Version 5.0 The LEDA User Manual

12.4 Min Cost Flow Algorithms ( min cost flow )
bool
MIN COST FLOW(graph& G, const edge array& lcap,
const edge array& ucap,
const edge array& cost,
const node array& supply,
edge array& 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. The algorithm
is based on capacity scaling and successive
shortest path computation (cf. [28] and [4]) and has
running time O(|E| log U(|E| + |V | log |V |)).
bool
MIN COST FLOW(graph& G, const edge array& cap,
const edge array& cost,
const node array& supply,
edge array& flow)
This variant of MIN COST FLOW assumes that
lcap[e] = 0 for every edge e ∈ E.
int MIN COST MAX FLOW(graph& G, node s, node t,
const edge array& cap,
const edge array& cost,
edge array& 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.