pgr_boykovKolmogorov - Proposed¶
Synopsis¶
pgr_boykovKolmogorov
— Calculates the flow on the graph edges that maximizes the flow from the sources to the targets using Boykov Kolmogorov algorithm.
Availability:
- Renamed 2.5.0, Previous name pgr_maxFlowBoykovKolmogorov
- New in 2.3.0
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
Characteristics
- 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
- Running time: Polynomial
Signature Summary¶
pgr_boykovKolmogorov(edges_sql, source, target) - Proposed
pgr_boykovKolmogorov(edges_sql, sources, target) - Proposed
pgr_boykovKolmogorov(edges_sql, source, targets) - Proposed
pgr_boykovKolmogorov(edges_sql, sources, targets) - Proposed
RETURNS SET OF (seq, edge, start_vid, end_vid, flow, residual_capacity)
OR EMPTY SET
One to One¶
Calculates the flow on the graph edges that maximizes the flow from the source to the target.
pgr_boykovKolmogorov(edges_sql, source, target)
RETURNS SET OF (seq, edge, start_vid, end_vid, flow, residual_capacity)
OR EMPTY SET
Example: |
---|
SELECT * FROM pgr_boykovKolmogorov(
'SELECT id,
source,
target,
capacity,
reverse_capacity
FROM edge_table'
, 6, 11
);
seq | edge | start_vid | end_vid | flow | residual_capacity
-----+------+-----------+---------+------+-------------------
1 | 10 | 5 | 10 | 100 | 30
2 | 8 | 6 | 5 | 100 | 30
3 | 11 | 6 | 11 | 130 | 0
4 | 12 | 10 | 11 | 100 | 0
(4 rows)
One to Many¶
Calculates the flow on the graph edges that maximizes the flow from the source to all of the targets.
pgr_boykovKolmogorov(edges_sql, source, targets)
RETURNS SET OF (seq, edge, start_vid, end_vid, flow, residual_capacity)
OR EMPTY SET
Example: |
---|
SELECT * FROM pgr_boykovKolmogorov(
'SELECT id,
source,
target,
capacity,
reverse_capacity
FROM edge_table'
, 6, ARRAY[1, 3, 11]
);
seq | edge | start_vid | end_vid | flow | residual_capacity
-----+------+-----------+---------+------+-------------------
1 | 1 | 2 | 1 | 50 | 80
2 | 3 | 4 | 3 | 80 | 50
3 | 4 | 5 | 2 | 50 | 0
4 | 10 | 5 | 10 | 80 | 50
5 | 8 | 6 | 5 | 130 | 0
6 | 9 | 6 | 9 | 80 | 50
7 | 11 | 6 | 11 | 130 | 0
8 | 16 | 9 | 4 | 80 | 0
9 | 12 | 10 | 11 | 80 | 20
(9 rows)
Many to One¶
Calculates the flow on the graph edges that maximizes the flow from all of the sources to the target.
pgr_boykovKolmogorov(edges_sql, sources, target)
RETURNS SET OF (seq, edge, start_vid, end_vid, flow, residual_capacity)
OR EMPTY SET
Example: |
---|
SELECT * FROM pgr_boykovKolmogorov(
'SELECT id,
source,
target,
capacity,
reverse_capacity
FROM edge_table'
, ARRAY[6, 8, 12], 11
);
seq | edge | start_vid | end_vid | flow | residual_capacity
-----+------+-----------+---------+------+-------------------
1 | 10 | 5 | 10 | 100 | 30
2 | 8 | 6 | 5 | 100 | 30
3 | 11 | 6 | 11 | 130 | 0
4 | 12 | 10 | 11 | 100 | 0
(4 rows)
Many to Many¶
Calculates the flow on the graph edges that maximizes the flow from all of the sources to all of the targets.
pgr_boykovKolmogorov(edges_sql, sources, targets)
RETURNS SET OF (seq, edge, start_vid, end_vid, flow, residual_capacity)
OR EMPTY SET
Example: |
---|
SELECT * FROM pgr_boykovKolmogorov(
'SELECT id,
source,
target,
capacity,
reverse_capacity
FROM edge_table'
, ARRAY[6, 8, 12], ARRAY[1, 3, 11]
);
seq | edge | start_vid | end_vid | flow | residual_capacity
-----+------+-----------+---------+------+-------------------
1 | 1 | 2 | 1 | 50 | 80
2 | 3 | 4 | 3 | 80 | 50
3 | 4 | 5 | 2 | 50 | 0
4 | 10 | 5 | 10 | 100 | 30
5 | 8 | 6 | 5 | 130 | 0
6 | 9 | 6 | 9 | 80 | 50
7 | 11 | 6 | 11 | 130 | 0
8 | 7 | 8 | 5 | 20 | 30
9 | 16 | 9 | 4 | 80 | 0
10 | 12 | 10 | 11 | 100 | 0
(10 rows)
Description of the Signatures¶
Description of the edges_sql query for Max-flow like functions¶
edges_sql: | an SQL query, 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 |
Weight of the edge (source, target)
|
|
reverse_capacity | ANY-INTEGER |
-1 | Weight of the edge (target, source),
|
Where:
ANY-INTEGER: | SMALLINT, INTEGER, BIGINT |
---|
Description of the Parameters of the Flow Signatures¶
Column | Type | Default | Description |
---|---|---|---|
edges_sql | TEXT |
The edges SQL query as described above. | |
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. |
Description of the Return Values¶
Column | Type | Description |
---|---|---|
seq | INT |
Sequential value starting from 1. |
edge_id | BIGINT |
Identifier of the edge in the original query(edges_sql). |
source | BIGINT |
Identifier of the first end point vertex of the edge. |
target | BIGINT |
Identifier of the second end point vertex of the edge. |
flow | BIGINT |
Flow through the edge in the direction (source, target). |
residual_capacity | BIGINT |
Residual capacity of the edge in the direction (source, target). |
See Also¶
- Flow - Family of functions, pgr_pushRelabel, pgr_EdmondsKarp
- http://www.boost.org/libs/graph/doc/boykov_kolmogorov_max_flow.html
Indices and tables