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  2. Network flow problem - Wikipedia

    en.wikipedia.org/wiki/Network_flow_problem

    In combinatorial optimization, network flow problems are a class of computational problems in which the input is a flow network (a graph with numerical capacities on its edges), and the goal is to construct a flow, numerical values on each edge that respect the capacity constraints and that have incoming flow equal to outgoing flow at all vertices except for certain designated terminals.

  3. Multi-commodity flow problem - Wikipedia

    en.wikipedia.org/wiki/Multi-commodity_flow_problem

    The minimum cost variant of the multi-commodity flow problem is a generalization of the minimum cost flow problem (in which there is merely one source and one sink ). Variants of the circulation problem are generalizations of all flow problems. That is, any flow problem can be viewed as a particular circulation problem.

  4. Push–relabel maximum flow algorithm - Wikipedia

    en.wikipedia.org/wiki/Push–relabel_maximum_flow...

    This pre-flow algorithm also used a push operation; however, it used distances in the auxiliary network to determine where to push the flow instead of a labeling system. [2] [7] The push-relabel algorithm was designed by Andrew V. Goldberg and Robert Tarjan. The algorithm was initially presented in November 1986 in STOC '86: Proceedings of the ...

  5. Assignment problem - Wikipedia

    en.wikipedia.org/wiki/Assignment_problem

    The problem can be solved by reduction to the minimum cost network flow problem. [11] Construct a flow network with the following layers: Layer 1: One source-node s. Layer 2: a node for each agent. There is an arc from s to each agent i, with cost 0 and capacity c i. Level 3: a node for each task.

  6. Flow network - Wikipedia

    en.wikipedia.org/wiki/Flow_network

    A flow must satisfy the restriction that the amount of flow into a node equals the amount of flow out of it, unless it is a source, which has only outgoing flow, or sink, which has only incoming flow. A network can be used to model traffic in a computer network, circulation with demands, fluids in pipes, currents in an electrical circuit, or ...

  7. Minimum-cost flow problem - Wikipedia

    en.wikipedia.org/wiki/Minimum-cost_flow_problem

    The idea is to reduce this problem to a network flow problem. Let G′ = (V′ = A ∪ B, E′ = E). Assign the capacity of all the edges in E′ to 1. Add a source vertex s and connect it to all the vertices in A′ and add a sink vertex t and connect all vertices inside group B′ to this vertex. The capacity of all the new edges is 1 and ...

  8. Ford–Fulkerson algorithm - Wikipedia

    en.wikipedia.org/wiki/Ford–Fulkerson_algorithm

    The Ford–Fulkerson method or Ford–Fulkerson algorithm (FFA) is a greedy algorithm that computes the maximum flow in a flow network.It is sometimes called a "method" instead of an "algorithm" as the approach to finding augmenting paths in a residual graph is not fully specified [1] or it is specified in several implementations with different running times. [2]

  9. Maximum flow problem - Wikipedia

    en.wikipedia.org/wiki/Maximum_flow_problem

    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 .