# pgr_dijkstra¶

pgr_dijkstra — Returns the shortest path(s) using Dijkstra algorithm. In particular, the Dijkstra algorithm implemented by Boost.Graph.

Availability

• pgr_dijkstra(one to one) 2.0.0, signature change 2.1.0
• pgr_dijkstra(other signatures) 2.1.0

## Synopsis¶

Dijkstra’s algorithm, conceived by Dutch computer scientist Edsger Dijkstra in 1956. It is a graph search algorithm that solves the shortest path problem for a graph with non-negative edge path costs, producing a shortest path from a starting vertex (start_vid) to an ending vertex (end_vid). This implementation can be used with a directed graph and an undirected graph.

## Characteristics¶

The main Characteristics are:
• Process is done only on edges with positive costs.
• Values are returned when there is a path.
• When the starting vertex and ending vertex are the same, there is no path.
• The agg_cost the non included values (v, v) is 0
• When the starting vertex and ending vertex are the different and there is no path:
• The agg_cost the non included values (u, v) is $$\infty$$
• For optimization purposes, any duplicated value in the start_vids or end_vids are ignored.
• The returned values are ordered:
• start_vid ascending
• end_vid ascending
• Running time: $$O(| start\_vids | * (V \log V + E))$$

## Signature Summary¶

pgr_dijkstra(edges_sql, start_vid,  end_vid)
pgr_dijkstra(edges_sql, start_vid,  end_vid,  directed:=true)
pgr_dijkstra(edges_sql, start_vid,  end_vids, directed:=true)
pgr_dijkstra(edges_sql, start_vids, end_vid,  directed:=true)
pgr_dijkstra(edges_sql, start_vids, end_vids, directed:=true)

RETURNS SET OF (seq, path_seq [, start_vid] [, end_vid], node, edge, cost, agg_cost)
OR EMPTY SET


## Signatures¶

### Minimal signature¶

pgr_dijkstra(TEXT edges_sql, BIGINT start_vid, BIGINT end_vid)
RETURNS SET OF (seq, path_seq, node, edge, cost, agg_cost) or EMPTY SET


The minimal signature is for a directed graph from one start_vid to one end_vid.

SELECT * FROM pgr_dijkstra(
'SELECT id, source, target, cost, reverse_cost FROM edge_table',
2, 3
);
seq | path_seq | node | edge | cost | agg_cost
-----+----------+------+------+------+----------
1 |        1 |    2 |    4 |    1 |        0
2 |        2 |    5 |    8 |    1 |        1
3 |        3 |    6 |    9 |    1 |        2
4 |        4 |    9 |   16 |    1 |        3
5 |        5 |    4 |    3 |    1 |        4
6 |        6 |    3 |   -1 |    0 |        5
(6 rows)



### pgr_dijkstra One to One¶

pgr_dijkstra(TEXT edges_sql, BIGINT start_vid, BIGINT end_vid,
BOOLEAN directed:=true);
RETURNS SET OF (seq, path_seq, node, edge, cost, agg_cost) or EMPTY SET

This signature finds the shortest path 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.
SELECT * FROM pgr_dijkstra(
'SELECT id, source, target, cost, reverse_cost FROM edge_table',
2, 3,
FALSE
);
seq | path_seq | node | edge | cost | agg_cost
-----+----------+------+------+------+----------
1 |        1 |    2 |    2 |    1 |        0
2 |        2 |    3 |   -1 |    0 |        1
(2 rows)



### pgr_dijkstra One to many¶

pgr_dijkstra(TEXT edges_sql, BIGINT start_vid, ARRAY[ANY_INTEGER] end_vids,
BOOLEAN directed:=true);
RETURNS SET OF (seq, path_seq, end_vid, node, edge, cost, agg_cost) or EMPTY SET

This signature finds the shortest path from one start_vid to each 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.

Using this signature, will load once the graph and perform a one to one pgr_dijkstra where the starting vertex is fixed, and stop when all end_vids are reached.

• The result is equivalent to the union of the results of the one to one pgr_dijkstra.
• The extra end_vid in the result is used to distinguish to which path it belongs.
SELECT * FROM pgr_dijkstra(
'SELECT id, source, target, cost FROM edge_table',
2, ARRAY[3,5],
FALSE
);
seq | path_seq | end_vid | node | edge | cost | agg_cost
-----+----------+---------+------+------+------+----------
1 |        1 |       3 |    2 |    4 |    1 |        0
2 |        2 |       3 |    5 |    8 |    1 |        1
3 |        3 |       3 |    6 |    5 |    1 |        2
4 |        4 |       3 |    3 |   -1 |    0 |        3
5 |        1 |       5 |    2 |    4 |    1 |        0
6 |        2 |       5 |    5 |   -1 |    0 |        1
(6 rows)



### pgr_dijkstra Many to One¶

pgr_dijkstra(TEXT edges_sql, ARRAY[ANY_INTEGER] start_vids, BIGINT end_vid,
BOOLEAN directed:=true);
RETURNS SET OF (seq, path_seq, start_vid, node, edge, cost, agg_cost) or EMPTY SET

This signature finds the shortest path from each start_vid in start_vids 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.

Using this signature, will load once the graph and perform several one to one pgr_dijkstra where the ending vertex is fixed.

• The result is the union of the results of the one to one pgr_dijkstra.
• The extra start_vid in the result is used to distinguish to which path it belongs.
SELECT * FROM pgr_dijkstra(
'SELECT id, source, target, cost, reverse_cost FROM edge_table',
ARRAY[2,11], 5
);
seq | path_seq | start_vid | node | edge | cost | agg_cost
-----+----------+-----------+------+------+------+----------
1 |        1 |         2 |    2 |    4 |    1 |        0
2 |        2 |         2 |    5 |   -1 |    0 |        1
3 |        1 |        11 |   11 |   13 |    1 |        0
4 |        2 |        11 |   12 |   15 |    1 |        1
5 |        3 |        11 |    9 |    9 |    1 |        2
6 |        4 |        11 |    6 |    8 |    1 |        3
7 |        5 |        11 |    5 |   -1 |    0 |        4
(7 rows)



### pgr_dijkstra Many to Many¶

pgr_dijkstra(TEXT edges_sql, ARRAY[ANY_INTEGER] start_vids, ARRAY[ANY_INTEGER] end_vids,
BOOLEAN directed:=true);
RETURNS SET OF (seq, path_seq, start_vid, end_vid, node, edge, cost, agg_cost) or EMPTY SET

This signature finds the shortest path from each start_vid in start_vids to each 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.

Using this signature, will load once the graph and perform several one to Many pgr_dijkstra for all start_vids.

• The result is the union of the results of the one to one pgr_dijkstra.
• The extra start_vid in the result is used to distinguish to which path it belongs.

The extra start_vid and end_vid in the result is used to distinguish to which path it belongs.

SELECT * FROM pgr_dijkstra(
'SELECT id, source, target, cost, reverse_cost FROM edge_table',
ARRAY[2,11], ARRAY[3,5],
FALSE
);
seq | path_seq | start_vid | end_vid | node | edge | cost | agg_cost
-----+----------+-----------+---------+------+------+------+----------
1 |        1 |         2 |       3 |    2 |    2 |    1 |        0
2 |        2 |         2 |       3 |    3 |   -1 |    0 |        1
3 |        1 |         2 |       5 |    2 |    4 |    1 |        0
4 |        2 |         2 |       5 |    5 |   -1 |    0 |        1
5 |        1 |        11 |       3 |   11 |   11 |    1 |        0
6 |        2 |        11 |       3 |    6 |    5 |    1 |        1
7 |        3 |        11 |       3 |    3 |   -1 |    0 |        2
8 |        1 |        11 |       5 |   11 |   11 |    1 |        0
9 |        2 |        11 |       5 |    6 |    8 |    1 |        1
10 |        3 |        11 |       5 |    5 |   -1 |    0 |        2
(10 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.

The examples of this section are based on the Sample Data network.

The examples include combinations from starting vertices 2 and 11 to ending vertices 3 and 5 in a directed and undirected graph with and with out reverse_cost.

### Examples for queries marked as directed with cost and reverse_cost columns¶

The examples in this section use the following Network for queries marked as directed and cost and reverse_cost columns are used

SELECT * FROM pgr_dijkstra(
'SELECT id, source, target, cost, reverse_cost FROM edge_table',
2, 3
);
seq | path_seq | node | edge | cost | agg_cost
-----+----------+------+------+------+----------
1 |        1 |    2 |    4 |    1 |        0
2 |        2 |    5 |    8 |    1 |        1
3 |        3 |    6 |    9 |    1 |        2
4 |        4 |    9 |   16 |    1 |        3
5 |        5 |    4 |    3 |    1 |        4
6 |        6 |    3 |   -1 |    0 |        5
(6 rows)

SELECT * FROM pgr_dijkstra(
'SELECT id, source, target, cost, reverse_cost FROM edge_table',
2, 5
);
seq | path_seq | node | edge | cost | agg_cost
-----+----------+------+------+------+----------
1 |        1 |    2 |    4 |    1 |        0
2 |        2 |    5 |   -1 |    0 |        1
(2 rows)

SELECT * FROM pgr_dijkstra(
'SELECT id, source, target, cost, reverse_cost FROM edge_table',
2, ARRAY[3,5]
);
seq | path_seq | end_vid | node | edge | cost | agg_cost
-----+----------+---------+------+------+------+----------
1 |        1 |       3 |    2 |    4 |    1 |        0
2 |        2 |       3 |    5 |    8 |    1 |        1
3 |        3 |       3 |    6 |    9 |    1 |        2
4 |        4 |       3 |    9 |   16 |    1 |        3
5 |        5 |       3 |    4 |    3 |    1 |        4
6 |        6 |       3 |    3 |   -1 |    0 |        5
7 |        1 |       5 |    2 |    4 |    1 |        0
8 |        2 |       5 |    5 |   -1 |    0 |        1
(8 rows)

SELECT * FROM pgr_dijkstra(
'SELECT id, source, target, cost, reverse_cost FROM edge_table',
11, 3
);
seq | path_seq | node | edge | cost | agg_cost
-----+----------+------+------+------+----------
1 |        1 |   11 |   13 |    1 |        0
2 |        2 |   12 |   15 |    1 |        1
3 |        3 |    9 |   16 |    1 |        2
4 |        4 |    4 |    3 |    1 |        3
5 |        5 |    3 |   -1 |    0 |        4
(5 rows)

SELECT * FROM pgr_dijkstra(
'SELECT id, source, target, cost, reverse_cost FROM edge_table',
11, 5
);
seq | path_seq | node | edge | cost | agg_cost
-----+----------+------+------+------+----------
1 |        1 |   11 |   13 |    1 |        0
2 |        2 |   12 |   15 |    1 |        1
3 |        3 |    9 |    9 |    1 |        2
4 |        4 |    6 |    8 |    1 |        3
5 |        5 |    5 |   -1 |    0 |        4
(5 rows)

SELECT * FROM pgr_dijkstra(
'SELECT id, source, target, cost, reverse_cost FROM edge_table',
ARRAY[2,11], 5
);
seq | path_seq | start_vid | node | edge | cost | agg_cost
-----+----------+-----------+------+------+------+----------
1 |        1 |         2 |    2 |    4 |    1 |        0
2 |        2 |         2 |    5 |   -1 |    0 |        1
3 |        1 |        11 |   11 |   13 |    1 |        0
4 |        2 |        11 |   12 |   15 |    1 |        1
5 |        3 |        11 |    9 |    9 |    1 |        2
6 |        4 |        11 |    6 |    8 |    1 |        3
7 |        5 |        11 |    5 |   -1 |    0 |        4
(7 rows)

SELECT * FROM pgr_dijkstra(
'SELECT id, source, target, cost, reverse_cost FROM edge_table',
ARRAY[2, 11], ARRAY[3,5]
);
seq | path_seq | start_vid | end_vid | node | edge | cost | agg_cost
-----+----------+-----------+---------+------+------+------+----------
1 |        1 |         2 |       3 |    2 |    4 |    1 |        0
2 |        2 |         2 |       3 |    5 |    8 |    1 |        1
3 |        3 |         2 |       3 |    6 |    9 |    1 |        2
4 |        4 |         2 |       3 |    9 |   16 |    1 |        3
5 |        5 |         2 |       3 |    4 |    3 |    1 |        4
6 |        6 |         2 |       3 |    3 |   -1 |    0 |        5
7 |        1 |         2 |       5 |    2 |    4 |    1 |        0
8 |        2 |         2 |       5 |    5 |   -1 |    0 |        1
9 |        1 |        11 |       3 |   11 |   13 |    1 |        0
10 |        2 |        11 |       3 |   12 |   15 |    1 |        1
11 |        3 |        11 |       3 |    9 |   16 |    1 |        2
12 |        4 |        11 |       3 |    4 |    3 |    1 |        3
13 |        5 |        11 |       3 |    3 |   -1 |    0 |        4
14 |        1 |        11 |       5 |   11 |   13 |    1 |        0
15 |        2 |        11 |       5 |   12 |   15 |    1 |        1
16 |        3 |        11 |       5 |    9 |    9 |    1 |        2
17 |        4 |        11 |       5 |    6 |    8 |    1 |        3
18 |        5 |        11 |       5 |    5 |   -1 |    0 |        4
(18 rows)



### Examples for queries marked as undirected with cost and reverse_cost columns¶

The examples in this section use the following Network for queries marked as undirected and cost and reverse_cost columns are used

SELECT * FROM pgr_dijkstra(
'SELECT id, source, target, cost, reverse_cost FROM edge_table',
2, 3,
FALSE
);
seq | path_seq | node | edge | cost | agg_cost
-----+----------+------+------+------+----------
1 |        1 |    2 |    2 |    1 |        0
2 |        2 |    3 |   -1 |    0 |        1
(2 rows)

SELECT * FROM pgr_dijkstra(
'SELECT id, source, target, cost, reverse_cost FROM edge_table',
2, 5,
FALSE
);
seq | path_seq | node | edge | cost | agg_cost
-----+----------+------+------+------+----------
1 |        1 |    2 |    4 |    1 |        0
2 |        2 |    5 |   -1 |    0 |        1
(2 rows)

SELECT * FROM pgr_dijkstra(
'SELECT id, source, target, cost, reverse_cost FROM edge_table',
11, 3,
FALSE
);
seq | path_seq | node | edge | cost | agg_cost
-----+----------+------+------+------+----------
1 |        1 |   11 |   11 |    1 |        0
2 |        2 |    6 |    5 |    1 |        1
3 |        3 |    3 |   -1 |    0 |        2
(3 rows)

SELECT * FROM pgr_dijkstra(
'SELECT id, source, target, cost, reverse_cost FROM edge_table',
11, 5,
FALSE
);
seq | path_seq | node | edge | cost | agg_cost
-----+----------+------+------+------+----------
1 |        1 |   11 |   11 |    1 |        0
2 |        2 |    6 |    8 |    1 |        1
3 |        3 |    5 |   -1 |    0 |        2
(3 rows)

SELECT * FROM pgr_dijkstra(
'SELECT id, source, target, cost, reverse_cost FROM edge_table',
ARRAY[2,11], 5,
FALSE
);
seq | path_seq | start_vid | node | edge | cost | agg_cost
-----+----------+-----------+------+------+------+----------
1 |        1 |         2 |    2 |    4 |    1 |        0
2 |        2 |         2 |    5 |   -1 |    0 |        1
3 |        1 |        11 |   11 |   12 |    1 |        0
4 |        2 |        11 |   10 |   10 |    1 |        1
5 |        3 |        11 |    5 |   -1 |    0 |        2
(5 rows)

SELECT * FROM pgr_dijkstra(
'SELECT id, source, target, cost, reverse_cost FROM edge_table',
2, ARRAY[3,5],
FALSE
);
seq | path_seq | end_vid | node | edge | cost | agg_cost
-----+----------+---------+------+------+------+----------
1 |        1 |       3 |    2 |    2 |    1 |        0
2 |        2 |       3 |    3 |   -1 |    0 |        1
3 |        1 |       5 |    2 |    4 |    1 |        0
4 |        2 |       5 |    5 |   -1 |    0 |        1
(4 rows)

SELECT * FROM pgr_dijkstra(
'SELECT id, source, target, cost, reverse_cost FROM edge_table',
ARRAY[2, 11], ARRAY[3,5],
FALSE
);
seq | path_seq | start_vid | end_vid | node | edge | cost | agg_cost
-----+----------+-----------+---------+------+------+------+----------
1 |        1 |         2 |       3 |    2 |    2 |    1 |        0
2 |        2 |         2 |       3 |    3 |   -1 |    0 |        1
3 |        1 |         2 |       5 |    2 |    4 |    1 |        0
4 |        2 |         2 |       5 |    5 |   -1 |    0 |        1
5 |        1 |        11 |       3 |   11 |   11 |    1 |        0
6 |        2 |        11 |       3 |    6 |    5 |    1 |        1
7 |        3 |        11 |       3 |    3 |   -1 |    0 |        2
8 |        1 |        11 |       5 |   11 |   11 |    1 |        0
9 |        2 |        11 |       5 |    6 |    8 |    1 |        1
10 |        3 |        11 |       5 |    5 |   -1 |    0 |        2
(10 rows)



### Examples for queries marked as directed with cost column¶

The examples in this section use the following Network for queries marked as directed and only cost column is used

SELECT * FROM pgr_dijkstra(
'SELECT id, source, target, cost FROM edge_table',
2, 3
);
seq | path_seq | node | edge | cost | agg_cost
-----+----------+------+------+------+----------
(0 rows)

SELECT * FROM pgr_dijkstra(
'SELECT id, source, target, cost FROM edge_table',
2, 5
);
seq | path_seq | node | edge | cost | agg_cost
-----+----------+------+------+------+----------
1 |        1 |    2 |    4 |    1 |        0
2 |        2 |    5 |   -1 |    0 |        1
(2 rows)

SELECT * FROM pgr_dijkstra(
'SELECT id, source, target, cost FROM edge_table',
11, 3
);
seq | path_seq | node | edge | cost | agg_cost
-----+----------+------+------+------+----------
(0 rows)

SELECT * FROM pgr_dijkstra(
'SELECT id, source, target, cost FROM edge_table',
11, 5
);
seq | path_seq | node | edge | cost | agg_cost
-----+----------+------+------+------+----------
(0 rows)

SELECT * FROM pgr_dijkstra(
'SELECT id, source, target, cost FROM edge_table',
ARRAY[2,11], 5
);
seq | path_seq | start_vid | node | edge | cost | agg_cost
-----+----------+-----------+------+------+------+----------
1 |        1 |         2 |    2 |    4 |    1 |        0
2 |        2 |         2 |    5 |   -1 |    0 |        1
(2 rows)

SELECT * FROM pgr_dijkstra(
'SELECT id, source, target, cost FROM edge_table',
2, ARRAY[3,5]
);
seq | path_seq | end_vid | node | edge | cost | agg_cost
-----+----------+---------+------+------+------+----------
1 |        1 |       5 |    2 |    4 |    1 |        0
2 |        2 |       5 |    5 |   -1 |    0 |        1
(2 rows)

SELECT * FROM pgr_dijkstra(
'SELECT id, source, target, cost FROM edge_table',
ARRAY[2, 11], ARRAY[3,5]
);
seq | path_seq | start_vid | end_vid | node | edge | cost | agg_cost
-----+----------+-----------+---------+------+------+------+----------
1 |        1 |         2 |       5 |    2 |    4 |    1 |        0
2 |        2 |         2 |       5 |    5 |   -1 |    0 |        1
(2 rows)



### Examples for queries marked as undirected with cost column¶

The examples in this section use the following Network for queries marked as undirected and only cost column is used

SELECT * FROM pgr_dijkstra(
'SELECT id, source, target, cost FROM edge_table',
2, 3,
FALSE
);
seq | path_seq | node | edge | cost | agg_cost
-----+----------+------+------+------+----------
1 |        1 |    2 |    4 |    1 |        0
2 |        2 |    5 |    8 |    1 |        1
3 |        3 |    6 |    5 |    1 |        2
4 |        4 |    3 |   -1 |    0 |        3
(4 rows)

SELECT * FROM pgr_dijkstra(
'SELECT id, source, target, cost FROM edge_table',
2, 5,
FALSE
);
seq | path_seq | node | edge | cost | agg_cost
-----+----------+------+------+------+----------
1 |        1 |    2 |    4 |    1 |        0
2 |        2 |    5 |   -1 |    0 |        1
(2 rows)

SELECT * FROM pgr_dijkstra(
'SELECT id, source, target, cost FROM edge_table',
11, 3,
FALSE
);
seq | path_seq | node | edge | cost | agg_cost
-----+----------+------+------+------+----------
1 |        1 |   11 |   11 |    1 |        0
2 |        2 |    6 |    5 |    1 |        1
3 |        3 |    3 |   -1 |    0 |        2
(3 rows)

SELECT * FROM pgr_dijkstra(
'SELECT id, source, target, cost FROM edge_table',
11, 5,
FALSE
);
seq | path_seq | node | edge | cost | agg_cost
-----+----------+------+------+------+----------
1 |        1 |   11 |   11 |    1 |        0
2 |        2 |    6 |    8 |    1 |        1
3 |        3 |    5 |   -1 |    0 |        2
(3 rows)

SELECT * FROM pgr_dijkstra(
'SELECT id, source, target, cost FROM edge_table',
ARRAY[2,11], 5,
FALSE
);
seq | path_seq | start_vid | node | edge | cost | agg_cost
-----+----------+-----------+------+------+------+----------
1 |        1 |         2 |    2 |    4 |    1 |        0
2 |        2 |         2 |    5 |   -1 |    0 |        1
3 |        1 |        11 |   11 |   12 |    1 |        0
4 |        2 |        11 |   10 |   10 |    1 |        1
5 |        3 |        11 |    5 |   -1 |    0 |        2
(5 rows)

SELECT * FROM pgr_dijkstra(
'SELECT id, source, target, cost FROM edge_table',
2, ARRAY[3,5],
FALSE
);
seq | path_seq | end_vid | node | edge | cost | agg_cost
-----+----------+---------+------+------+------+----------
1 |        1 |       3 |    2 |    4 |    1 |        0
2 |        2 |       3 |    5 |    8 |    1 |        1
3 |        3 |       3 |    6 |    5 |    1 |        2
4 |        4 |       3 |    3 |   -1 |    0 |        3
5 |        1 |       5 |    2 |    4 |    1 |        0
6 |        2 |       5 |    5 |   -1 |    0 |        1
(6 rows)

SELECT * FROM pgr_dijkstra(
'SELECT id, source, target, cost FROM edge_table',
ARRAY[2, 11], ARRAY[3,5],
FALSE
);
seq | path_seq | start_vid | end_vid | node | edge | cost | agg_cost
-----+----------+-----------+---------+------+------+------+----------
1 |        1 |         2 |       3 |    2 |    4 |    1 |        0
2 |        2 |         2 |       3 |    5 |    8 |    1 |        1
3 |        3 |         2 |       3 |    6 |    5 |    1 |        2
4 |        4 |         2 |       3 |    3 |   -1 |    0 |        3
5 |        1 |         2 |       5 |    2 |    4 |    1 |        0
6 |        2 |         2 |       5 |    5 |   -1 |    0 |        1
7 |        1 |        11 |       3 |   11 |   11 |    1 |        0
8 |        2 |        11 |       3 |    6 |    5 |    1 |        1
9 |        3 |        11 |       3 |    3 |   -1 |    0 |        2
10 |        1 |        11 |       5 |   11 |   11 |    1 |        0
11 |        2 |        11 |       5 |    6 |    8 |    1 |        1
12 |        3 |        11 |       5 |    5 |   -1 |    0 |        2
(12 rows)



### Equvalences between signatures¶

Examples: For queries marked as directed with cost and reverse_cost columns

The examples in this section use the following:

SELECT * FROM pgr_dijkstra(
'SELECT id, source, target, cost, reverse_cost FROM edge_table',
2, 3,
TRUE
);
seq | path_seq | node | edge | cost | agg_cost
-----+----------+------+------+------+----------
1 |        1 |    2 |    4 |    1 |        0
2 |        2 |    5 |    8 |    1 |        1
3 |        3 |    6 |    9 |    1 |        2
4 |        4 |    9 |   16 |    1 |        3
5 |        5 |    4 |    3 |    1 |        4
6 |        6 |    3 |   -1 |    0 |        5
(6 rows)

SELECT * FROM pgr_dijkstra(
'SELECT id, source, target, cost, reverse_cost FROM edge_table',
2,3
);
seq | path_seq | node | edge | cost | agg_cost
-----+----------+------+------+------+----------
1 |        1 |    2 |    4 |    1 |        0
2 |        2 |    5 |    8 |    1 |        1
3 |        3 |    6 |    9 |    1 |        2
4 |        4 |    9 |   16 |    1 |        3
5 |        5 |    4 |    3 |    1 |        4
6 |        6 |    3 |   -1 |    0 |        5
(6 rows)

SELECT * FROM pgr_dijkstra(
'SELECT id, source, target, cost, reverse_cost FROM edge_table',
2, ARRAY[3],
TRUE
);
seq | path_seq | end_vid | node | edge | cost | agg_cost
-----+----------+---------+------+------+------+----------
1 |        1 |       3 |    2 |    4 |    1 |        0
2 |        2 |       3 |    5 |    8 |    1 |        1
3 |        3 |       3 |    6 |    9 |    1 |        2
4 |        4 |       3 |    9 |   16 |    1 |        3
5 |        5 |       3 |    4 |    3 |    1 |        4
6 |        6 |       3 |    3 |   -1 |    0 |        5
(6 rows)

SELECT * FROM pgr_dijkstra(
'SELECT id, source, target, cost, reverse_cost FROM edge_table',
2, ARRAY[3]
);
seq | path_seq | end_vid | node | edge | cost | agg_cost
-----+----------+---------+------+------+------+----------
1 |        1 |       3 |    2 |    4 |    1 |        0
2 |        2 |       3 |    5 |    8 |    1 |        1
3 |        3 |       3 |    6 |    9 |    1 |        2
4 |        4 |       3 |    9 |   16 |    1 |        3
5 |        5 |       3 |    4 |    3 |    1 |        4
6 |        6 |       3 |    3 |   -1 |    0 |        5
(6 rows)

SELECT * FROM pgr_dijkstra(
'SELECT id, source, target, cost, reverse_cost FROM edge_table',
ARRAY[2], ARRAY[3],
TRUE
);
seq | path_seq | start_vid | end_vid | node | edge | cost | agg_cost
-----+----------+-----------+---------+------+------+------+----------
1 |        1 |         2 |       3 |    2 |    4 |    1 |        0
2 |        2 |         2 |       3 |    5 |    8 |    1 |        1
3 |        3 |         2 |       3 |    6 |    9 |    1 |        2
4 |        4 |         2 |       3 |    9 |   16 |    1 |        3
5 |        5 |         2 |       3 |    4 |    3 |    1 |        4
6 |        6 |         2 |       3 |    3 |   -1 |    0 |        5
(6 rows)

SELECT * FROM pgr_dijkstra(
'SELECT id, source, target, cost, reverse_cost FROM edge_table',
ARRAY[2], ARRAY[3]
);
seq | path_seq | start_vid | end_vid | node | edge | cost | agg_cost
-----+----------+-----------+---------+------+------+------+----------
1 |        1 |         2 |       3 |    2 |    4 |    1 |        0
2 |        2 |         2 |       3 |    5 |    8 |    1 |        1
3 |        3 |         2 |       3 |    6 |    9 |    1 |        2
4 |        4 |         2 |       3 |    9 |   16 |    1 |        3
5 |        5 |         2 |       3 |    4 |    3 |    1 |        4
6 |        6 |         2 |       3 |    3 |   -1 |    0 |        5
(6 rows)


Examples: For queries marked as undirected with cost and reverse_cost columns

The examples in this section use the following:

SELECT * FROM pgr_dijkstra(
'SELECT id, source, target, cost, reverse_cost FROM edge_table',
2, 3,
FALSE
);
seq | path_seq | node | edge | cost | agg_cost
-----+----------+------+------+------+----------
1 |        1 |    2 |    2 |    1 |        0
2 |        2 |    3 |   -1 |    0 |        1
(2 rows)

SELECT * FROM pgr_dijkstra(
'SELECT id, source, target, cost, reverse_cost FROM edge_table',
2, ARRAY[3],
FALSE
);
seq | path_seq | end_vid | node | edge | cost | agg_cost
-----+----------+---------+------+------+------+----------
1 |        1 |       3 |    2 |    2 |    1 |        0
2 |        2 |       3 |    3 |   -1 |    0 |        1
(2 rows)

SELECT * FROM pgr_dijkstra(
'SELECT id, source, target, cost, reverse_cost FROM edge_table',
ARRAY[2], 3,
FALSE
);
seq | path_seq | start_vid | node | edge | cost | agg_cost
-----+----------+-----------+------+------+------+----------
1 |        1 |         2 |    2 |    2 |    1 |        0
2 |        2 |         2 |    3 |   -1 |    0 |        1
(2 rows)

SELECT * FROM pgr_dijkstra(
'SELECT id, source, target, cost, reverse_cost FROM edge_table',
ARRAY[2], ARRAY[3],
FALSE
);
seq | path_seq | start_vid | end_vid | node | edge | cost | agg_cost
-----+----------+-----------+---------+------+------+------+----------
1 |        1 |         2 |       3 |    2 |    2 |    1 |        0
2 |        2 |         2 |       3 |    3 |   -1 |    0 |        1
(2 rows)