A fast algorithm for optimum height-limited alphabetic binary trees

In this paper, an $O(nL\log n)$-time algorithm is presented for construction of an optimal alphabetic binary tree with height restricted to $L$. This algorithm is an alphabetic version of the Package Merge algorithm, and yields an $O(nL\log n)$-time algorithm for the alphabetic Huffman coding proble...

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Published in:SIAM journal on computing 1994-12, Vol.23 (6), p.1283-1312
Main Authors: LARMORE, L. L, PRZYTYCKA, T. M
Format: Article
Language:English
Subjects:
Algorithms
Applied sciences
Binary system
Codes
Computer science
Computer science
control theory
systems
Data processing. List processing. Character string processing
Exact sciences and technology
Leaves
Memory organisation. Data processing
Software
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PRZYTYCKA, T. M
description In this paper, an $O(nL\log n)$-time algorithm is presented for construction of an optimal alphabetic binary tree with height restricted to $L$. This algorithm is an alphabetic version of the Package Merge algorithm, and yields an $O(nL\log n)$-time algorithm for the alphabetic Huffman coding problem. The Alphabetic Package Merge algorithm is quite simple to describe, but appears hard to prove correct. Garey [SIAM J Comput., 3 (1974), pp. 101-110] gives an $O(n^3 \log n)$-time algorithm for the height-limited alphabetic binary tree problem. Itai [SIAM J. Comput., 5 (1976), pp. 9-18] and Wessner [Inform. Process. Lett., 4 (1976), pp. 90-94] independently reduce this time to $O(n^2 L)$ for the alphabetic problem. In [SIAM J. Comput., 16 (1987), pp. 1115-1123], a rather complex $O(n^{{3 / 2}} L\log ^{{1 / 2}} n)$ -time "hybrid" algorithm is given for length-limited Huffman coding. The Package Merge algorithm, discussed in this paper, first appeared in [Tech. Report, 88-01, ICS Dept. Univ. of California, Irvine, CA], but without proof of correctness.
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source ABI/INFORM Global; LOCUS - SIAM's Online Journal Archive
subjects Algorithms
Applied sciences
Binary system
Codes
Computer science
Computer science
control theory
systems
Data processing. List processing. Character string processing
Exact sciences and technology
Leaves
Memory organisation. Data processing
Software
title A fast algorithm for optimum height-limited alphabetic binary trees
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