# pgr_edgeDisjointPaths¶

pgr_edgeDisjointPaths — Calculates edge disjoint paths between two groups of vertices.

Availability

• Version 3.2.0

• New proposed function:

• pgr_edgeDisjointPaths(Combinations)

• 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 SET OF (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 SET OF (seq, path_id, path_seq, node, edge, cost, agg_cost)
OR EMPTY SET
Example

From vertex $$6$$ to vertex $$11$$

SELECT * FROM pgr_edgeDisjointPaths(
'SELECT id, source, target, cost, reverse_cost
FROM edge_table',
6, 11);
seq | path_id | path_seq | node | edge | cost | agg_cost
-----+---------+----------+------+------+------+----------
1 |       1 |        1 |    6 |    8 |    1 |        0
2 |       1 |        2 |    5 |   10 |    1 |        1
3 |       1 |        3 |   10 |   12 |    1 |        2
4 |       1 |        4 |   11 |   -1 |    0 |        3
5 |       2 |        1 |    6 |   11 |    1 |        0
6 |       2 |        2 |   11 |   -1 |    0 |        1
(6 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 $$6$$ to vertices $$\{1, 3, 11\}$$

SELECT * FROM pgr_edgeDisjointPaths(
'SELECT id, source, target, cost, reverse_cost
FROM edge_table',
6, ARRAY[1, 3, 11]);
seq | path_id | path_seq | end_vid | node | edge | cost | agg_cost
-----+---------+----------+---------+------+------+------+----------
1 |       1 |        1 |       1 |    6 |    8 |    1 |        0
2 |       1 |        2 |       1 |    5 |    4 |    1 |        1
3 |       1 |        3 |       1 |    2 |    1 |    1 |        2
4 |       1 |        4 |       1 |    1 |   -1 |    0 |        3
5 |       2 |        1 |       3 |    6 |    9 |    1 |        0
6 |       2 |        2 |       3 |    9 |   16 |    1 |        1
7 |       2 |        3 |       3 |    4 |    3 |    1 |        2
8 |       2 |        4 |       3 |    3 |   -1 |    0 |        3
9 |       3 |        1 |      11 |    6 |    8 |    1 |        0
10 |       3 |        2 |      11 |    5 |   10 |    1 |        1
11 |       3 |        3 |      11 |   10 |   12 |    1 |        2
12 |       3 |        4 |      11 |   11 |   -1 |    0 |        3
13 |       4 |        1 |      11 |    6 |   11 |    1 |        0
14 |       4 |        2 |      11 |   11 |   -1 |    0 |        1
(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 $$\{6, 8, 12\}$$ to vertex $$11$$

SELECT * FROM pgr_edgeDisjointPaths(
'SELECT id, source, target, cost, reverse_cost
FROM edge_table',
ARRAY[6, 8, 12], 11);
seq | path_id | path_seq | start_vid | node | edge | cost | agg_cost
-----+---------+----------+-----------+------+------+------+----------
1 |       1 |        1 |         6 |    6 |    8 |    1 |        0
2 |       1 |        2 |         6 |    5 |   10 |    1 |        1
3 |       1 |        3 |         6 |   10 |   12 |    1 |        2
4 |       1 |        4 |         6 |   11 |   -1 |    0 |        3
5 |       2 |        1 |         6 |    6 |   11 |    1 |        0
6 |       2 |        2 |         6 |   11 |   -1 |    0 |        1
7 |       3 |        1 |         8 |    8 |    7 |    1 |        0
8 |       3 |        2 |         8 |    5 |    8 |    1 |        1
9 |       3 |        3 |         8 |    6 |   11 |    1 |        2
10 |       3 |        4 |         8 |   11 |   -1 |    0 |        3
11 |       4 |        1 |        12 |   12 |   15 |    1 |        0
12 |       4 |        2 |        12 |    9 |    9 |    1 |        1
13 |       4 |        3 |        12 |    6 |   11 |    1 |        2
14 |       4 |        4 |        12 |   11 |   -1 |    0 |        3
(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 $$\{6, 8, 12\}$$ to vertices $$\{1, 3, 11\}$$

SELECT * FROM pgr_edgeDisjointPaths(
'SELECT id, source, target, cost, reverse_cost
FROM edge_table',
ARRAY[6, 8, 12], ARRAY[1, 3, 11]);
seq | path_id | path_seq | start_vid | end_vid | node | edge | cost | agg_cost
-----+---------+----------+-----------+---------+------+------+------+----------
1 |       1 |        1 |         6 |       1 |    6 |    8 |    1 |        0
2 |       1 |        2 |         6 |       1 |    5 |    4 |    1 |        1
3 |       1 |        3 |         6 |       1 |    2 |    1 |    1 |        2
4 |       1 |        4 |         6 |       1 |    1 |   -1 |    0 |        3
5 |       2 |        1 |         6 |       3 |    6 |    9 |    1 |        0
6 |       2 |        2 |         6 |       3 |    9 |   16 |    1 |        1
7 |       2 |        3 |         6 |       3 |    4 |    3 |    1 |        2
8 |       2 |        4 |         6 |       3 |    3 |   -1 |    0 |        3
9 |       3 |        1 |         6 |      11 |    6 |    8 |    1 |        0
10 |       3 |        2 |         6 |      11 |    5 |   10 |    1 |        1
11 |       3 |        3 |         6 |      11 |   10 |   12 |    1 |        2
12 |       3 |        4 |         6 |      11 |   11 |   -1 |    0 |        3
13 |       4 |        1 |         6 |      11 |    6 |   11 |    1 |        0
14 |       4 |        2 |         6 |      11 |   11 |   -1 |    0 |        1
15 |       5 |        1 |         8 |       1 |    8 |    7 |    1 |        0
16 |       5 |        2 |         8 |       1 |    5 |    4 |    1 |        1
17 |       5 |        3 |         8 |       1 |    2 |    1 |    1 |        2
18 |       5 |        4 |         8 |       1 |    1 |   -1 |    0 |        3
19 |       6 |        1 |         8 |       3 |    8 |    7 |    1 |        0
20 |       6 |        2 |         8 |       3 |    5 |    8 |    1 |        1
21 |       6 |        3 |         8 |       3 |    6 |    9 |    1 |        2
22 |       6 |        4 |         8 |       3 |    9 |   16 |    1 |        3
23 |       6 |        5 |         8 |       3 |    4 |    3 |    1 |        4
24 |       6 |        6 |         8 |       3 |    3 |   -1 |    0 |        5
25 |       7 |        1 |         8 |      11 |    8 |    7 |    1 |        0
26 |       7 |        2 |         8 |      11 |    5 |    8 |    1 |        1
27 |       7 |        3 |         8 |      11 |    6 |   11 |    1 |        2
28 |       7 |        4 |         8 |      11 |   11 |   -1 |    0 |        3
29 |       8 |        1 |        12 |       1 |   12 |   15 |    1 |        0
30 |       8 |        2 |        12 |       1 |    9 |    9 |    1 |        1
31 |       8 |        3 |        12 |       1 |    6 |    8 |    1 |        2
32 |       8 |        4 |        12 |       1 |    5 |    4 |    1 |        3
33 |       8 |        5 |        12 |       1 |    2 |    1 |    1 |        4
34 |       8 |        6 |        12 |       1 |    1 |   -1 |    0 |        5
35 |       9 |        1 |        12 |       3 |   12 |   15 |    1 |        0
36 |       9 |        2 |        12 |       3 |    9 |   16 |    1 |        1
37 |       9 |        3 |        12 |       3 |    4 |    3 |    1 |        2
38 |       9 |        4 |        12 |       3 |    3 |   -1 |    0 |        3
39 |      10 |        1 |        12 |      11 |   12 |   15 |    1 |        0
40 |      10 |        2 |        12 |      11 |    9 |    9 |    1 |        1
41 |      10 |        3 |        12 |      11 |    6 |   11 |    1 |        2
42 |      10 |        4 |        12 |      11 |   11 |   -1 |    0 |        3
(42 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 $$\{1, 2\}$$ to vertices $$\{3, 4, 17\}$$ on an undirected graph.

The combinations table:

SELECT source, target FROM combinations_table
WHERE target NOT IN (1, 2);
source | target
--------+--------
1 |      3
2 |      4
2 |     17
(3 rows)



The query:

SELECT * FROM pgr_edgeDisjointPaths(
'SELECT id, source, target, cost, reverse_cost
FROM edge_table',
'SELECT * FROM combinations_table
WHERE target NOT IN (1, 2)',
directed => false);
seq | path_id | path_seq | start_vid | end_vid | node | edge | cost | agg_cost
-----+---------+----------+-----------+---------+------+------+------+----------
1 |       1 |        1 |         1 |       3 |    1 |    1 |    1 |        0
2 |       1 |        2 |         1 |       3 |    2 |    2 |   -1 |        1
3 |       1 |        3 |         1 |       3 |    3 |   -1 |    0 |        0
4 |       2 |        1 |         2 |       4 |    2 |    2 |   -1 |        0
5 |       2 |        2 |         2 |       4 |    3 |    3 |   -1 |       -1
6 |       2 |        3 |         2 |       4 |    4 |   -1 |    0 |       -2
7 |       3 |        1 |         2 |       4 |    2 |    4 |    1 |        0
8 |       3 |        2 |         2 |       4 |    5 |    8 |    1 |        1
9 |       3 |        3 |         2 |       4 |    6 |    9 |    1 |        2
10 |       3 |        4 |         2 |       4 |    9 |   16 |    1 |        3
11 |       3 |        5 |         2 |       4 |    4 |   -1 |    0 |        4
(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

• When true the graph is considered Directed

• When false the graph is considered as Undirected.

## 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 (target, source)

• When negative: edge (target, source) does not exist, therefore it’s not part of the graph.

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

## Return 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.

• Has value 1 for the first of a path from start_vid to end_vid.

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.

Example

Manually assigned vertex combinations on an undirected graph.

SELECT * FROM pgr_edgeDisjointPaths(
'SELECT id, source, target, cost, reverse_cost
FROM edge_table',
'SELECT * FROM (VALUES (1, 3), (2, 4), (2, 17)) AS t(source, target)',
directed => false);
seq | path_id | path_seq | start_vid | end_vid | node | edge | cost | agg_cost
-----+---------+----------+-----------+---------+------+------+------+----------
1 |       1 |        1 |         1 |       3 |    1 |    1 |    1 |        0
2 |       1 |        2 |         1 |       3 |    2 |    2 |   -1 |        1
3 |       1 |        3 |         1 |       3 |    3 |   -1 |    0 |        0
4 |       2 |        1 |         2 |       4 |    2 |    2 |   -1 |        0
5 |       2 |        2 |         2 |       4 |    3 |    3 |   -1 |       -1
6 |       2 |        3 |         2 |       4 |    4 |   -1 |    0 |       -2
7 |       3 |        1 |         2 |       4 |    2 |    4 |    1 |        0
8 |       3 |        2 |         2 |       4 |    5 |    8 |    1 |        1
9 |       3 |        3 |         2 |       4 |    6 |    9 |    1 |        2
10 |       3 |        4 |         2 |       4 |    9 |   16 |    1 |        3
11 |       3 |        5 |         2 |       4 |    4 |   -1 |    0 |        4
(11 rows)