Abstract
We show that optimal alphabetic binary trees can be constructed in O(n) time if the elements of the initial sequence are drawn from a domain that can be sorted in linear time. We describe a [6] hybrid algorithm that combines the bottom-up approach of the original Hu-Tucker algorithm with the top-down approach of Larmore and Przytycka’s Cartesian tree algorithms. The hybrid algorithm demonstrates the computational equivalence of sorting and level tree construction.
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References
Huffman, D.A.: A method for the construction of minimum redundancy codes. Proceedings of the IRE 40, 1098–1101 (1952)
Abrahams, J.: Code and parse trees for lossless source encoding. In: Proceedings Compression and Complexity of Sequences, pp. 146–171 (1997)
Gilbert, E.N., Moore, E.F.: Variable length binary encodings. Bell System Technical Journal 38, 933–968 (1959)
Knuth, D.E.: Optimum binary search tree. Acta Informatica 1, 14–25 (1971)
Hu, T.C., Tucker, A.C.: Optimal computer search trees and variable-length alphabetic codes. SIAM Journal on Applied Mathematics 21, 514–532 (1971)
Garsia, A.M., Wachs, M.L.: A new algorithm for minimal binary search trees. SIAM Journal on Computing 6, 622–642 (1977)
Hu, T.C., Morgenthaler, J.D.: Optimum alphabetic binary trees. In: Deza, M., Manoussakis, I., Euler, R. (eds.) CCS 1995. LNCS, vol. 1120, pp. 234–243. Springer, Heidelberg (1996)
Klawe, M.M., Mumey, B.: Upper and lower bounds on constructing alphabetic binary trees. SIAM Journal on Discrete Mathematics 8, 638–651 (1995)
Larmore, L.L., Przytycka, T.M.: The optimal alphabetic tree problem revisited. Journal of Algorithms 28, 1–20 (1998)
Hu, T.C.: A new proof of the T-C algorithm. SIAM Journal on Applied Mathematics 25, 83–94 (1973)
Hu, T.C., Shing, M.T.: Combinatorial Algorithms, 2nd edn. Dover, New York (2002)
Karpinski, M., Larmore, L.L., Rytter, W.: Correctness of constructing optimal alphabetic trees revisited. Theoretical Computer Science 180, 309–324 (1997)
Ramanan, P.: Testing the optimality of alphabetic trees. Theoretical Computer Science 93, 279–301 (1992)
Gabow, H.N., Bentley, J.L., Tarjan, R.E.: Scaling and related techniques for geometry problems. In: Proceedings of the 16th ACM Symposium on Theory of Computation, pp. 135–143 (1984)
Gabow, H.N., Tarjan, R.E.: A linear-time algorithm for a special case of disjoint set union. Journal of Computer and System Sciences 30, 209–221 (1985)
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Hu, T.C., Larmore, L.L., Morgenthaler, J.D. (2005). Optimal Integer Alphabetic Trees in Linear Time. In: Brodal, G.S., Leonardi, S. (eds) Algorithms – ESA 2005. ESA 2005. Lecture Notes in Computer Science, vol 3669. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11561071_22
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DOI: https://doi.org/10.1007/11561071_22
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-29118-3
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