NAME

       v.net.flow  - Computes the maximum flow between two sets of nodes in the network.

KEYWORDS

       vector, network, flow

SYNOPSIS

       v.net.flow
       v.net.flow help
       v.net.flow    input=name     [layer=integer]     output=name   cut=name    [afcolumn=name]
       [abcolumn=name]   [source_layer=integer]   [source_cats=range]    [source_where=sql_query]
       [sink_layer=integer]      [sink_cats=range]      [sink_where=sql_query]      [--overwrite]
       [--verbose]  [--quiet]

   Flags:
       --overwrite
           Allow output files to overwrite existing files

       --verbose
           Verbose module output

       --quiet
           Quiet module output

   Parameters:
       input=name
           Name of input vector map

       layer=integer
           Layer number
           A single vector map  can  be  connected  to  multiple  database  tables.  This  number
           determines which table to use.
           Default: 1

       output=name
           Name for output vector map

       cut=name
           Name for output vector map containing a minimum cut

       afcolumn=name
           Name of arc forward/both direction(s) capacity column

       abcolumn=name
           Name of arc backward direction capacity column

       source_layer=integer
           Source layer number or name
           A  single  vector  map  can  be  connected  to  multiple  database tables. This number
           determines which table to use.
           Default: 1

       source_cats=range
           Source category values
           Example: 1,3,7-9,13

       source_where=sql_query
           Source WHERE conditions of SQL statement without 'where' keyword
           Example: income = 10000

       sink_layer=integer
           Sink layer number or name
           A single vector map  can  be  connected  to  multiple  database  tables.  This  number
           determines which table to use.
           Default: 1

       sink_cats=range
           Sink category values
           Example: 1,3,7-9,13

       sink_where=sql_query
           Sink WHERE conditions of SQL statement without 'where' keyword
           Example: income = 10000

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: 2013-05-23 13:01:55 -0700 (Thu, 23 May 2013) $

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