Bicomponent sorting algorithms

Abstract

he possibilities of improving sorting time parameters through preprocessing by stochastic sorting were investigated. The hypothesis that two-component stochastic + classical sorting outperforms classic one-component sorting in terms of time efficiency was experimentally confirmed. Sorting with different computational complexity is accepted as classical sorting algorithms: shaker sort- ing with computational complexity O(n2), insertions O(n2), Shell O(n·(log n)2) ... O(n3/2), fast with optimization of ending sequences O(n·log n). The greatest effect is obtained when performing comparisons using stochastic sorting in the amount of 160 percent of the array’s size. Indicators of the efficiency of the exchange of two elements, as well as series of exchanges, are introduced. This allowed to determine the highest efficiency of stochastic sorting (as the first component of two-component sorting), when one element for comparison is chosen from the first part of the array and the other from the second. For algorithms with a computational complexity of O(n2) the improvement in time efficiency reached 70–80 percent. However, for Shell sort and quick sort, the stochas- tic presort has no positive effect, but instead increases the total sorting time, which is apparently due to the initial high efficiency of these sorting methods. The hypothesis that three-component sorting fast + stochastic + insertions would increase sorting time efficiency was not confirmed. However, during the experiment, the recommended size of the array was determined, at which point the two-component quick + insertion sort must be switched to the second component – insertion sorting. The optimal length of the ending sequences is between 60 and 80 elements. Given that algorithm time efficiency is affected by computer architecture, operat- ing system, software development and execution environment, data types, data sizes, and their values, time efficiency indicators should be specified in each specific case.