A generic top-down dynamic-programming approach to prefix-free coding

Given a probability distribution over a set of n words to be transmitted, the Huffman Coding problem is to find a minimal-cost prefix free code for transmitting those words. The basic Huffman coding problem can be solved in O(n log n) time but variations are more difficult. One of the standard techniques for solving these variations utilizes a top-down dynamic programming approach. In this paper we show that this approach is amenable to dynamic programming speedup techniques, permitting a speedup of an order of magnitude for many algorithms in the literature for such variations as mixed radix, reserved length and one-ended coding. These speedups are immediate implications of a general structural property that permits batching together the calculation of many DP entries. Work of all of the authors was partially supported by Hong Kong CERG grant 613507. Work of the 2nd and 3rd authors also partially supported by a grant from the National Natural Science Foundation of China (No. 60573025) and by the Shanghai Leading Academic Discipline Project, project number B114.