A Comprehensive Review of the Ford-fulkerson Algorithm for Network Flow Problems

Abstract

The Ford-Fulkerson method is one of the basic algorithms for computing the maximum flow in a flow network. This identifies more frequent traversed paths as a means of maximizing the flow between a source node and a downstream node in a directed network. Therefore, this paper will present a literature review, the principles of the algorithm, its mathematical foundation, applications and improvements made to the algorithm, such as the use of breadth-first search (BFS) as in the Edmonds-Karp algorithm, parallel computing techniques and predictive modeling to enhance efficiency. However, the algorithm is not without its issues, such as the effect of dense networks, loss of correctness in capacities, and static structure of networks. Furthermore, it is compared with other algorithms like Dinic and Edmonds-Karp to understand their relative benefits and drawbacks. We conclude that the Ford-Fulkerson algorithm is still a basis method with broad application in many fields, including traffic network, logistics, and communication networks, but its performance can be greatly improvedas a result of the advances in modern computation approaches including parallel computing and adaptive dynamic path-propagation. Moreover, comparative studies showcase that alternative algorithms such as Dinic and Edmonds-Karp provide distinct advantages in specific settings, such as in dense and dynamic networks, underscoring that depending on the application the most effective algorithm may vary.