Alireza Akbarian - Computer Engineering Student of Sharif University of Technology, International Campus-Kish, Iran
Arian Akbarian - High School Mathematics Student, Kerman, Iran

Sorting algorithms are central to computational theory and widely used in data-centricapplications across fields such as machine learning, data analysis, and computationalgeometry. This paper presents an in-depth analysis of sorting efficiency, focusing on classicalalgorithms (QuickSort, MergeSort, HeapSort) and their optimization through parallelization,hybrid memory, and advanced data structures. We review seminal works by Aho, Hopcroft,and Ullman (۱۹۸۳) and Knuth (۱۹۷۳), establishing a foundation for performance evaluationand optimization strategies. Recent advancements, including in-memory parallel sortingarchitectures like IMC-Sort (Li et al., ۲۰۲۰), are explored to enhance computational efficiency.Further, this study investigates complex applications of sorting algorithms, such as their usein unstructured video classification (Morris & Kender, ۲۰۰۹) and eco-efficiency modeling fortropical systems (Peters et al., ۲۰۱۳). A novel sorting approach based on identifying thelongest increasing subsequences is presented, building on our previous work (Akbarian &Keyhanipour, ۲۰۲۳) to achieve optimized sequence sorting. By integrating classicaltechniques with modern innovations, this paper contributes to the ongoing evolution ofsorting algorithms, highlighting their relevance in diverse domains and their potential to meetthe demands of future computational challenges.

Sorting Algorithms, Optimization, Efficiency in Algorithms, Longest Increasing Subsequence, Parallel Computing