Abstract
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), 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), 9--18] and Wessner [Inform. Process. Lett., 4 (1976), pp. 90--94] independently reduce this time to $O(n^2L)$ 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.
Published Version
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