pgr_edgeDisjointPaths

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

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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

Support

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])
pgr_edgeDisjointPaths(Edges SQL, Combinations SQL [, directed]) -- Proposed on v3.2

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)

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 \(\{3, 6\}\) to vertices \(\{4, 5, 10\}\) on a directed graph.

SELECT * FROM pgr_edgeDisjointPaths(
    'SELECT id, source, target, cost, reverse_cost FROM edge_table',
    'SELECT * FROM ( VALUES (3, 4), (6, 5), (3, 10) ) AS t(source, target)'
);
 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

Edges query as described below

Combinations SQL

TEXT

Combinations 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 queries

Edges 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

Combinations query

Combinations SQL

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

Column

Type

Default

Description

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.

Where:

ANY-INTEGER

SMALLINT, INTEGER, BIGINT

The function aggregates the sources and the targets, removes the duplicates, and then it calculates the result from the resultant source vertices to the target vertices.

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.

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_v to node.

See Also

Indices and tables