Optimization in Cost of Sorting by CRCW PRAM Model

Abstract

This paper is aimed at studying and comparing the efficiency gained by various modes of embedding parallelism in the process of enumeration sort which calculates the position of each of the input values and places them accordingly to generate an output array containing the values in sorted order. Each of the parallel algorithms are individually analysed from the perspective of time complexity and the efficiency gained by each over the sequential method. Increase in the level of parallelism leads to decrease in the time demanded in generating output, at the cost of increase in the number of processing units. Time demanded could be minimized by maximizing the number of processing elements, but optimization in the overall cost, product of number of processing elements enrolled and time taken in generating the output, could be achieved at an intermediate level. We illustrate the scenario in which the product, which illustrates the overall cost, is minimized.