Linearithmic Mean and Standard Deviation Sorting Method (LMDSM): Efficient and Stable Algorithm

Sorting algorithms have significance in the field of big data and high-performance computing, where effective data processing is of major significance. This paper presents the Linearithmic Mean and Standard Deviation Sorting Method (LMDSM), a new sorting method designed to handle enormous datasets and complex computational environments. Further this paper present a comprehensive comparative analysis of LMDSM with conventional sorting algorithms like Merge Sort and Quick Sort, emphasizing its efficiency and stability in different scenarios. LMDSM consistently outperforms other sorting algorithms in terms of sorting time when tested on arrays of 850,292 data in various orders. Furthermore, paper provide a rigorous theoretical analysis of LMDSM, encompassing its recurrence relation and time complexity derivation. Our research highlights the importance of LMDSM as an effective option for organizing jobs in current computing environments, providing significant importance in speed and reliability.