A General Framework for Sorting Large Data Sets Using Independent Subarrays of Approximately Equal Length

Abstract

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.

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…”

“…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.…”

A Threshold-Based Sorting Algorithm for Dense Wireless Communication Networks

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

“…Besides, for making one subarray in the length of n 1 , whose elements are greater than the exact (or approximate) threshold level, it is also in a linear order of O(n t ). Moreover, according to the results of [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 1 (> n 1 ) are O(n 1 logn 1 ) and O(n 1 logn 1 ). Hence, in the mentioned methods, the total complexity order is as (29), (30).…”