Optimizing Graph Algorithms for Large-Scale Networks: A Mathematical Framework

Abstract

A mathematical framework for optimising graph algorithms for large-scale networks is presented in this paper. The effectiveness and scalability of classical graph algorithms are severely hampered by the growing complexity and scale of networks. This study presents new optimisation strategies, such as graph partitioning, heuristics, and parallel computing tactics, that improve algorithm performance using sophisticated mathematical models. The framework exhibits enhanced computing efficiency and decreased processing time for a variety of graph-related activities, including network flows, connectivity assessments, and shortest path computations, by utilising rigorous theoretical analysis in conjunction with empirical testing. The results offer a significant step in facilitating the management of large datasets found in contemporary applications, such as social networks, biological systems, and telecommunications. In the end, by providing workable methods suited to the requirements of large-scale networks, this study advances the fields of graph theory and network optimisation and makes data administration and analysis more efficient.