Approximating Huffman Codes in Parallel

In this paper we present some new results on the approximate parallel construction of Huuman codes. Our algorithm achieves linear work and logarithmic time, provided that the initial set of elements is sorted. This is the rst 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 Huuman tree with optimal time and work. This also leads to the rst parallel algorithm that constructs exact Huuman codes with maximum codeword length H in time O(H) and with n processors. This represents a useful improvement since most practical situations satisfy H = O(logn).