On the Performance of Mean-Based Sort for Large Data Sets

Abstract

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.

A threshold‐based sorting algorithm for dense wireless sensor systems and communication networks

“…The time complexity order (TCO) of Quick, Merge, and K-S mean-based sorting algorithms, in the average-case [6,7], is…”

“…Moreover, according to the results of refs. [6,7], the average-case complexity order for sorting the selected subarray in known and unknown pdf versions, respectively in the length of n 1 and n 0…”

“…The time complexity order (TCO) of Quick, Merge, and K‐S mean‐based sorting algorithms, in the average‐case [6, 7], is $$$TC{O}_{\mathit{Conv. }}=O\left({n}_{t}log{n}_{t}\right)$$$ …”

“…A major category is based on the divide-and-conquer method that first divides the initial problem into several subproblems, the same in goals with a smaller scale [3]. In this category, Quick, Merge, and mean-based sorting methods have been widely used in data processing [4][5][6] and this paper. Essential sorting applications include fast search in searching, speed-up data retrieval and comparison, and clustering [6][7][8] and speed it up.…”

“…In this category, Quick, Merge, and mean-based sorting methods have been widely used in data processing [4][5][6] and this paper. Essential sorting applications include fast search in searching, speed-up data retrieval and comparison, and clustering [6][7][8] and speed it up. Wireless communication systems and Wireless sensor networks (WSNs) need sorting quantities, such as distance, time of arrival, velocity, time difference or delay, received signal strength indicator (RSSI), channel state information or channel gain including multipath and shadowing effects, path-loss, signal to noise ratio (SNR), carrier to interference ratio, signal to interference-plusnoise ratio (SINR), sum-rate, outage probability, bit or symbol error rate (BER or SER), and the number of free channels as positive (or negative in dB) numbers.…”