A Two-phase Practical Parallel Algorithm for Construction of Huffman Codes

The construction of optimal prefix codes plays a significant and influential role in applications concerning information processing and communication. For decades, different algorithms were proposed treating the issue of Huffman codes construction and various optimizations were introduced. In this paper we propose a detailed practical time-efficient parallel algorithm for generating Huffman codes on CREW PRAM model exploiting n processors, where n is equal to the number of symbols in alphabet. We first compute the codewords lengths for all symbols concurrently with an innovative direct parallelization of the Huffman tree construction algorithm, alleviating the complexity of dealing with the original tree-like data structure. Then Huffman codes corresponding to symbols are generated in parallel based on a recursive formula introduced in [5]. The proposed algorithm achieves an O(n) time in the worst case when one-sided Huffman tree is formed, which is rarely encountered in practice, and O(log((logn – 1)!)) time in the best case when Huffman tree is nearly balanced.