# pgRouting Manual (3.6)

## pgr_edgeDisjointPaths

# `pgr_edgeDisjointPaths`

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

Boost Graph Inside

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 \(11\) 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 set of `(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 set of `(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 set of `(seq, path_id, 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 set of `(seq, path_id, 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`

- 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`

## 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.

- 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.

- Many to One

- Many to Many

- Combinations

`end_vid`

`BIGINT`

Identifier of the ending vertex. Returned when multiple ending vertices are in the query.

- One to Many

- Many to Many

- Combinations

`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)

## See Also

- Flow - Family of functions

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