There is no best algorithm for max-flow problems. It all depends on the constraints of the problems.

You should make your own judgment of what to use based on what you know. Here are some facts you should consider.

• Ford-Fulkerson has complexity $$$O(E f)$$$, where $$$f$$$ is the maximum flow. In competitive programming problems, often $$$f$$$ will not be very big. For example in maximum matching between two sets of sizes $$$n$$$ and $$$m$$$, the maximum flow is bounded by $$$\min(n, m)$$$.
• Edmonds-Karp is the same as Ford-Fulkerson except that it searches for augmenting paths with BFS instead of DFS. The importance is that it has polynomial time of $$$O(V E^2)$$$. So, even if the maximum flow can be very large, you have this guarantee that Ford-Fulkerson doesn't give you. Edmonds-Karp still has the guarantee $$$O(E f)$$$ so it won't perform worse than Ford-Fulkerson except possibly by a constant.
• Dinic's Algorithm is an optimization on Edmonds-Karp with an improved guarantee of $$$O(V^2 E)$$$.
• In practice, these worst-case complexities are often overestimates. In the special case of unit networks such as maximum matching, you get smaller complexity guarantees. In maximum matching, it guarantees $$$O(\sqrt V)$$$ flow iterations for a complexity of $$$O(\sqrt V E)$$$
• These are not the only three flow algorithms and you can find other algorithms, heuristics, etc.
• Dinic's algorithm requires more code than Ford-Fulkerson or Edmonds-Karp.

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