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).
Warning
Possible server crash
These functions might create a server crash
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 ANYINTEGER and ANYNUMERICAL
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 3.2.0
New experimental function:
pgr_maxFlowMinCost_Cost(Combinations)
Version 3.0.0
New experimental function
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)
pgr_maxFlowMinCost_Cost(Edges SQL, Combinations SQL)
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)
Combinations¶
pgr_maxFlowMinCost_Cost(Edges SQL, Combinations SQL)
RETURNS FLOAT
 Example
Using a combinations table, equivalent to calculating result 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',
'SELECT * FROM ( VALUES (7, 3), (13, 9) ) AS t(source, target)'
);
pgr_maxflowmincost_cost

600
(1 row)
Parameters¶
Column 
Type 
Default 
Description 

Edges SQL 

Edges query as described in Inner Queries. 

Combinations SQL 

Combinations query as described in Inner Queries. 

source 

Identifier of the starting vertex of the flow. 

sources 

Array of identifiers of the starting vertices of the flow. 

target 

Identifier of the ending vertex of the flow. 

targets 

Array of identifiers of the ending vertices of the flow. 
Inner queries¶
 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 

Identifier of the edge. 

source 

Identifier of the first end point vertex of the edge. 

target 

Identifier of the second end point vertex of the edge. 

capacity 

Capacity of the edge (source, target)


reverse_capacity 

1 
Capacity of the edge (target, source),

cost 

Weight of the edge (source, target) if it exists. 

reverse_cost 

0 
Weight of the edge (target, source) if it exists. 
Where:
 ANYINTEGER
SMALLINT, INTEGER, BIGINT
 ANYNUMERICAL
smallint, int, bigint, real, float
 Combinations SQL
an SQL query which should return a set of rows with the following columns:
Column 
Type 
Default 
Description 

source 

Identifier of the first end point vertex of the edge. 

target 

Identifier of the second end point vertex of the edge. 
Where:
 ANYINTEGER
SMALLINT, INTEGER, BIGINT
The function aggregates the sources and the targets, removes the duplicates, and then it calculates the result from the resultant source vertices to the target vertices.
Result Columns¶
Type 
Description 


Minimum Cost Maximum Flow possible from the source(s) to the target(s) 
See Also¶
Indices and tables