# pgRouting Manual (3.0-rc1)

## pgr_edgeDisjointPaths

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

Boost Graph Inside

Availability

- Version 3.0.0
  - Official function
- Version 2.5.0
  - Proposed function
- Version 2.3.0
  - New Experimental function

Support

- Supported versions: current(3.0)
- Unsupported versions: 2.6 2.5 2.4 2.3

## 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])

    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)

## Parameters

Parameter | Type | Default | Description
--- | --- | --- | ---
edges_sql | `TEXT` |  | Inner SQL 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`

- When `true` Graph is considered Directed
- When `false` the graph is considered as Undirected.

## Inner 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)

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

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

## 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.

- Many to One
- Many to Many

end_vid

`BIGINT`

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

- One to Many
- Many to Many

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`.

## See Also

- Flow - Family of functions

Indices and tables

- Index
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