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Approximate max-flow min-cut theorem : ウィキペディア英語版
Approximate max-flow min-cut theorem

==Muticommodity flow problem==
A commodity is a pair of source and sink nodes in a network flow problem. For detailed definition of multicommodity flow problem, see Multi-commodity flow problem.
In a multicommodity flow problem, there are k≥1 commodities, each with its own source s_}, and demand D_} units of commodity i from s_} for each i, such that the total amount of all commodities passing through any edge is no greater than its capacity. (In the case of undirected edges, the sum of the flows in both directions can't exceed the capacity of the edge.).
Specially, a 1-commodity (or single commodity) flow problem is also known as a maximum flow problem (see Maximum flow problem). According to the famous Ford–Fulkerson algorithm (see Ford–Fulkerson algorithm),the max-flow and min-cut are always equal in a 1-commodity flow problem.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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