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
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)
|
|
reverse_capacity | ANY-INTEGER |
-1 | Capacity of the edge (target, source),
|
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) |