Algorithms
Journal of the ACM (JACM)
Parallel construction of optimal alphabetic trees
SPAA '93 Proceedings of the fifth annual ACM symposium on Parallel algorithms and architectures
Efficient Generation of Optimal Prefix Code: Equiprobable Words Using Unequal Cost Letters
Journal of the ACM (JACM)
Codes: Unequal Probabilities, Unequal Letter Cost
Journal of the ACM (JACM)
A Dynamic Programming Algorithm for Constructing Optimal Refix-Free Codes for Unequal Letter Costs
ICALP '95 Proceedings of the 22nd International Colloquium on Automata, Languages and Programming
Lopsided Trees: Analyses, Algorithms, and Applications
ICALP '96 Proceedings of the 23rd International Colloquium on Automata, Languages and Programming
Code and Parse Trees for Lossless Source Encoding
SEQUENCES '97 Proceedings of the Compression and Complexity of Sequences 1997
Coding with digits of unequal cost
IEEE Transactions on Information Theory
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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(n2+max(αβ)) time to construct such a minimal-cost set of n codewords. In this paper we provide an O(nmax(αβ)) 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.