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

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.

Example:

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.

Example:

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.

Example:

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.

Example:

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.

Example:

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
ANY-NUMERICAL:	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`.

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 Graph 1: Directed, with cost and reverse cost

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 Graph 2: Undirected, with cost and reverse cost

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 Graph 3: Directed, with cost

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 Graph 4: Undirected, with cost

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:

Graph 1: Directed, with cost and reverse cost

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)

SET client_min_messages TO NOTICE;
SET
SELECT * FROM pgr_dijkstra(
    'SELECT id::INTEGER, source::INTEGER, target::INTEGER, cost, reverse_cost FROM edge_table',
    2, 3,
    TRUE,    
    TRUE      
);
NOTICE:  Deprecated function
 seq | id1 | id2 | cost 
-----+-----+-----+------
   0 |   2 |   4 |    1
   1 |   5 |   8 |    1
   2 |   6 |   9 |    1
   3 |   9 |  16 |    1
   4 |   4 |   3 |    1
   5 |   3 |  -1 |    0
(6 rows)

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