Optimal Prefix-Free Codes for Unequal Letter Costs: Dynamic Programming with the Monge Property [chapter]

Phil Bradford, Mordecai J. Golin, Lawrence L. Larmore, Wojciech Rytter
1998 Lecture Notes in Computer Science  
In this paper we discuss a variation of the classical 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 α and β. The most efficient algorithm known previously required O(n 2+max(α,β) ) time to construct such a minimal-cost set of n codewords. In this paper we provide an O(n max(α,β) ) time algorithm. Our
more » ... nt 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.
doi:10.1007/3-540-68530-8_4 fatcat:kjxnmw4jbzh2th5jvytrsz57ei