Sorting on a Ring of Processors

Abstract We study the time necessary to sort on a ring of processors. We show that the amount of space available to each processor determines the time required. We prove a lower bound of 2[ n 2 ] − 1 steps for sorting on a ring of n processors, under the constraint that each processor retains only a single value at any time. In contrast, we show an algorithm that sorts in [ n 2 ] + 1 steps if each processor is allowed to store six values.