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A comment on the double-chained tree

Author: T. C. HuAuthors Info & Claims

Communications of the ACM, Volume 15, Issue 4

Page 276

https://doi.org/10.1145/361284.361301

Published: 01 April 1972 Publication History

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Abstract

In 1963, Sussenguth [8] suggested that a file should be organized as a double-chained tree for searching and updating. Patt [5] then obtained the optimum double-chained tree under the assumption that no key may prefix another and that all terminal nodes (items of information) have equal probabilities of being searched. Stanfel [6, 7] explored the relation between the double-chained tree and variable length code [3] and solved a special integer programming problem which corresponds to the case of equal probabilities of terminal nodes and a finite set of available symbols for keys with different costs.

References

[1]

Hu, T. C. and Tan, K. C. Path length of binary search trees. Rep. 1111, Mathematics Res. Ct., U. of Wisc., Mar. 1971.

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[2]

Hu, T. C. and Tucker, A. C. Optimum binary search trees. Rep. 1049, Mathematics Res. Ctr., U. of Wisc., Mar. 1970.

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[3]

Karp, R. M. Minimum redundancy coding for the discrete, noiseless channel. IRE Trans. IT-7 (1961), 27-35.

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[4]

Knuth, D. E. Fundamental Algorithms. Addison-Wesley, Reading, Mass., 1968, p. 333.

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[5]

Patt, Y. Variable length tree structures having minimum average search time. Comm. ACM 12, 2 (Feb. 1969), 72-76.

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[6]

Stanfel, L. E. Tree structures for optimal seaching. J. ACM 17, 3 (July 1970), 508-517.

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[7]

Stanfel, L. E. A comment on optimum tree structures. Comm. ACM 12, 10 (Oct. 1969), 582.

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[8]

Sussenguth, E. H., Jr. Use of tree structures for processing files. Comm. ACM 6, 5 (May 1963), pp. 272-279.

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Visscher P(1984)Simple compact tree storage of a multidimensional arrayComputer Physics Communications10.1016/0010-4655(84)90016-X31:4(311-318)Online publication date: Mar-1984
https://doi.org/10.1016/0010-4655(84)90016-X
Cardenas ASagamang J(1975)Modeling and analysis of data base organizationInformation Systems10.1016/0306-4379(75)90016-21:2(57-67)Online publication date: Apr-1975
https://doi.org/10.1016/0306-4379(75)90016-2
Kennedy S(1972)A note on optimal doubly-chained treesCommunications of the ACM10.1145/355606.36189415:11(997-998)Online publication date: 1-Nov-1972
https://dl.acm.org/doi/10.1145/355606.361894

Index Terms

A comment on the double-chained tree
1. Mathematics of computing
  1. Discrete mathematics
    1. Graph theory
      1. Trees
2. Theory of computation
  1. Design and analysis of algorithms
    1. Data structures design and analysis
      1. Sorting and searching

Index terms have been assigned to the content through auto-classification.

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A note on optimal doubly-chained trees

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The height of a random binary search tree

Let H_n be the height of a random binary search tree on n nodes. We show that there exist constants α = 4.311… and β = 1.953… such that E(H_n) = αln n − βln ln n + O(1), We also show that Var(H_n) = O(1).

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Published In

Communications of the ACM Volume 15, Issue 4

April 1972

70 pages

ISSN:0001-0782

EISSN:1557-7317

DOI:10.1145/361284

Editor:
M. Stuart Lynn
Rice Univ., Houston, TX

Issue’s Table of Contents

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Association for Computing Machinery

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Publication History

Published: 01 April 1972

Published in CACM Volume 15, Issue 4

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Visscher P(1984)Simple compact tree storage of a multidimensional arrayComputer Physics Communications10.1016/0010-4655(84)90016-X31:4(311-318)Online publication date: Mar-1984
https://doi.org/10.1016/0010-4655(84)90016-X
Cardenas ASagamang J(1975)Modeling and analysis of data base organizationInformation Systems10.1016/0306-4379(75)90016-21:2(57-67)Online publication date: Apr-1975
https://doi.org/10.1016/0306-4379(75)90016-2
Kennedy S(1972)A note on optimal doubly-chained treesCommunications of the ACM10.1145/355606.36189415:11(997-998)Online publication date: 1-Nov-1972
https://dl.acm.org/doi/10.1145/355606.361894

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A note on optimal doubly-chained trees

The suffix binary search tree and suffix AVL tree

The height of a random binary search tree

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