Optimal prefix codes with fewer distinct codeword lengths are faster to construct

Abstract

A new method for constructing minimum-redundancy binary prefix codes is described. Our method does not explicitly build a Huffman tree; instead it uses a property of optimal prefix codes to compute the codeword lengths corresponding to the input weights. Let n be the number of weights and k be the number of distinct codeword lengths as produced by the algorithm for the optimum codes. The running time of our algorithm is O(k · n). Following our previous work in [1], no algorithm can possibly construct optimal prefix codes in o(k · n) time. When the given weights are presorted our algorithm performs O(9 k · log 2k n) comparisons. * A preliminary version of the