مقایسهٔ روش‌ها

	الگوریتم Push-Relabel	الگوریتم بلمن-فورد	الگوریتم دایکسترا	الگوریتم فورد-فالکرسون
حوزه	پژوهش عملیات	پژوهش عملیات	پژوهش عملیات	پژوهش عملیات
خانواده	Machine learning	Machine learning	Machine learning	Machine learning
سال پیدایش	1988	1956	1956	1956
پدیدآور	Andrew V. Goldberg and Robert E. Tarjan	Richard Bellman and Lester R. Ford	Edsger W. Dijkstra	Lester R. Ford and Delbert R. Fulkerson
نوع	algorithm	algorithm	algorithm	algorithm
منبع بنیادین	Goldberg, A. V., & Tarjan, R. E. (1988). A new approach to the maximum flow problem. Journal of the ACM, 35(4), 921-940.	Bellman, R. (1958). On a routing problem. Quarterly of Applied Mathematics, 16(1), 87-90.	Dijkstra, E. W. (1959). A note on two problems in connexion with graphs. Numerische Mathematik, 1(1), 269-271.	Ford, L. R., & Fulkerson, D. R. (1956). Maximal flow through a network. Canadian Journal of Mathematics, 8(3), 399-404.
نام‌های دیگر	preflow-push algorithm, Goldberg-Tarjan algorithm	Bellman-Ford method, Bellman algorithm	Dijkstra's algorithm, shortest path algorithm	Ford-Fulkerson method, augmenting path method
مرتبط	3	3	3	4
خلاصه	The Push-Relabel Algorithm, developed by Andrew V. Goldberg and Robert E. Tarjan in 1988, is a highly efficient method for computing maximum flow in networks. Unlike augmenting path methods, it maintains a preflow and uses local push and global relabeling operations to drive flow toward the sink, achieving superior worst-case complexity.	The Bellman-Ford Algorithm, developed by Richard Bellman and Lester R. Ford in the 1950s, is a fundamental algorithm for computing shortest paths in weighted graphs that may contain negative edge weights. Unlike Dijkstra's algorithm, it correctly handles negative weights and can detect the presence of negative-weight cycles.	Dijkstra's Algorithm, introduced by Edsger W. Dijkstra in 1956, is one of the most fundamental algorithms in computer science for solving the single-source shortest path problem. It finds the shortest path from a starting vertex to all other vertices in a weighted graph with non-negative edge weights.	The Ford-Fulkerson Algorithm, developed by Lester R. Ford and Delbert R. Fulkerson in 1956, is a foundational method for computing the maximum flow in a flow network. It finds the maximum amount of flow that can be sent from a source to a sink through a directed graph with capacity constraints on edges.