DESCRIPTION
v.net.flow computes the maximum flow and minimum cut
between two sets of nodes.
NOTES
The two sets of nodes are called sources and sink
and v.net.flow finds the maximimum flow from the former to
the latter ones. Edge capacities can be specified by afcolumn
for forward direction and abcolumn for backward direction. If
the latter parameter is ommited then the same capacity is used in
either direction. The sets are given by the respective cats,
layer and where parameters. Maximum flow corresponds
to the maximum amount of water possibly flowing through the network
preserving the capacity constraints and minimum cut to the set of edges
of minimum total capacity completely separating sources from sinks.
The cut produced by this module corresponds to the first fully
saturated edges from sources to sinks. An attribute table containing
the flow information is linked to the output map. The table
consists of two columns: cat and flow and stores
the flow along each line. Negative flow means that "water" is
flowing in the backward direction. Cut map contains the edges
in the minimum cut.
A famous result
says that the total amount of water flowing is equal to the minimum
cut.
EXAMPLES
Find maximum flow from factories to stores using SPEED for the capacities.
v.net.flow input=roads output=roads_flow cut=roads_cut afcolumn=SPEED \
source_where="type=factory" sink_where="type=store"
If all the capacties are one then the minimum cut corresponds to the
minimum number of edges separating sources from sinks.
v.net.flow input=network output=flow cut=cut afcolumn=ones \
source_cats=1-10 sink_cats=100-100
SEE ALSO
v.net,
v.net.connectivity
AUTHORS
Daniel Bundala, Google Summer of Code 2009, Student
Wolf Bergenheim, Mentor
Last changed: $Date$