# pgRouting Manual (2.5)

## pgr_edgeDisjointPaths - Proposed

## Name

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

Boost Graph Inside

Availability: 2.3.0

Warning

Experimental functions

- They are not officially of the current release.
- They likely will not be officially be part of the next release:
  - The functions might not make use of ANY-INTEGER and ANY-NUMERICAL
  - Name might change.
  - Signature might change.
  - Functionality might change.
  - pgTap tests might be missing.
  - Might need c/c++ coding.
  - May lack documentation.
  - Documentation if any might need to be rewritten.
  - Documentation examples might need to be automatically generated.
  - Might need a lot of feedback from the comunity.
  - Might depend on a proposed function of pgRouting
  - Might depend on a deprecated function of pgRouting

## Synopsis

Calculates the edge disjoint paths between two groups of vertices. Utilizes underlying maximum flow algorithms to calculate the paths.

## Characteristics:

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 - Proposed to calculate the paths.

## Signature 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

## Signatures

### Minimal use

    pgr_edgeDisjointPaths(edges_sql, start_vid, end_vid)
    RETURNS SET OF (seq, path_id, path_seq, node, edge, cost, agg_cost)
    OR EMPTY SET

The minimal use is for a directed graph from one `start_vid` to one `end_vid`.

Example: |

    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

This signature finds the set of dijoint paths from one `start_vid` to one `end_vid`:
  - on a directed graph when `directed` flag is missing or is set to `true`.
  - on an undirected graph when `directed` flag is set to `false`.

    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: |

    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

This signature finds the sset of disjoint paths from the `start_vid` to each one of the `end_vid` in `end_vids`:
  - on a directed graph when `directed` flag is missing or is set to `true`.
  - on an undirected graph when `directed` flag is set to `false`.
  - The result is equivalent to the union of the results of the one to one pgr_edgeDisjointPaths.
  - The extra `end_vid` in the result is used to distinguish to which path it belongs.

    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: |

    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

This signature finds the set of disjoint paths from each one of the `start_vid` in `start_vids` to the `end_vid`:
  - on a directed graph when `directed` flag is missing or is set to `true`.
  - on an undirected graph when `directed` flag is set to `false`.
  - The result is equivalent to the union of the results of the one to one pgr_edgeDisjointPaths.
  - The extra `start_vid` in the result is used to distinguish to which path it belongs.

    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: |

    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

This signature finds the set of disjoint paths from each one of the `start_vid` in `start_vids` to each one of the `end_vid` in `end_vids`:
  - on a directed graph when `directed` flag is missing or is set to `true`.
  - on an undirected graph when `directed` flag is set to `false`.
  - The result is equivalent to the union of the results of the one to one pgr_edgeDisjointPaths.
  - The extra `start_vid` and `end_vid` in the result is used to distinguish to which path it belongs.

    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: |

    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)

## Description of the Signatures

### Description of the edges_sql query for dijkstra like functions

edges_sql: | an SQL query, which should return a set of rows with the following columns:

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

### Description of the parameters of the signatures

Column | Type | Default | Description
--- | --- | --- | ---
sql | `TEXT` |  | SQL query as described above.
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.

### Description of the return values for a path

Returns set of `(seq, 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. Used when multiple starting vetrices are in the query.
end_vid | `BIGINT` | Identifier of the ending vertex. Used 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`.

## See Also

- Flow - Family of functions

Indices and tables

- Index
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