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 |         0 |       4 |    3 |    5 |    1 |        0
|       1 |        2 |         0 |       4 |    6 |    9 |    1 |        1
|       1 |        3 |         0 |       4 |    9 |   16 |    1 |        2
|       1 |        4 |         0 |       4 |    4 |   -1 |    0 |        3
|       2 |        1 |         1 |       5 |    3 |    2 |    1 |        0
|       2 |        2 |         1 |       5 |    2 |    4 |    1 |        1
|       2 |        3 |         1 |       5 |    5 |   -1 |    0 |        2
|       3 |        1 |         2 |       5 |    3 |    5 |    1 |        0
|       3 |        2 |         2 |       5 |    6 |    8 |    1 |        1
|       3 |        3 |         2 |       5 |    5 |   -1 |    0 |        2
|       4 |        1 |         3 |      10 |    3 |    2 |    1 |        0
|       4 |        2 |         3 |      10 |    2 |    4 |    1 |        1
|       4 |        3 |         3 |      10 |    5 |   10 |    1 |        2
|       4 |        4 |         3 |      10 |   10 |   -1 |    0 |        3
|       5 |        1 |         4 |       4 |    6 |    9 |    1 |        0
|       5 |        2 |         4 |       4 |    9 |   16 |    1 |        1
|       5 |        3 |         4 |       4 |    4 |   -1 |    0 |        2
|       6 |        1 |         5 |       5 |    6 |    8 |    1 |        0
|       6 |        2 |         5 |       5 |    5 |   -1 |    0 |        1
|       7 |        1 |         6 |       5 |    6 |    9 |    1 |        0
|       7 |        2 |         6 |       5 |    9 |   16 |    1 |        1
|       7 |        3 |         6 |       5 |    4 |    3 |    1 |        2
|       7 |        4 |         6 |       5 |    3 |    2 |    1 |        3
|       7 |        5 |         6 |       5 |    2 |    4 |    1 |        4
|       7 |        6 |         6 |       5 |    5 |   -1 |    0 |        5
|       8 |        1 |         7 |      10 |    6 |    8 |    1 |        0
|       8 |        2 |         7 |      10 |    5 |   10 |    1 |        1
|       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`.

pgRouting Manual (3.0-rc1)

pgr_edgeDisjointPaths