Designing an efficient data sorting algorithm that requires less time and space complexity is essential for computer science, different engineering disciplines, data mining systems, wireless networks, and the Internet of things. This paper proposes a general low-complex data sorting framework that distinguishes the sorted or similar data, makes independent subarrays approximately in equal length, and sorts the subarrays' data using one of the popular comparison-based sorting algorithms. Two frameworks, one for serial realization and another for parallel realization, are proposed. The time complexity analyses of the proposed framework demonstrate an improvement compared to the conventional Merge and Quick sorting algorithms. Following complexity analysis, the simulation results indicate slight improvements in the elapsed time and the number of swaps of the proposed serial Merge-based and Quick-based frameworks compared to the conventional ones for low/high variance integer/non-integer data sets, in different data sizes and the number of divisions. It is about (1−1.6%) to (3.5−4%) and (0.3−1.8%) to (2−4%) improvements in the elapsed times for 1, 2, 3, and 4 divisions, respectively for small and very large data sets in Mergebased and Quick-based scenarios. Although these improvements in serial realization are minor, making independent low-variance subarrays allows the sorted components to be extracted sequentially and gradually before the end of the sorting process. Also, it proposes a general framework for parallelizing conventional sorting algorithms using non-connected (independent) or connected (dependent) multi-core structures. As the second experiment, the numerical analyses that compare the results of the parallel realization of the proposed framework to the serial one in 1, 2, 3, and 4 divisions, show a speedup factor of (2 − 4) for small to (2 − 16) for very large data sets. The third experiment shows the effectiveness of the proposed parallel framework to the parallel sorting based on the random-access machine model. Finally, we prove that the mean-based pivot is as efficient as the median-based and much better than the random pivot for making subarrays of approximately equal length.

Computer and communication systems and networks deal with many cases that require rearrangement of data either in descending or ascending order. This operation is called sorting, and the purpose of an efficient sorting algorithm is to reduce the computational complexity and time taken to perform the comparison, swapping, and assignment operations. In this paper, we propose an efficient mean-based sorting algorithm that sorts integer/non-integer data by making approximately the same length independent quasi-sorted subarrays. It gradually finds sorted data and checks if the elements are partially sorted or have similar values. The elapsed time, the number of divisions and swaps, and the difference between the locations of the sorted and unsorted data in different samples demonstrate the superiority of the proposed algorithm to the Merge, Quick, Heap, and conventional mean-based sorts for both integer and non-integer large data sets which are random or partially/entirely sorted. Numerical analyses indicate that the mean-based pivot is appropriate for making subarrays with approximately similar lengths. Also, the complexity study shows that the proposed mean-based sorting algorithm offers a memory complexity same as the Quick-sort and a time complexity better than the Merge, Heap, and Quick sorts in the best-case. It is similar to the Merge and Heap sorts in view of the time complexity of the worst-case much better than the Quick-sort while these algorithms experience identical complexity in the average-case. In addition to finding part by part incremental (or decremental) sorted data before reaching the end, it can be implemented by parallel processing the sections running at the same time faster than the other conventional algorithms due to having independent subarrays with similar lengths.

No abstract

No abstract

Design an efficient data sorting algorithm that requires less time and space complexity is essential for large data sets in wireless networks, the Internet of things, data mining systems, computer science, and communications engineering. This paper proposes a low-complex data sorting algorithm that distinguishes the sorted/similar data, makes independent subarrays, and sorts the subarrays’ data using one of the popular sorting algorithms. It is proved that the mean-based pivot is as efficient as the median-based pivot for making equal-length subarrays. The numerical analyses indicate slight improvements in the elapsed time and the number of swaps of the proposed serial Merge-based and Quick-based algorithms compared to the conventional ones for low/high variance integer/non-integer uniform/Gaussian data, in different data lengths. However, using the gradual data extraction feature, the sorted parts can be extracted sequentially before ending the sorting process. Also, making independent subarrays proposes a general framework to parallel realization of sorting algorithms with separate parts. Simulation results indicate the effectiveness of the proposed parallel Merge-based and Quick-based algorithms to the conventional serial and multi-core parallel algorithms. Finally, the complexity of the proposed algorithm in both serial and parallel realizations is analyzed that shows an impressive improvement.