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Min Cost Flow Algorithms ( min_cost_flow )

bool FEASIBLE_FLOW(const graph& G, const node_array< int> & supply, const edge_array< int> & lcap, const edge_array< int> & ucap, edge_array< int> & flow)
    FEASIBLE_FLOW takes as arguments a directed graph G , two edge_arrays lcap and ucap giving for each edge a lower and upper capacity bound, an edge_array cost specifying for each edge an integer cost and a node_array supply defining for each node v a supply or demand (if supply[v] < 0 ). If a feasible flow (fulfilling the capacity and mass balance conditions) exists it computes such a flow and returns true, otherwise false is returned.

bool FEASIBLE_FLOW(const graph& G, const node_array< int> & supply, const edge_array< int> & cap, edge_array< int> & flow)
    as above, but assumes that lcap[e] = 0 for every edge e $ \in$ E .

bool MIN_COST_FLOW(const graph& G, const edge_array< int> & lcap, const edge_array< int> & ucap, const edge_array< int> & cost, const node_array< int> & supply, edge_array< int> & flow)
    MIN_COST_FLOW takes as arguments a directed graph G(V, E) , an edge_array lcap (ucap ) giving for each edge a lower (upper) capacity bound, an edge_array cost specifying for each edge an integer cost and a node_array supply defining for each node v a supply or demand (if supply[v] < 0 ). If a feasible flow (fulfilling the capacity and mass balance conditions) exists it computes such a flow of minimal cost and returns true, otherwise false is returned.

bool MIN_COST_FLOW(const graph& G, const edge_array< int> & cap, const edge_array< int> & cost, const node_array< int> & supply, edge_array< int> & flow)
    This variant of MIN_COST_FLOW assumes that lcap[e] = 0 for every edge e $ \in$ E .

int MIN_COST_MAX_FLOW(const graph& G, node s, node t, const edge_array< int> & cap, const edge_array< int> & cost, edge_array< int> & flow)
    MIN_COST_MAX_FLOW takes as arguments a directed graph G(V, E) , a source node s , a sink node t , an edge_array cap giving for each edge in G a capacity, and an edge_array cost specifying for each edge an integer cost. It computes for every edge e in G a flow flow[e] such that the total flow from s to t is maximal, the total cost of the flow is minimal, and 0 < = flow[e] < = cap[e] for all edges e . MIN_COST_MAX_FLOW returns the total flow from s to t .



next up previous contents index
Next: Minimum Cut ( min_cut Up: Graph Algorithms Previous: Maximum Flow ( max_flow   Contents   Index
Christian Uhrig 2017-04-07