Abstract
Given an alphabet Σ = {a 1,...,a n} and a corresponding list of weights [w 1,...,w n], an optimal prefix code is a prefix code for Σ that minimizes the weighted length of a code string, defined to be \(\sum_{i=1}^{n} w_i l_i\), where l i is the length of the codeword assigned to a i. This problem is equivalent to the following problem: given a list of weights [w 1,...,w n], find an optimal binary code tree, that is, a binary tree T that minimizes the weighted path length \(\sum_{i=1}^{n} w_i l_i\), where l i is the level of the i-th leaf of T from left to right. If the list of weights is sorted, this problem can be solved in O(n) by one of the efficient implementations of Huffman’s Algorithm [Huf52]. Any tree constructed by Huffman’s Algorithm is called a Huffman tree.
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© 2000 Springer-Verlag Berlin Heidelberg
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Milidiú, R.L., Laber, E.S. (2000). Linear Time Recognition of Optimal L-Restricted Prefix Codes. In: Gonnet, G.H., Viola, A. (eds) LATIN 2000: Theoretical Informatics. LATIN 2000. Lecture Notes in Computer Science, vol 1776. Springer, Berlin, Heidelberg. https://doi.org/10.1007/10719839_23
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DOI: https://doi.org/10.1007/10719839_23
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