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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.
|Keywords: ||Dynamic programming|
|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.|
|Appears in Collections:||CSE TCSC Research Reports|
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