A systematic analysis on performance and computational complexity of sorting algorithms

Abstract With the exponential growth of digital data, efficient sorting techniques has becomes essential for real-time and large-scale computing applications. This review systematically evaluates the performance and computational complexity of twelve classical sorting techniques. This study considers both theoretical aspects, such as time, space complexity, and algorithmic stability, and complements them with empirical analysis using the MATLAB platform. Execution times were benchmarked across a variety of data types, including positive and negative integers, decimal numbers, and characters, over data sizes ranging from 100 to 100,000 elements. Results indicate that the bucket sort delivers the fastest performance for uniformly distributed numeric and character data, while the counting sort excels with positive integers. Merge and heap sort provide stable and scalable performance across data volumes due to their consistent O(n log n) complexity. In contrast, simpler sorting techniques, such as bubble and selection sorting, show significant inefficiency on larger data sizes. This study bridges the gap between theoretical analysis and empirical behavior, offering practical insight to help researchers and developers select optimal sorting techniques based on specific application needs and input characteristics.