Determining the minimum flow in a graph with minimum overhead

Question

Recently, I was preparing for the acm-icpc contest. Here I want to know how to find the minimum flow with the lowest cost, provided that each edge on the graph has a capacity C, a cost V, and a lower flow L (L ≤ C).

Answer 1

Firstly, I'm not sure what the “least cost least flow” means, but I suspect you just mean the “least cost flow”.

Secondly, the flows of the lower boundary mean that it is not trivial to find a “legitimate flow”, which is a flow in which mass conservation is observed, i.e. the sum of the incoming flows is equal to the sum of the outgoing flows for all nodes except the source and receiver. (Typically, flow problems have L = 0, which means that zero flow is legal.) In fact, there are variants of L and C for which there is no legitimate flow.

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, Ford-Fulkerson preflow-push ( ).

Answer 2

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Answer 3

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