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Title: Optimal prefix-free codes for unequal letter costs : dynamic programming with the Monge property
Authors: Bradford, Phil
Golin, Mordecai J.
Larmore, Lawrence L.
Rytter, Wojciech
Keywords: Dynamic programming
Huffman codes
Lopsided trees
Monge matrix
Monotone matrix
Prefix-free codes
Issue Date: 2000
Series/Report no.: HKUST Theoretical Computer Science Center Research Report ; HKUST-TCSC-2000-05
Abstract: In this paper we discuss the problem of finding optimal prefix-free codes for unequal letter costs, a variation of the classical Huffman coding problem. Our problem consists of finding a minimal cost prefix-free code in which the encoding alphabet consists of unequal cost (length) letters, with lengths α and β. The most efficient algorithm known previously requires O(n2+max(α,β)) time to construct such a minimal-cost set of n codewords, provided α and β are integers. In this paper we provide an O(nmax(α,β)) 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.
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