pgr_dijkstra

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

images/boost-inside.jpeg

Boost Graph Inside

Availability

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

Using defaults

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
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(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
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(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
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(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
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(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
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)

Parameters

Parameter

Type

Default

Description

edges_sql

TEXT

Inner SQL query as described below.

start_vid

BIGINT

Identifier of the starting vertex of the path.

start_vids

ARRAY[BIGINT]

Array of identifiers of starting vertices.

end_vid

BIGINT

Identifier of the ending vertex of the path.

end_vids

ARRAY[BIGINT]

Array of identifiers of ending vertices.

directed

BOOLEAN

true

  • When true Graph is considered Directed

  • When false the graph is considered as Undirected .

Inner query

Column

Type

Default

Description

id

ANY-INTEGER

Identifier of the edge.

source

ANY-INTEGER

Identifier of the first end point vertex of the edge.

target

ANY-INTEGER

Identifier of the second end point vertex of the edge.

cost

ANY-NUMERICAL

Weight of the edge (source, target)

  • When negative: edge (source, target) does not exist, therefore it’s not part of the graph.

reverse_cost

ANY-NUMERICAL

-1

Weight of the edge (target, source) ,

  • When negative: edge (target, source) does not exist, therefore it’s not part of the graph.

Where:

ANY-INTEGER

SMALLINT, INTEGER, BIGINT

ANY-NUMERICAL

SMALLINT, INTEGER, BIGINT, REAL, FLOAT

Return Columns

Returns set of (seq, path_id, path_seq [, start_vid] [, end_vid], node, edge, cost, agg_cost)

Column

Type

Description

seq

INT

Sequential value starting from 1 .

path_id

INT

Path identifier. Has value 1 for the first of a path. Used when there are multiple paths for the same start_vid to end_vid combination.

path_seq

INT

Relative position in the path. Has value 1 for the beginning of a path.

start_vid

BIGINT

Identifier of the starting vertex. Returned when multiple starting vetrices are in the query.

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)

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)

See Also

Indices and tables