Bounding the Depth of Search

For an ordered sequence of n weights, Huuman's algorithm constructs in time and space O(n) a search tree with minimum average path length, or, which is equivalent, a minimum redundancy code. However, if an upper bound B is imposed on the length of the codewords, the best known algorithms for the construction of an optimal code have time and space complexities O(Bn 2). A new algorithm is presented, which yields sub-optimal codes, but in time O(n log n) and space O(n). Under certain conditions, these codes are shown to be close to optimal, and extensive experiments suggest that in many practical applications, the deviation from the optimum is negligible.