6.1 Maximum Flows
نویسنده
چکیده
6. Lecture notes on flows and cuts 6.1 Maximum Flows Network flows deals with modelling the flow of a commodity (water, electricity, packets, gas, cars, trains, money, or any abstract object) in a network. The links in the network are capacitated and the commodity does not vanish in the network except at specified locations where we can either inject or extract some amount of commodity. The main question is how much can be sent in this network. Here is a more formal definition of the maximum flow problem. We have a digraph (directed graph) G = (V,E) and two special vertices s and t; s is called the source and t the sink. We have an upper capacity function u : E → R and also a lower capacity function l : E → R (sometimes chosen to be 0 everywhere). A flow x will be an assignment of values to the arcs (directed edges) so that: 1. for every e ∈ E: l(e) ≤ xe ≤ u(e), 2. for every v ∈ V \ {s, t}:
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