The Search-o-Sort Theory

In the modern era of informatics, where data are very important, efficient management of data is necessary and critical. Two of the most important data management techniques are searching and data ordering (technically sorting). Traditional sorting algorithms work in quadratic time Ox2, and in the optimized cases, they take linearithmic time Ox·logx, with no existing method surpass this lower bound, given arbitrary data, i.e., ordering a list of cardinality x in Ox·logx−ϵ(x)∀ϵ(x)>0. This research proposes Search-o-Sort, which reinterprets sorting in terms of searching, thereby offering a new framework for ordering arbitrary data. The framework is applied to classical search algorithms,–Linear Search, Binary Search (in general, k-ary Search), and extended to more optimized methods such as Interpolation and Jump Search. The analysis suggests theoretical pathways to reduce the computational complexity of sorting algorithms, thus enabling algorithmic development based on the proposed viewpoint.