Version 5.0 The LEDA User Manual

The algorithms have the following arithmetic demands. Let C be the maximal absolute
value of any edge capacity. If all capacities are integral then all intermediate values are
bounded by d · C, where d is the out-degree of the source.
The pre-instantiations for number type double compute the maximum flow for a modified
capacity function cap1 , where for every edge e
cap1 [e] = sign(cap[e])⌊|cap[e]| · S⌋/S
and S is the largest power of two such that S < 2 53 /(d · C).
The value of the maximum flow for the modified capacity function and the value of the
maximum flow for the original capacity function differ by at most m · d · C · 2 −52 .
The following functions are available:
template
inline NT MAX FLOW T(const graph& G, node s, node t,
const edge array& cap, edge array& f)
computes a maximum (s, t)-flow f in the network (G, s, t, cap) and returns the
value of the flow.
The implementation uses the preflow-push method of Goldberg and Tarjan [43]
with the local and global relabeling heuristic and the gap heuristic. The highest
level rule is used to select active nodes. The section on maximum flow of the
LEDA book gives full information.
template
inline NT MAX FLOW T(const graph& G, node s, node t,
const edge array& cap, edge array& f,
list& st cut)
as above, also computes a minimum s − t cut in G.
template
inline NT MAX FLOW T(const graph& G, node s, node t,
const edge array& cap, edge array& f,
int& num pushes, int& num edge inspections,
int& num relabels, int& num global relabels, int& num gaps,
float h)
as above;
The additional parameter report some statistics of the execution (the number
of pushes, the number of edge inspections, the number of relabels, the number
of global relabels, and the number of nodes moved by the gap heuristic.
The parameter h controls the global relabeling heuristic. The global relabeling
heuristic is called every h · m edge inspections. The choice h = 5 seems
reasonable.
template