# pgr_dijkstra¶

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

Boost Graph Inside

Availability

• Version 3.1.0

• New Proposed functions:

• pgr_dijkstra(combinations)

• Version 3.0.0

• Official functions

• Version 2.2.0

• New proposed functions:

• pgr_dijkstra(One to Many)

• pgr_dijkstra(Many to One)

• pgr_dijkstra(Many to Many)

• Version 2.1.0

• Signature change on pgr_dijkstra(One to One)

• Version 2.0.0

• Official pgr_dijkstra(One to One)

Support

## Description¶

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.

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: $$O(| start\_vids | * (V \log V + E))$$

## Signatures¶

Summary

pgr_dijkstra(Edges SQL, start_vid,  end_vid  [, directed])
pgr_dijkstra(Edges SQL, start_vid,  end_vids [, directed])
pgr_dijkstra(Edges SQL, start_vids, end_vid  [, directed])
pgr_dijkstra(Edges SQL, start_vids, end_vids [, directed])
pgr_dijkstra(Edges SQL, Combinations SQL [, directed]) -- Proposed on v3.1
RETURNS SET OF (seq, path_seq [, start_vid] [, end_vid], node, edge, cost, agg_cost)
OR EMPTY SET


Using defaults

pgr_dijkstra(Edges SQL, start_vid, end_vid)
RETURNS SET OF (seq, path_seq, node, edge, cost, agg_cost) or EMPTY SET

Example

From vertex $$2$$ to vertex $$3$$ on a directed graph

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)



### One to One¶

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

Example

From vertex $$2$$ to vertex $$3$$ on an undirected graph

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)



### One to many¶

pgr_dijkstra(Edges SQL, start_vid, end_vids, [, directed])
RETURNS SET OF (seq, path_seq, end_vid, node, edge, cost, agg_cost)
OR EMPTY SET

Example

From vertex $$2$$ to vertices $$\{3, 5\}$$ on an undirected graph

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)



### Many to One¶

pgr_dijkstra(Edges SQL, start_vids, end_vid, [, directed])
RETURNS SET OF (seq, path_seq, start_vid, node, edge, cost, agg_cost)
OR EMPTY SET

Example

From vertices $$\{2, 11\}$$ to vertex $$5$$ on a directed graph

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)



### Many to Many¶

pgr_dijkstra(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 $$\{2, 11\}$$ to vertices $$\{3, 5\}$$ on an undirected graph

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)



### Combinations¶

pgr_dijkstra(Edges SQL, Combinations SQL, end_vids, [, directed])
RETURNS SET OF (seq, path_seq, start_vid, end_vid, node, edge, cost, agg_cost)
OR EMPTY SET

Example

Using a combinations table on an undirected graph

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

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

## 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.

## Additional Examples¶

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)

SELECT * FROM pgr_dijkstra(
'SELECT id, source, target, cost, reverse_cost FROM edge_table',
'SELECT * FROM (VALUES (2, 3), (2, 5), (11, 3), (11, 5)) AS combinations (source, target)'
);
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)

SELECT * FROM pgr_dijkstra(
'SELECT id, source, target, cost, reverse_cost FROM edge_table',
'SELECT * FROM (VALUES (2, 3), (2, 5), (11, 3), (11, 5)) AS combinations (source, target)',
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)

SELECT * FROM pgr_dijkstra(
'SELECT id, source, target, cost FROM edge_table',
'SELECT * FROM (VALUES (2, 3), (2, 5), (11, 3), (11, 5)) AS combinations (source, target)'
);
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)

SELECT * FROM pgr_dijkstra(
'SELECT id, source, target, cost FROM edge_table',
'SELECT * FROM (VALUES (2, 3), (2, 5), (11, 3), (11, 5)) AS combinations (source, target)',
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)

SELECT * FROM pgr_dijkstra(
'SELECT id, source, target, cost, reverse_cost FROM edge_table',
'SELECT * FROM (VALUES(2, 3)) AS combinations (source, target)'
);
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)

SELECT * FROM pgr_dijkstra(
'SELECT id, source, target, cost, reverse_cost FROM edge_table',
'SELECT * FROM (VALUES(2, 3)) AS combinations (source, target)',
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)



## See Also¶

Indices and tables