pgr_maxFlowMinCost_Cost - Experimental¶
pgr_maxFlowMinCost_Cost — Calculates the minimum total cost of the maximum
flow on a graph
Boost Graph Inside¶
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 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 3.2.0
New experimental function:
pgr_maxFlowMinCost_Cost(Combinations)
Version 3.0.0
New experimental function
Description¶
The main characteristics are:
The graph is directed.
Process is done only on edges with positive capacities.
When the maximum flow is 0 then there is no flow and EMPTY SET 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.
Calculates the flow/residual capacity for each edge. In the output
Edges with zero flow are omitted.
Creates a super source and edges to all the source(s), and a super target and the edges from all the targets(s).
The maximum flow through the graph is guaranteed to be the value returned by pgr_maxFlow when executed with the same parameters and can be calculated:
By aggregation of the outgoing flow from the sources
By aggregation of the incoming flow to the targets
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.
Running time: \(O(U * (E + V * logV))\)
where \(U\) is the value of the max flow.
\(U\) is upper bound on number of iterations. In many real world cases number of iterations is much smaller than \(U\).
Signatures¶
Summary
One to One¶
- Example:
From vertex \(11\) to vertex \(12\)
SELECT * FROM pgr_maxFlowMinCost_Cost(
'SELECT id, source, target, capacity, reverse_capacity, cost, reverse_cost
FROM edges',
11, 12);
pgr_maxflowmincost_cost
-------------------------
430
(1 row)
One to Many¶
- Example:
From vertex \(11\) to vertices \(\{5, 10, 12\}\)
SELECT * FROM pgr_maxFlowMinCost_Cost(
'SELECT id, source, target, capacity, reverse_capacity, cost, reverse_cost
FROM edges',
ARRAY[11, 3, 17], 12);
pgr_maxflowmincost_cost
-------------------------
430
(1 row)
Many to One¶
- Example:
From vertices \(\{11, 3, 17\}\) to vertex \(12\)
SELECT * FROM pgr_maxFlowMinCost_Cost(
'SELECT id, source, target, capacity, reverse_capacity, cost, reverse_cost
FROM edges',
11, ARRAY[5, 10, 12]);
pgr_maxflowmincost_cost
-------------------------
760
(1 row)
Many to Many¶
- Example:
From vertices \(\{11, 3, 17\}\) to vertices \(\{5, 10, 12\}\)
SELECT * FROM pgr_maxFlowMinCost_Cost(
'SELECT id, source, target, capacity, reverse_capacity, cost, reverse_cost
FROM edges',
ARRAY[11, 3, 17], ARRAY[5, 10, 12]);
pgr_maxflowmincost_cost
-------------------------
820
(1 row)
Combinations¶
- Example:
Using a combinations table, equivalent to calculating result from vertices \(\{5, 6\}\) to vertices \(\{10, 15, 14\}\).
The combinations table:
SELECT source, target FROM combinations
WHERE target NOT IN (5, 6);
source | target
--------+--------
5 | 10
6 | 15
6 | 14
(3 rows)
The query:
SELECT * FROM pgr_maxFlowMinCost_Cost(
'SELECT id, source, target, capacity, reverse_capacity, cost, reverse_cost
FROM edges',
'SELECT * FROM combinations WHERE target NOT IN (5, 6)');
pgr_maxflowmincost_cost
-------------------------
320
(1 row)
Parameters¶
Column |
Type |
Description |
|---|---|---|
|
Edges SQL as described below |
|
|
Combinations SQL as described below |
|
start vid |
|
Identifier of the starting vertex of the path. |
start vids |
|
Array of identifiers of starting vertices. |
end vid |
|
Identifier of the ending vertex of the path. |
end vids |
|
Array of identifiers of ending vertices. |
Inner Queries¶
Edges SQL¶
Column |
Type |
Default |
Description |
|---|---|---|---|
|
ANY-INTEGER |
Identifier of the edge. |
|
|
ANY-INTEGER |
Identifier of the first end point vertex of the edge. |
|
|
ANY-INTEGER |
Identifier of the second end point vertex of the edge. |
|
|
ANY-INTEGER |
Capacity of the edge (
|
|
|
ANY-INTEGER |
-1 |
Capacity of the edge (
|
|
ANY-NUMERICAL |
Weight of the edge ( |
|
|
ANY-NUMERICAL |
\(-1\) |
Weight of the edge ( |
Where:
- ANY-INTEGER:
SMALLINT,INTEGER,BIGINT- ANY-NUMERICAL:
SMALLINT,INTEGER,BIGINT,REAL,FLOAT
Combinations SQL¶
Parameter |
Type |
Description |
|---|---|---|
|
ANY-INTEGER |
Identifier of the departure vertex. |
|
ANY-INTEGER |
Identifier of the arrival vertex. |
Where:
- ANY-INTEGER:
SMALLINT,INTEGER,BIGINT
Resturn Columns¶
Type |
Description |
|---|---|
|
Minimum Cost Maximum Flow possible from the source(s) to the target(s) |
Additional Examples¶
- Example:
Manually assigned vertex combinations.
SELECT * FROM pgr_maxFlowMinCost_Cost(
'SELECT id, source, target, capacity, reverse_capacity, cost, reverse_cost
FROM edges',
'SELECT * FROM (VALUES (5, 10), (6, 15), (6, 14)) AS t(source, target)');
pgr_maxflowmincost_cost
-------------------------
320
(1 row)
See Also¶
Indices and tables