pgr_maxFlowMinCost_Cost - Experimental

pgr_maxFlowMinCost_Cost — Calculates the minmum cost maximum flow in a directed graph from the source(s) to the targets(s).

_images/boost-inside.jpeg

Boost Graph Inside

Warning

Experimental functions

  • They are not officially of the current release.
  • They likely will not be officially be part of the next release:
    • The functions might not make use of ANY-INTEGER and ANY-NUMERICAL
    • Name might change.
    • Signature might change.
    • Functionality might change.
    • pgTap tests might be missing.
    • Might need c/c++ coding.
    • May lack documentation.
    • Documentation if any might need to be rewritten.
    • Documentation examples might need to be automatically generated.
    • Might need a lot of feedback from the comunity.
    • Might depend on a proposed function of pgRouting
    • Might depend on a deprecated function of pgRouting

Availability

  • Version 3.0.0
    • New experimental function

Support

  • Supported versions: current(3.0)

Description

The main characteristics are:

  • The graph is directed.
  • The cost value of all input edges must be nonnegative.
  • When the maximum flow is 0 then there is no flow and 0 is returned.
    • There is no flow when a source is the same as a target.
  • Any duplicated value in the source(s) or target(s) are ignored.
  • Uses the pgr_maxFlowMinCost algorithm.
  • Running time: \(O(U * (E + V * logV))\), where \(U\) is the value of the max flow. \(U\) is upper bound on number of iteration. In many real world cases number of iterations is much smaller than \(U\).

Signatures

Summary

pgr_maxFlowMinCost_Cost(Edges SQL, source, target)
pgr_maxFlowMinCost_Cost(Edges SQL, sources, target)
pgr_maxFlowMinCost_Cost(Edges SQL, source, targets)
pgr_maxFlowMinCost_Cost(Edges SQL, sources, targets)
RETURNS FLOAT

One to One

pgr_maxFlowMinCost_Cost(Edges SQL, source, target)
RETURNS FLOAT
Example:From vertex \(2\) to vertex \(3\)
SELECT * FROM pgr_MaxFlowMinCost_Cost(
    'SELECT id,
     source, target,
     capacity, reverse_capacity,
     cost, reverse_cost FROM edge_table',
    2, 3
);
 pgr_maxflowmincost_cost
-------------------------
                     400
(1 row)

One to Many

pgr_maxFlowMinCost_Cost(Edges SQL, source, targets)
RETURNS FLOAT
Example:From vertex \(13\) to vertices \(\{7, 1, 4\}\)
SELECT * FROM pgr_MaxFlowMinCost_Cost(
    'SELECT id,
     source, target,
     capacity, reverse_capacity,
     cost, reverse_cost FROM edge_table',
    13, ARRAY[7, 1, 4]
);
 pgr_maxflowmincost_cost
-------------------------
                     450
(1 row)

Many to One

pgr_maxFlowMinCost_Cost(Edges SQL, sources, target)
RETURNS FLOAT
Example:From vertices \(\{1, 7, 14\}\) to vertex \(12\)
SELECT * FROM pgr_MaxFlowMinCost_Cost(
    'SELECT id,
     source, target,
     capacity, reverse_capacity,
     cost, reverse_cost FROM edge_table',
    ARRAY[1, 7, 14], 12
);
 pgr_maxflowmincost_cost
-------------------------
                     650
(1 row)

Many to Many

pgr_maxFlowMinCost_Cost(Edges SQL, sources, targets)
RETURNS FLOAT
Example:From vertices \(\{7, 13\}\) to vertices \(\{3, 9\}\)
SELECT * FROM pgr_MaxFlowMinCost_Cost(
    'SELECT id,
     source, target,
     capacity, reverse_capacity,
     cost, reverse_cost FROM edge_table',
    ARRAY[7, 13], ARRAY[3, 9]
);
 pgr_maxflowmincost_cost
-------------------------
                     600
(1 row)

Parameters

Column Type Default Description
Edges SQL TEXT   The edges SQL query as described in Inner Query.
source BIGINT   Identifier of the starting vertex of the flow.
sources ARRAY[BIGINT]   Array of identifiers of the starting vertices of the flow.
target BIGINT   Identifier of the ending vertex of the flow.
targets ARRAY[BIGINT]   Array of identifiers of the ending vertices of the flow.

Inner query

Edges SQL:an SQL query of a directed graph of capacities, which should return a set of rows with the following columns:
Column Type Default Description
id ANY-INTEGER   Identifier of the edge.
source ANY-INTEGER   Identifier of the first end point vertex of the edge.
target ANY-INTEGER   Identifier of the second end point vertex of the edge.
capacity ANY-INTEGER  

Capacity of the edge (source, target)

  • When negative: edge (source, target) does not exist, therefore it’s not part of the graph.
reverse_capacity ANY-INTEGER -1

Capacity of the edge (target, source),

  • When negative: edge (target, source) does not exist, therefore it’s not part of the graph.
cost ANY-NUMERICAL   Weight of the edge (source, target) if it exists.
reverse_cost ANY-NUMERICAL 0 Weight of the edge (target, source) if it exists.

Where:

ANY-INTEGER:SMALLINT, INTEGER, BIGINT
ANY-NUMERICAL:smallint, int, bigint, real, float

Result Columns

Type Description
FLOAT Minimum Cost Maximum Flow possible from the source(s) to the target(s)