Algorithms for Construction of Optimal and Almost-Optimal Length-Restricted Codes (Abstract)

Given a list of items.. with weights p =.. respectively, a code with codeword lengths.., is a length-restricted prefix-free code, if no codeword is a prefix of another one and L for some constant L and all i. A code is a minimum redundancy length-restricted code if p) = is minimal among all length-restricted prefix-free codes. The problem of length-restricted coding is motivated by practical implementations of coding algorithms. See for a description of the previous work on this topic. In this paper we present a parallel algorithm for the construction of redundancy length-restricted codes that is based on the Package-Merge algorithm of Larmore and Hirschberg Our algorithm constructs a length-restricted code in time with n processors on a CREW PRAM. Thus our algorithm has the same time-processor product as the sequential algorithm of Our parallelization of the Package-Merge is based on dividing elements into classes which contain elements in range 2'). Relative weight of an element is We maintain for every item e and every + logn the value o