L. Snyder, Optimal 2,3-tree,SIAM J. Comp.,8:1(1979), 42–59.CrossRefMathSciNetGoogle Scholar

Copyright information

© Science Press, Beijing China and Allerton Press Inc. 1986

Authors and Affiliations

  • Li Wanxue 
    • 1
  1. 1.Nankai UniversityTianjin

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