Approximating Huffman codes in parallel

In this paper we present new results on the approximate parallel construction of Huffman codes. Our algorithm achieves linear work and logarithmic time, provided that the initial set of elements is sorted. This is the first parallel algorithm for that problem with the optimal time and work. Combining our approach with the best known parallel sorting algorithms we can construct an almost optimal Huffman tree with optimal time and work. This also leads to the first parallel algorithm that constructs exact Huffman codes with maximum codeword length H   in time O(H)O(H) with n/lognn/logn processors, if the elements are sorted.