Rheinische Friedrich-Wilhelms-Universität Bonn Institut für Informatik
 
Abteilung V

 
Universität Bonn -> Institut für Informatik -> Abteilung V
CS-Reports 1998 Copyright 1998 Universität Bonn, Institut für Informatik, Abt. V
85197

Optimal Prefix-Free Codes for Unequal Letter Costs: Dynamic Programming with the Monge Property
Phil Bradford, Mordecai J. Golin, Lawrence L. Larmore, Wojciech Rytter
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In this paper we discuss a variation of the classical {\em Huffman coding problem\/}: finding optimal prefix-free codes for unequal letter costs. Our problem consists of finding a minimal cost prefix-free code in which the encoding alphabet consists of unequal cost (length) letters, with lengths $\alpha$ and $\beta$. The most efficient algorithm known previously required $O(n^{2+\max(\alpha,\beta)})$ time to construct such a minimal-cost set of $n$ codewords. In this paper we provide an $O(n^{\max(\alpha,\beta)})$ time algorithm. Our improvement comes from the use of a more sophisticated modeling of the problem combined with the observation that the problem possesses a `Monge property'' and that the SMAWK algorithm on monotone matrices can therefore be applied.

Last Change: 08/18/99 at 13:00:38
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Universität Bonn -> Institut für Informatik -> Abteilung V

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