Effective Implementation of Sorting Algorithms Using the Concept of Q-determinant

The present paper is devoted to the possibility of efficient implementation for sorting algorithms using the Q-determinant concept. We have investigated four algorithms: shaker sort, Shell sort, quicksort and Batcher’s odd-even mergesort. To sort small arrays, we obtained representations in the form of Q-determinants for these algorithms. Then the structures of the obtained representations were analyzed and, as a result, for the general case we have described the representations of the sorting algorithms in the form of a Q-determinant. Also, for sorting algorithms there was considered the application of the method of designing effective programs using the concept of Q-determinant. This application has been tested on shared and distributed memory of parallel computing systems by developing eff ective programs for the Shell sort.