pgr_edgeDisjointPaths¶
pgr_edgeDisjointPaths
— Calculates edge disjoint paths between two groups of vertices.
Availability
- Version 3.2.0
- New proposed function:
- pgr_edgeDisjointPaths(Combinations)
- New proposed function:
- Version 3.0.0
- Official function
- Version 2.5.0
- Proposed function
- Version 2.3.0
- New Experimental function
Description¶
Calculates the edge disjoint paths between two groups of vertices. Utilizes underlying maximum flow algorithms to calculate the paths.
- The main characterics are:
- Calculates the edge disjoint paths between any two groups of vertices.
- Returns EMPTY SET when source and destination are the same, or cannot be reached.
- The graph can be directed or undirected.
- One to many, many to one, many to many versions are also supported.
- Uses pgr_boykovKolmogorov to calculate the paths.
Signatures¶
Summary
pgr_edgeDisjointPaths(Edges SQL, start_vid, end_vid)
pgr_edgeDisjointPaths(Edges SQL, start_vid, end_vid [, directed])
pgr_edgeDisjointPaths(Edges SQL, start_vid, end_vids [, directed])
pgr_edgeDisjointPaths(Edges SQL, start_vids, end_vid [, directed])
pgr_edgeDisjointPaths(Edges SQL, start_vids, end_vids [, directed])
pgr_edgeDisjointPaths(Edges SQL, Combinations SQL [, directed])
RETURNS SET OF (seq, path_id, path_seq, [start_vid,] [end_vid,] node, edge, cost, agg_cost)
OR EMPTY SET
Using defaults
pgr_edgeDisjointPaths(Edges SQL, start_vid, end_vid)
RETURNS SET OF (seq, path_id, path_seq, node, edge, cost, agg_cost)
OR EMPTY SET
Example: | From vertex \(3\) to vertex \(5\) on a directed graph |
---|
SELECT * FROM pgr_edgeDisjointPaths(
'SELECT id, source, target, cost, reverse_cost FROM edge_table',
3, 5
);
seq | path_id | path_seq | node | edge | cost | agg_cost
-----+---------+----------+------+------+------+----------
1 | 1 | 1 | 3 | 2 | 1 | 0
2 | 1 | 2 | 2 | 4 | 1 | 1
3 | 1 | 3 | 5 | -1 | 0 | 2
4 | 2 | 1 | 3 | 5 | 1 | 0
5 | 2 | 2 | 6 | 8 | 1 | 1
6 | 2 | 3 | 5 | -1 | 0 | 2
(6 rows)
One to One¶
pgr_edgeDisjointPaths(Edges SQL, start_vid, end_vid, directed)
RETURNS SET OF (seq, path_id, path_seq, node, edge, cost, agg_cost)
OR EMPTY SET
Example: | From vertex \(3\) to vertex \(5\) on an undirected graph |
---|
SELECT * FROM pgr_edgeDisjointPaths(
'SELECT id, source, target, cost, reverse_cost FROM edge_table',
3, 5,
directed := false
);
seq | path_id | path_seq | node | edge | cost | agg_cost
-----+---------+----------+------+------+------+----------
1 | 1 | 1 | 3 | 2 | 1 | 0
2 | 1 | 2 | 2 | 4 | 1 | 1
3 | 1 | 3 | 5 | -1 | 0 | 2
4 | 2 | 1 | 3 | 3 | -1 | 0
5 | 2 | 2 | 4 | 16 | 1 | -1
6 | 2 | 3 | 9 | 9 | 1 | 0
7 | 2 | 4 | 6 | 8 | 1 | 1
8 | 2 | 5 | 5 | -1 | 0 | 2
9 | 3 | 1 | 3 | 5 | 1 | 0
10 | 3 | 2 | 6 | 11 | 1 | 1
11 | 3 | 3 | 11 | 12 | -1 | 2
12 | 3 | 4 | 10 | 10 | 1 | 1
13 | 3 | 5 | 5 | -1 | 0 | 2
(13 rows)
One to Many¶
pgr_edgeDisjointPaths(Edges SQL, start_vid, end_vids, directed)
RETURNS SET OF (seq, path_id, path_seq, end_vid, node, edge, cost, agg_cost)
OR EMPTY SET
Example: | From vertex \(3\) to vertices \(\{4, 5, 10\}\) on a directed graph |
---|
SELECT * FROM pgr_edgeDisjointPaths(
'SELECT id, source, target, cost, reverse_cost FROM edge_table',
3, ARRAY[4, 5, 10]
);
seq | path_id | path_seq | end_vid | node | edge | cost | agg_cost
-----+---------+----------+---------+------+------+------+----------
1 | 1 | 1 | 4 | 3 | 5 | 1 | 0
2 | 1 | 2 | 4 | 6 | 9 | 1 | 1
3 | 1 | 3 | 4 | 9 | 16 | 1 | 2
4 | 1 | 4 | 4 | 4 | -1 | 0 | 3
5 | 2 | 1 | 5 | 3 | 2 | 1 | 0
6 | 2 | 2 | 5 | 2 | 4 | 1 | 1
7 | 2 | 3 | 5 | 5 | -1 | 0 | 2
8 | 3 | 1 | 5 | 3 | 5 | 1 | 0
9 | 3 | 2 | 5 | 6 | 8 | 1 | 1
10 | 3 | 3 | 5 | 5 | -1 | 0 | 2
11 | 4 | 1 | 10 | 3 | 2 | 1 | 0
12 | 4 | 2 | 10 | 2 | 4 | 1 | 1
13 | 4 | 3 | 10 | 5 | 10 | 1 | 2
14 | 4 | 4 | 10 | 10 | -1 | 0 | 3
(14 rows)
Many to One¶
pgr_edgeDisjointPaths(Edges SQL, start_vids, end_vid, directed)
RETURNS SET OF (seq, path_id, path_seq, start_vid, node, edge, cost, agg_cost)
OR EMPTY SET
Example: | From vertices \(\{3, 6\}\) to vertex \(5\) on a directed graph |
---|
SELECT * FROM pgr_edgeDisjointPaths(
'SELECT id, source, target, cost, reverse_cost FROM edge_table',
ARRAY[3, 6], 5
);
seq | path_id | path_seq | start_vid | node | edge | cost | agg_cost
-----+---------+----------+-----------+------+------+------+----------
1 | 1 | 1 | 0 | 3 | 2 | 1 | 0
2 | 1 | 2 | 0 | 2 | 4 | 1 | 1
3 | 1 | 3 | 0 | 5 | -1 | 0 | 2
4 | 2 | 1 | 1 | 3 | 5 | 1 | 0
5 | 2 | 2 | 1 | 6 | 8 | 1 | 1
6 | 2 | 3 | 1 | 5 | -1 | 0 | 2
7 | 3 | 1 | 2 | 6 | 8 | 1 | 0
8 | 3 | 2 | 2 | 5 | -1 | 0 | 1
9 | 4 | 1 | 3 | 6 | 9 | 1 | 0
10 | 4 | 2 | 3 | 9 | 16 | 1 | 1
11 | 4 | 3 | 3 | 4 | 3 | 1 | 2
12 | 4 | 4 | 3 | 3 | 2 | 1 | 3
13 | 4 | 5 | 3 | 2 | 4 | 1 | 4
14 | 4 | 6 | 3 | 5 | -1 | 0 | 5
(14 rows)
Many to Many¶
pgr_edgeDisjointPaths(Edges SQL, start_vids, end_vids, directed)
RETURNS SET OF (seq, path_seq, start_vid, end_vid, node, edge, cost, agg_cost)
OR EMPTY SET
Example: | From vertices \(\{3, 6\}\) to vertices \(\{4, 5, 10\}\) on a directed graph |
---|
SELECT * FROM pgr_edgeDisjointPaths(
'SELECT id, source, target, cost, reverse_cost FROM edge_table',
ARRAY[3, 6], ARRAY[4, 5, 10]
);
seq | path_id | path_seq | start_vid | end_vid | node | edge | cost | agg_cost
-----+---------+----------+-----------+---------+------+------+------+----------
1 | 1 | 1 | 0 | 4 | 3 | 5 | 1 | 0
2 | 1 | 2 | 0 | 4 | 6 | 9 | 1 | 1
3 | 1 | 3 | 0 | 4 | 9 | 16 | 1 | 2
4 | 1 | 4 | 0 | 4 | 4 | -1 | 0 | 3
5 | 2 | 1 | 1 | 5 | 3 | 2 | 1 | 0
6 | 2 | 2 | 1 | 5 | 2 | 4 | 1 | 1
7 | 2 | 3 | 1 | 5 | 5 | -1 | 0 | 2
8 | 3 | 1 | 2 | 5 | 3 | 5 | 1 | 0
9 | 3 | 2 | 2 | 5 | 6 | 8 | 1 | 1
10 | 3 | 3 | 2 | 5 | 5 | -1 | 0 | 2
11 | 4 | 1 | 3 | 10 | 3 | 2 | 1 | 0
12 | 4 | 2 | 3 | 10 | 2 | 4 | 1 | 1
13 | 4 | 3 | 3 | 10 | 5 | 10 | 1 | 2
14 | 4 | 4 | 3 | 10 | 10 | -1 | 0 | 3
15 | 5 | 1 | 4 | 4 | 6 | 9 | 1 | 0
16 | 5 | 2 | 4 | 4 | 9 | 16 | 1 | 1
17 | 5 | 3 | 4 | 4 | 4 | -1 | 0 | 2
18 | 6 | 1 | 5 | 5 | 6 | 8 | 1 | 0
19 | 6 | 2 | 5 | 5 | 5 | -1 | 0 | 1
20 | 7 | 1 | 6 | 5 | 6 | 9 | 1 | 0
21 | 7 | 2 | 6 | 5 | 9 | 16 | 1 | 1
22 | 7 | 3 | 6 | 5 | 4 | 3 | 1 | 2
23 | 7 | 4 | 6 | 5 | 3 | 2 | 1 | 3
24 | 7 | 5 | 6 | 5 | 2 | 4 | 1 | 4
25 | 7 | 6 | 6 | 5 | 5 | -1 | 0 | 5
26 | 8 | 1 | 7 | 10 | 6 | 8 | 1 | 0
27 | 8 | 2 | 7 | 10 | 5 | 10 | 1 | 1
28 | 8 | 3 | 7 | 10 | 10 | -1 | 0 | 2
(28 rows)
Combinations¶
pgr_edgeDisjointPaths(Edges SQL, Combinations SQL, directed)
RETURNS SET OF (seq, path_seq, start_vid, end_vid, node, edge, cost, agg_cost)
OR EMPTY SET
Example: | Using a combinations table, equivalent to calculating result from vertices \(\{3, 6\}\) to vertices \(\{4, 5, 10\}\) on a directed graph. |
---|
SELECT * FROM pgr_edgeDisjointPaths(
'SELECT id, source, target, cost, reverse_cost FROM edge_table',
'SELECT * FROM ( VALUES (3, 4), (6, 5), (3, 10) ) AS t(source, target)'
);
seq | path_id | path_seq | start_vid | end_vid | node | edge | cost | agg_cost
-----+---------+----------+-----------+---------+------+------+------+----------
1 | 1 | 1 | 0 | 4 | 3 | 5 | 1 | 0
2 | 1 | 2 | 0 | 4 | 6 | 9 | 1 | 1
3 | 1 | 3 | 0 | 4 | 9 | 16 | 1 | 2
4 | 1 | 4 | 0 | 4 | 4 | -1 | 0 | 3
5 | 2 | 1 | 1 | 5 | 3 | 2 | 1 | 0
6 | 2 | 2 | 1 | 5 | 2 | 4 | 1 | 1
7 | 2 | 3 | 1 | 5 | 5 | -1 | 0 | 2
8 | 3 | 1 | 2 | 5 | 3 | 5 | 1 | 0
9 | 3 | 2 | 2 | 5 | 6 | 8 | 1 | 1
10 | 3 | 3 | 2 | 5 | 5 | -1 | 0 | 2
11 | 4 | 1 | 3 | 10 | 3 | 2 | 1 | 0
12 | 4 | 2 | 3 | 10 | 2 | 4 | 1 | 1
13 | 4 | 3 | 3 | 10 | 5 | 10 | 1 | 2
14 | 4 | 4 | 3 | 10 | 10 | -1 | 0 | 3
15 | 5 | 1 | 4 | 4 | 6 | 9 | 1 | 0
16 | 5 | 2 | 4 | 4 | 9 | 16 | 1 | 1
17 | 5 | 3 | 4 | 4 | 4 | -1 | 0 | 2
18 | 6 | 1 | 5 | 5 | 6 | 8 | 1 | 0
19 | 6 | 2 | 5 | 5 | 5 | -1 | 0 | 1
20 | 7 | 1 | 6 | 5 | 6 | 9 | 1 | 0
21 | 7 | 2 | 6 | 5 | 9 | 16 | 1 | 1
22 | 7 | 3 | 6 | 5 | 4 | 3 | 1 | 2
23 | 7 | 4 | 6 | 5 | 3 | 2 | 1 | 3
24 | 7 | 5 | 6 | 5 | 2 | 4 | 1 | 4
25 | 7 | 6 | 6 | 5 | 5 | -1 | 0 | 5
26 | 8 | 1 | 7 | 10 | 6 | 8 | 1 | 0
27 | 8 | 2 | 7 | 10 | 5 | 10 | 1 | 1
28 | 8 | 3 | 7 | 10 | 10 | -1 | 0 | 2
(28 rows)
Parameters¶
Parameter | Type | Default | Description |
---|---|---|---|
Edges SQL | TEXT |
Edges query as described below | |
Combinations SQL | TEXT |
Combinations query as described below | |
start_vid | BIGINT |
Identifier of the starting vertex of the path. | |
start_vids | ARRAY[BIGINT] |
Array of identifiers of starting vertices. | |
end_vid | BIGINT |
Identifier of the ending vertex of the path. | |
end_vids | ARRAY[BIGINT] |
Array of identifiers of ending vertices. | |
directed | BOOLEAN |
true |
|
Inner queries¶
Edges query¶
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. | |
cost | ANY-NUMERICAL |
Weight of the edge (source, target)
|
|
reverse_cost | ANY-NUMERICAL |
-1 | Weight of the edge (target, source),
|
Where:
ANY-INTEGER: | SMALLINT, INTEGER, BIGINT |
---|---|
ANY-NUMERICAL: | SMALLINT, INTEGER, BIGINT, REAL, FLOAT |
Combinations query¶
Combinations SQL: | |
---|---|
an SQL query which should return a set of rows with the following columns: |
Column | Type | Default | Description |
---|---|---|---|
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. |
Where:
ANY-INTEGER: | 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.
Return Columns¶
Returns set of (seq, path_id, path_seq [, start_vid] [, end_vid], node, edge, cost, agg_cost)
Column | Type | Description |
---|---|---|
seq | INT |
Sequential value starting from 1. |
path_id | INT |
Path identifier. Has value 1 for the first of a path. Used when there are multiple paths for the same start_vid to end_vid combination. |
path_seq | INT |
Relative position in the path. Has value 1 for the beginning of a path. |
start_vid | BIGINT |
Identifier of the starting vertex. Returned when multiple starting vetrices are in the query. |
end_vid | BIGINT |
Identifier of the ending vertex. Returned when multiple ending vertices are in the query. |
node | BIGINT |
Identifier of the node in the path from start_vid to end_vid . |
edge | BIGINT |
Identifier of the edge used to go from node to the next node in the path sequence. -1 for the last node of the path. |
cost | FLOAT |
Cost to traverse from node using edge to the next node in the path sequence. |
agg_cost | FLOAT |
Aggregate cost from start_v to node . |