IJLTEMAS International Journal of Latest Technology in Engineering, Management & Applied Science (IJLTEMAS) IJLTEMAS 2278-2540 IJLTEMAS 72 10.51583/IJLTEMAS.2026.150700067 Computer Science Comprehensive Empirical Benchmarking of Twelve Sorting Algorithms Across Comparison-Based, Non-Comparison-Based, and Hybrid Paradigms: A Multi-Dimensional Performance Model for Algorithm Selection at Practical Data Scales (n up to 100,000) M. Balala, MIT Brenda Faculty, Computer Studies Department Notre Dame of Marbel University, Koronadal City, South Cotabato Philippines 15 7 803 822 29 07 2026 03 08 2026 12 08 2026 Sorting Algorithms Timsort Non-Comparison Sorting Empirical Algorithmics Algorithm Selection Abstract

This study extends the five-algorithm benchmark of Wibowo and Faisal [12] — which compared Heap, Shell, Merge, and Quick Sort against Python's built-in Timsort — to a twelve-algorithm framework spanning comparison-based, non-comparison-based, and hybrid/adaptive paradigms. Execution time (time.perf_counter()) and peak memory (tracemalloc) were measured across data sizes from 100 to 100,000 elements under random, ascending, and descending distributions, with stability and adaptivity empirically verified rather than only theoretically asserted. Results show that Counting Sort empirically breaks the Ω(n log n) comparison-sort lower bound under bounded key-range conditions, completing in 39.29 ms at n=100,000 versus 1,607.65–14,818.08 ms for the comparison-based algorithms tested (Mann-Whitney U test, p < 0.001). A key-range scaling experiment locates this advantage's precise boundary: it holds while the value range k remains at or below roughly 10 times n and inverts once k approaches 100 times n. Tim Sort remained the fastest overall algorithm (14.12 ms), while Bucket Sort's performance proved highly sensitive to its assumed value-range parameter, degrading toward quadratic behavior when that assumption diverged from the actual data range. All theoretical stability classifications were empirically confirmed, and a systematic rank-correlation analysis shows distribution sensitivity concentrated in adaptive algorithms' response to best-case ordering (ρ = 0.11–0.71 between random and ascending rankings) rather than in uniform reshuffling under any non-random input (ρ = 0.90–0.95 between random and descending rankings). The study contributes a reproducible, rule-based, multi-dimensional (time-space-stability-adaptivity) decision-support framework, presented as a decision-tree and rule table and checked, where independent data permits, against a held-out supplementary dataset, for algorithm selection at the moderate-to-large data scales tested here (n up to 100,000).

 References Alkharabsheh, K., Alturani, I., Alturani, A., & Zanoon, N. (2013). Review on sorting algorithms: A comparative study. International Journal of Computer Science and Security, 7(3), 120–126. Auger, N., Jugé, V., Nicaud, C., & Pivoteau, C. (2018). On the worst-case complexity of TimSort. In 26th Annual European Symposium on Algorithms (ESA 2018). https://doi.org/10.48550/arXiv.1805.08612 Balasubramanian, S. A. (2025). Adaptive hybrid sort: Dynamic strategy selection for optimal sorting across diverse data distributions. arXiv. https://doi.org/10.48550/arXiv.2506.20677 Cormen, T. H., Leiserson, C. E., Rivest, R. L., & Stein, C. (2009). Introduction to algorithms (3rd ed.). MIT Press. Goel, K., Dwivedi, P., & Sharma, O. (2023). Performance analysis of various sorting algorithms: Comparison and optimization. 2023 11th International Conference on Intelligent Systems and Embedded Design (ISED), 1–5. https://doi.org/10.1109/ISED59382.2023.10444609 Golonka, J., & Krużel, F. (2026). Empirical evaluation of unoptimized sorting algorithms on 8-bit AVR Arduino microcontrollers. Sensors, 26(1), 214. https://doi.org/10.3390/s26010214 Oladipupo, E. T., Abikoye, O. C., Akande, N. O., Kayode, A. A., & Adeniyi, J. K. (2020). Comparative study of two divide and conquer sorting algorithms: Quicksort and mergesort. Procedia Computer Science, 171, 2532–2540. https://doi.org/10.1016/j.procs.2020.04.274 Peters, T. (2002). listsort.txt. CPython git repository. https://svn.python.org/projects/python/trunk/Objects/listsort.txt Romano, J., Kromrey, J. D., Coraggio, J., & Skowronek, J. (2006). Appropriate statistics for ordinal level data: Should we really be using t-test and Cohen's d for evaluating group differences on the NSSE and other surveys? Annual Meeting of the Florida Association of Institutional Research. Sarwar, S. M., Jaragh, M. H. A., & Wind, M. (1994). An empirical study of the run-time behavior of quicksort, Shellsort and mergesort for medium to large size data. Computer Languages, 20(2), 127–134. https://doi.org/10.1016/0096-0551(94)90019-1 Sundaramoorthy, S., & Karunanidhi, G. (2025). A systematic analysis on performance and computational complexity of sorting algorithms. Discover Computing. https://doi.org/10.1007/s10791-025-09724-w Wibowo, F. R., & Faisal, M. (2024). Comparative analysis of sorting algorithms: TimSort Python and classical sorting methods. JISA (Jurnal Informatika dan Sains), 7(1), 11–18.