Parallel construction of Huffman Codes

For decades, different algorithms were proposed addressing the issue of constructing Huffman Codes. In this paper we propose a detailed time-efficient three-phase parallel algorithm for generating Huffman codes on CREW PRAM model exploiting n processors, where n is equal to the number of symbols in the input alphabet. First the codeword length for each symbol is computed concurrently with a direct parallelization of the Huffman tree construction algorithm eliminating the complexity of dealing with the original tree-like data structure. Then the Huffman codes corresponding to symbols are generated in parallel based on a recursive formula. The performance of the proposed algorithm depends directly on the height of the corresponding Huffman tree. It achieves an O(n) time complexity in the worst case which is rarely encountered in practice.