An Optimal Systolic Algorithm for Generating Permutations in Lexicographic Order

Abstract

A systolic algorithm is described for generating all permutations of n elements in lexicographic order. The algorithm is designed to be executed on a linear array of n processors, each having constant size memory, and each being responsible for producing one element of a given permutation. There is a constant delay per permutation, leading to an O( n!) time solution. This is an improvement over the best previously known techniques in two respects: the algorithm runs on the (arguably) weakest model of parallel computation, and is cost optimal (assuming the time to output the permutations is counted). The algorithm is extended to run adaptively, i.e., when the number of available processors is other than n.