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.
- Uses pgr_boykovKolmogorov to calculate the paths.
Signatures¶
Summary
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 (seq, path_id, path_seq, [start_vid,] [end_vid,] node, edge, cost, agg_cost) OR EMPTY SET
One to One¶
pgr_edgeDisjointPaths(Edges SQL, start vid, end vid [, directed]) RETURNS (seq, path_id, path_seq, node, edge, cost, agg_cost) OR EMPTY SET
Example: | From vertex \(11\) to vertex \(12\) |
---|
SELECT * FROM pgr_edgeDisjointPaths(
'SELECT id, source, target, cost, reverse_cost
FROM edges',
11, 12);
seq | path_id | path_seq | node | edge | cost | agg_cost
-----+---------+----------+------+------+------+----------
1 | 1 | 1 | 11 | 8 | 1 | 0
2 | 1 | 2 | 7 | 10 | 1 | 1
3 | 1 | 3 | 8 | 12 | 1 | 2
4 | 1 | 4 | 12 | -1 | 0 | 3
5 | 2 | 1 | 11 | 11 | 1 | 0
6 | 2 | 2 | 12 | -1 | 0 | 1
(6 rows)
One to Many¶
pgr_edgeDisjointPaths(Edges SQL, start vid, end vids [, directed]) RETURNS (seq, path_id, path_seq, end_vid, node, edge, cost, agg_cost) OR EMPTY SET
Example: | From vertex \(11\) to vertices \(\{5, 10, 12\}\) |
---|
SELECT * FROM pgr_edgeDisjointPaths(
'SELECT id, source, target, cost, reverse_cost
FROM edges',
11, ARRAY[5, 10, 12]);
seq | path_id | path_seq | end_vid | node | edge | cost | agg_cost
-----+---------+----------+---------+------+------+------+----------
1 | 1 | 1 | 5 | 11 | 8 | 1 | 0
2 | 1 | 2 | 5 | 7 | 4 | 1 | 1
3 | 1 | 3 | 5 | 6 | 1 | 1 | 2
4 | 1 | 4 | 5 | 5 | -1 | 0 | 3
5 | 2 | 1 | 10 | 11 | 9 | 1 | 0
6 | 2 | 2 | 10 | 16 | 16 | 1 | 1
7 | 2 | 3 | 10 | 15 | 3 | 1 | 2
8 | 2 | 4 | 10 | 10 | -1 | 0 | 3
9 | 3 | 1 | 12 | 11 | 8 | 1 | 0
10 | 3 | 2 | 12 | 7 | 10 | 1 | 1
11 | 3 | 3 | 12 | 8 | 12 | 1 | 2
12 | 3 | 4 | 12 | 12 | -1 | 0 | 3
13 | 4 | 1 | 12 | 11 | 11 | 1 | 0
14 | 4 | 2 | 12 | 12 | -1 | 0 | 1
(14 rows)
Many to One¶
pgr_edgeDisjointPaths(Edges SQL, start vids, end vid [, directed]) RETURNS (seq, path_id, path_seq, start_vid, node, edge, cost, agg_cost) OR EMPTY SET
Example: | From vertices \(\{11, 3, 17\}\) to vertex \(12\) |
---|
SELECT * FROM pgr_edgeDisjointPaths(
'SELECT id, source, target, cost, reverse_cost
FROM edges',
ARRAY[11, 3, 17], 12);
seq | path_id | path_seq | start_vid | node | edge | cost | agg_cost
-----+---------+----------+-----------+------+------+------+----------
1 | 1 | 1 | 3 | 3 | 7 | 1 | 0
2 | 1 | 2 | 3 | 7 | 8 | 1 | 1
3 | 1 | 3 | 3 | 11 | 11 | 1 | 2
4 | 1 | 4 | 3 | 12 | -1 | 0 | 3
5 | 2 | 1 | 11 | 11 | 8 | 1 | 0
6 | 2 | 2 | 11 | 7 | 10 | 1 | 1
7 | 2 | 3 | 11 | 8 | 12 | 1 | 2
8 | 2 | 4 | 11 | 12 | -1 | 0 | 3
9 | 3 | 1 | 11 | 11 | 11 | 1 | 0
10 | 3 | 2 | 11 | 12 | -1 | 0 | 1
11 | 4 | 1 | 17 | 17 | 15 | 1 | 0
12 | 4 | 2 | 17 | 16 | 9 | 1 | 1
13 | 4 | 3 | 17 | 11 | 11 | 1 | 2
14 | 4 | 4 | 17 | 12 | -1 | 0 | 3
(14 rows)
Many to Many¶
pgr_edgeDisjointPaths(Edges SQL, start vids, end vids [, directed]) RETURNS (seq, path_seq, start_vid, end_vid, node, edge, cost, agg_cost) OR EMPTY SET
Example: | From vertices \(\{11, 3, 17\}\) to vertices \(\{5, 10, 12\}\) |
---|
SELECT * FROM pgr_edgeDisjointPaths(
'SELECT id, source, target, cost, reverse_cost
FROM edges',
ARRAY[11, 3, 17], ARRAY[5, 10, 12]);
seq | path_id | path_seq | start_vid | end_vid | node | edge | cost | agg_cost
-----+---------+----------+-----------+---------+------+------+------+----------
1 | 1 | 1 | 3 | 5 | 3 | 7 | 1 | 0
2 | 1 | 2 | 3 | 5 | 7 | 4 | 1 | 1
3 | 1 | 3 | 3 | 5 | 6 | 1 | 1 | 2
4 | 1 | 4 | 3 | 5 | 5 | -1 | 0 | 3
5 | 2 | 1 | 3 | 10 | 3 | 7 | 1 | 0
6 | 2 | 2 | 3 | 10 | 7 | 8 | 1 | 1
7 | 2 | 3 | 3 | 10 | 11 | 9 | 1 | 2
8 | 2 | 4 | 3 | 10 | 16 | 16 | 1 | 3
9 | 2 | 5 | 3 | 10 | 15 | 3 | 1 | 4
10 | 2 | 6 | 3 | 10 | 10 | -1 | 0 | 5
11 | 3 | 1 | 3 | 12 | 3 | 7 | 1 | 0
12 | 3 | 2 | 3 | 12 | 7 | 8 | 1 | 1
13 | 3 | 3 | 3 | 12 | 11 | 11 | 1 | 2
14 | 3 | 4 | 3 | 12 | 12 | -1 | 0 | 3
15 | 4 | 1 | 11 | 5 | 11 | 8 | 1 | 0
16 | 4 | 2 | 11 | 5 | 7 | 4 | 1 | 1
17 | 4 | 3 | 11 | 5 | 6 | 1 | 1 | 2
18 | 4 | 4 | 11 | 5 | 5 | -1 | 0 | 3
19 | 5 | 1 | 11 | 10 | 11 | 9 | 1 | 0
20 | 5 | 2 | 11 | 10 | 16 | 16 | 1 | 1
21 | 5 | 3 | 11 | 10 | 15 | 3 | 1 | 2
22 | 5 | 4 | 11 | 10 | 10 | -1 | 0 | 3
23 | 6 | 1 | 11 | 12 | 11 | 8 | 1 | 0
24 | 6 | 2 | 11 | 12 | 7 | 10 | 1 | 1
25 | 6 | 3 | 11 | 12 | 8 | 12 | 1 | 2
26 | 6 | 4 | 11 | 12 | 12 | -1 | 0 | 3
27 | 7 | 1 | 11 | 12 | 11 | 11 | 1 | 0
28 | 7 | 2 | 11 | 12 | 12 | -1 | 0 | 1
29 | 8 | 1 | 17 | 5 | 17 | 15 | 1 | 0
30 | 8 | 2 | 17 | 5 | 16 | 16 | 1 | 1
31 | 8 | 3 | 17 | 5 | 15 | 3 | 1 | 2
32 | 8 | 4 | 17 | 5 | 10 | 2 | 1 | 3
33 | 8 | 5 | 17 | 5 | 6 | 1 | 1 | 4
34 | 8 | 6 | 17 | 5 | 5 | -1 | 0 | 5
35 | 9 | 1 | 17 | 10 | 17 | 15 | 1 | 0
36 | 9 | 2 | 17 | 10 | 16 | 16 | 1 | 1
37 | 9 | 3 | 17 | 10 | 15 | 3 | 1 | 2
38 | 9 | 4 | 17 | 10 | 10 | -1 | 0 | 3
39 | 10 | 1 | 17 | 12 | 17 | 15 | 1 | 0
40 | 10 | 2 | 17 | 12 | 16 | 9 | 1 | 1
41 | 10 | 3 | 17 | 12 | 11 | 11 | 1 | 2
42 | 10 | 4 | 17 | 12 | 12 | -1 | 0 | 3
(42 rows)
Combinations¶
pgr_edgeDisjointPaths(Edges SQL, Combinations SQL [, directed]) RETURNS (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 \(\{5, 6\}\) to vertices \(\{10, 15, 14\}\) on an undirected graph. |
---|
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_edgeDisjointPaths(
'SELECT id, source, target, cost, reverse_cost
FROM edges',
'SELECT * FROM combinations WHERE target NOT IN (5, 6)',
directed => false);
seq | path_id | path_seq | start_vid | end_vid | node | edge | cost | agg_cost
-----+---------+----------+-----------+---------+------+------+------+----------
1 | 1 | 1 | 5 | 10 | 5 | 1 | 1 | 0
2 | 1 | 2 | 5 | 10 | 6 | 2 | -1 | 1
3 | 1 | 3 | 5 | 10 | 10 | -1 | 0 | 0
4 | 2 | 1 | 6 | 15 | 6 | 4 | 1 | 0
5 | 2 | 2 | 6 | 15 | 7 | 8 | 1 | 1
6 | 2 | 3 | 6 | 15 | 11 | 9 | 1 | 2
7 | 2 | 4 | 6 | 15 | 16 | 16 | 1 | 3
8 | 2 | 5 | 6 | 15 | 15 | -1 | 0 | 4
9 | 3 | 1 | 6 | 15 | 6 | 2 | -1 | 0
10 | 3 | 2 | 6 | 15 | 10 | 3 | -1 | -1
11 | 3 | 3 | 6 | 15 | 15 | -1 | 0 | -2
(11 rows)
Parameters¶
Column | Type | Description |
---|---|---|
Edges SQL | TEXT |
Edges SQL as described below |
Combinations SQL | TEXT |
Combinations SQL 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. |
Optional parameters¶
Column | Type | Default | Description |
---|---|---|---|
directed |
BOOLEAN |
true |
|
Inner Queries¶
Edges SQL¶
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 (
|
Where:
ANY-INTEGER: | SMALLINT , INTEGER , BIGINT |
---|---|
ANY-NUMERICAL: | SMALLINT , INTEGER , BIGINT , REAL , FLOAT |
Combinations SQL¶
Parameter | Type | Description |
---|---|---|
source |
ANY-INTEGER | Identifier of the departure vertex. |
target |
ANY-INTEGER | Identifier of the arrival vertex. |
Where:
ANY-INTEGER: | SMALLINT , INTEGER , BIGINT |
---|
Result Columns¶
Set of (seq, path_id, path_seq [, start_vid] [, end_vid], node, edge, cost,
agg_cost)
Column | Type | Description |
---|---|---|
seq |
INTEGER |
Sequential value starting from 1. |
path_id |
INTEGER |
Path identifier.
|
path_seq |
INTEGER |
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_vid to node . |
Additional Examples¶
Example: | Manually assigned vertex combinations on an undirected graph. |
---|
SELECT * FROM pgr_edgeDisjointPaths(
'SELECT id, source, target, cost, reverse_cost
FROM edges',
'SELECT * FROM (VALUES (5, 10), (6, 15), (6, 14)) AS t(source, target)',
directed => false);
seq | path_id | path_seq | start_vid | end_vid | node | edge | cost | agg_cost
-----+---------+----------+-----------+---------+------+------+------+----------
1 | 1 | 1 | 5 | 10 | 5 | 1 | 1 | 0
2 | 1 | 2 | 5 | 10 | 6 | 2 | -1 | 1
3 | 1 | 3 | 5 | 10 | 10 | -1 | 0 | 0
4 | 2 | 1 | 6 | 15 | 6 | 4 | 1 | 0
5 | 2 | 2 | 6 | 15 | 7 | 8 | 1 | 1
6 | 2 | 3 | 6 | 15 | 11 | 9 | 1 | 2
7 | 2 | 4 | 6 | 15 | 16 | 16 | 1 | 3
8 | 2 | 5 | 6 | 15 | 15 | -1 | 0 | 4
9 | 3 | 1 | 6 | 15 | 6 | 2 | -1 | 0
10 | 3 | 2 | 6 | 15 | 10 | 3 | -1 | -1
11 | 3 | 3 | 6 | 15 | 15 | -1 | 0 | -2
(11 rows)