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 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 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.
