Maximum flow problem

（重定向自Maximal flow）

A network with an example of maximum flow. The source is s, and the sink t. The numbers denote flow and capacity.

A flow network, with source s and sink t. The numbers next to the edge are the capacities.

Fig. 4.1.1. Transformation of a multi-source multi-sink maximum flow problem into a single-source single-sink maximum flow problem

Fig. 4.3.1. Transformation of a maximum bipartite matching problem into a maximum flow problem

In optimization theory, maximum flow problems involve finding a feasible flow through a single-source, single-sink flow network that is maximum.

The maximum flow problem can be seen as a special case of more complex network flow problems, such as the circulation problem. The maximum value of an s-t flow (i.e., flow from source s to sink t) is equal to the minimum capacity of an s-t cut (i.e., cut severing s from t) in the network, as stated in the max-flow min-cut theorem.

单词	Maximal flow
释义	Maximal flow 英语百科 Maximum flow problem （重定向自Maximal flow） In optimization theory, maximum flow problems involve finding a feasible flow through a single-source, single-sink flow network that is maximum. The maximum flow problem can be seen as a special case of more complex network flow problems, such as the circulation problem. The maximum value of an s-t flow (i.e., flow from source s to sink t) is equal to the minimum capacity of an s-t cut (i.e., cut severing s from t) in the network, as stated in the max-flow min-cut theorem.
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