pgr_edgeDisjointPaths

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

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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.
  • 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 (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 (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 (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 (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 (seq, 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 (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 \(\{5, 6\}\) 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.

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_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

Indices and tables