research-article

Optimum Sequence Trees

Authors:

Masahiro Miyakawa,

Toshitsugu Yuba,

Yoshio Sugito,

Mamoru HoshiAuthors Info & Claims

SIAM Journal on Computing, Volume 6, Issue 2

Pages 201 - 234

https://doi.org/10.1137/0206016

Published: 01 June 1977 Publication History

Abstract

The construction problems of optimum sequence trees (or digital search trees) are considered in the following frameworks: 1. construction of optimum trees from a set of keys, 2. transformation of an arbitrary tree into an optimum one, 3. optimum insertions of keys into an optimum tree, 4. optimum deletions of keys from an optimum tree.

Algorithms are shown. The number of operations needed for the algorithm in the framework 1 is at most $O(N^{2}L)$, and in the framework 2 it is at most $O(N^{3}L)$ both with $O(N)$ storage locations, where N and L are the number of keys and the length of coded keys respectively.

Necessary and sufficient conditions for the optimality of sequence trees are also given.

References

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T. C. Hu, A. C. Tucker, Optimal computer search trees and variable-length alphabetical codes, SIAM J. Appl. Math., 21 (1971), 514–532

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D. E. Knuth, Optimum binary search trees, Acta Informat., 1 (1971), 14–25

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Donald E. Knuth, The art of computer programming. Volume 3, Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont., 1973xi+722 pp. (1 foldout)

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W. A. Martin, D. N. Ness, Optimizing binary trees grown with a sorting algorithm, Comm. ACM, 15 (1972), 88–93

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M. Miyakawa, T. Yuba, M. Hoshi, Construction of optimum sequence trees with weighted codes, Res. Rep., EC72-35, Inst. Electronics and Communication Engrs., Japan, 1972

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Toshitsugu Yuba, Masahiro Miyakawa, Optimum sequence hash trees, Systems-Computer-Controls, 4 (1973), 10–17, Trans. Inst. Electronics and Communication Engrs. of Japan, 56-D (1973), pp. 9–16

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T. Yuba, M. Miyakawa, M. Hoshi, Optimization problems of sequence trees, Trans. Inst. Electronics and Communication Engrs. of Japan, 57-D (1974), 238–239

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Optimum Sequence Trees

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Published In

SIAM Journal on Computing Volume 6, Issue 2

Jun 1977

202 pages

ISSN:0097-5397

DOI:10.1137/smjcat.1977.6.issue-2

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Publisher

Society for Industrial and Applied Mathematics

United States

Publication History

Published: 01 June 1977

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Abstract

References

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Recommendations

Representing Trees of Higher Degree

Deletion in two-dimensional quad trees

Deletion Without Rebalancing in Binary Search Trees

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