pgr_edgeDisjointPaths

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

_images/boost-inside.jpeg

Boost Graph Inside

Availability

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])

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