Utilization of Graph Algorithms in Allocation Problems Solving

Graph algorithms play a pivotal role in solving allocation problems, which are fundamental across diverse domains such as transportation, telecommunications, supply chain management, and resource planning. This review examines the application of graph-theoretic methods to address allocation challenges, focusing on classical and emerging approaches to optimize resource utilization and system performance. Key topics include the Shortest Path Problem for efficient routing and navigation, the Maximum Flow Problem for optimizing network capacity, the Assignment Problem for resource-to-task allocation, and Capacity Planning Problem for scalable and resilient systems. We also deal with Traveling Salesman Problem, Partitioning Problem, Batch Assignment Problem, and Bin Packing/Container Loading Problem. The review highlights foundational algorithms such as Dijkstra’s and Bellman-Ford for pathfinding, the Ford-Fulkerson and Edmonds-Karp methods for flow optimization, the Hungarian algorithm for optimal assignments, and similar. In the study we provide number of examples of real-world applicability of these methods in solving problems of various diciplines. The insights gained provide a comprehensive understanding of graph algorithms’ capabilities in addressing allocation problems and inspire innovative solutions for next-generation challenges in optimization and resource management.