research-article

A New Algorithm for Minimum Cost Binary Trees

Authors:

Adriano M. Garsia,

Michelle L. WachsAuthors Info & Claims

SIAM Journal on Computing, Volume 6, Issue 4

Pages 622 - 642

https://doi.org/10.1137/0206045

Published: 01 December 1977 Publication History

Abstract

A new algorithm for constructing minimum cost binary trees in $O(n \log n)$ time is presented. The algorithm is similar to the well-known Hu-Tucker algorithm. Our proof of validity is based on finite variational methods and is therefore quite different and somewhat simpler than the proof for the Hu-Tucker algorithm. Our proof also yields some additional information about the structure of minimum cost binary trees. This permits a linear time implementation of our algorithm in a special case.

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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T. C. HU, A new proof of the $T-C$ algorithm, SIAM J. Appl. Math., 25 (1971), 83–94

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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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D. E. Knuth, The art of computer programming. Vol. 1: Fundamental algorithms, Addison-Wesley, Reading, MA, 1973

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Robert Tarjan, Depth-first search and linear graph algorithms, SIAM J. Comput., 1 (1972), 146–160

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Li YChasseur CPatel JSellis TDavidson SIves Z(2015)A Padded Encoding Scheme to Accelerate Scans by Leveraging SkewProceedings of the 2015 ACM SIGMOD International Conference on Management of Data10.1145/2723372.2737787(1509-1524)Online publication date: 27-May-2015
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A New Algorithm for Minimum Cost Binary Trees

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Published In

SIAM Journal on Computing Volume 6, Issue 4

Dec 1977

152 pages

ISSN:0097-5397

DOI:10.1137/smjcat.1977.6.issue-4

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Publisher

Society for Industrial and Applied Mathematics

United States

Publication History

Published: 01 December 1977

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Jugé V(2024)Adaptive Shivers Sort: An Alternative Sorting AlgorithmACM Transactions on Algorithms10.1145/366419520:4(1-55)Online publication date: 5-Aug-2024
https://dl.acm.org/doi/10.1145/3664195
Ding XGu YSun YAgrawal KPetrank E(2024)Parallel and (Nearly) Work-Efficient Dynamic ProgrammingProceedings of the 36th ACM Symposium on Parallelism in Algorithms and Architectures10.1145/3626183.3659958(219-232)Online publication date: 17-Jun-2024
https://dl.acm.org/doi/10.1145/3626183.3659958
Li YChasseur CPatel JSellis TDavidson SIves Z(2015)A Padded Encoding Scheme to Accelerate Scans by Leveraging SkewProceedings of the 2015 ACM SIGMOD International Conference on Management of Data10.1145/2723372.2737787(1509-1524)Online publication date: 27-May-2015
https://dl.acm.org/doi/10.1145/2723372.2737787
Bent SSleator DTarjan R(1985)Biased Search TreesSIAM Journal on Computing10.1137/021404114:3(545-568)Online publication date: 1-Aug-1985
https://dl.acm.org/doi/10.1137/0214041
Kirkpatrick DKlawe M(1985)Alphabetic Minimax TreesSIAM Journal on Computing10.1137/021403914:3(514-526)Online publication date: 1-Aug-1985
https://dl.acm.org/doi/10.1137/0214039

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