# pgr_edgeDisjointPaths - Proposed¶

## Name¶

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

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.

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

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

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

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

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 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.