Supported versions: latest (3.6) 3.5 3.4 3.3 3.2 3.1 3.0 main dev
Unsupported versions:2.6 2.5 2.4 2.3 2.2 2.1 2.0

pgr_dijkstra

pgr_dijkstra — Shortest path using Dijkstra algorithm.

Boost Graph Inside

Availability

• Version 3.5.0

  • Standarizing output columns to (seq, path_seq, start_vid, end_vid, node, edge, cost, agg_cost)

    • pgr_dijkstra (One to One) added start_vid and end_vid columns.

    • pgr_dijkstra (One to Many) added end_vid column.

    • pgr_dijkstra (Many to One) added start_vid column.

• 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)

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 to an ending vertex. This implementation can be used with a directed graph and an undirected graph.

• Process is done only on edges with positive costs.

  • A negative value on a cost column is interpreted as the edge does not exist.

• Values are returned when there is a path.

• When there is no path:

  • When the starting vertex and ending vertex are the same.

    • The aggregate cost of the non included values $(v,v)$ is $0$

  • When the starting vertex and ending vertex are the different and there is no path:

    • The aggregate cost the non included values $(u,v)$ is $\mathrm{\infty }$

• For optimization purposes, any duplicated value in the starting vertices or on the ending vertices are ignored.

• Running time: $O(|startvids|\ast (V\log V+E))$

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])

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

OR EMPTY SET

Warning

Breaking change on 3.5.0

Read the Migration guide about how to migrate from the old result columns to the new result columns.

One to One

pgr_dijkstra(Edges SQL, start vid, end vid, [directed])

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

OR EMPTY SET

Example:

From vertex $6$ to vertex $10$ on a directed graph

SELECT * FROM pgr_Dijkstra(
  'select id, source, target, cost, reverse_cost from edges',
  6, 10, true);
 seq | path_seq | start_vid | end_vid | node | edge | cost | agg_cost
-----+----------+-----------+---------+------+------+------+----------
   1 |        1 |         6 |      10 |    6 |    4 |    1 |        0
   2 |        2 |         6 |      10 |    7 |    8 |    1 |        1
   3 |        3 |         6 |      10 |   11 |    9 |    1 |        2
   4 |        4 |         6 |      10 |   16 |   16 |    1 |        3
   5 |        5 |         6 |      10 |   15 |    3 |    1 |        4
   6 |        6 |         6 |      10 |   10 |   -1 |    0 |        5
(6 rows)

One to Many

pgr_dijkstra(Edges SQL, start vid, end vids, [directed])

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

OR EMPTY SET

Example:

From vertex $6$ to vertices $\{10,17\}$ on a directed

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

Many to One

pgr_dijkstra(Edges SQL, start vids, end vid, [directed])

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

OR EMPTY SET

Example:

From vertices $\{6,1\}$ to vertex $17$ on a directed graph

SELECT * FROM pgr_Dijkstra(
  'select id, source, target, cost, reverse_cost from edges',
  ARRAY[6, 1], 17);
 seq | path_seq | start_vid | end_vid | node | edge | cost | agg_cost
-----+----------+-----------+---------+------+------+------+----------
   1 |        1 |         1 |      17 |    1 |    6 |    1 |        0
   2 |        2 |         1 |      17 |    3 |    7 |    1 |        1
   3 |        3 |         1 |      17 |    7 |    8 |    1 |        2
   4 |        4 |         1 |      17 |   11 |   11 |    1 |        3
   5 |        5 |         1 |      17 |   12 |   13 |    1 |        4
   6 |        6 |         1 |      17 |   17 |   -1 |    0 |        5
   7 |        1 |         6 |      17 |    6 |    4 |    1 |        0
   8 |        2 |         6 |      17 |    7 |    8 |    1 |        1
   9 |        3 |         6 |      17 |   11 |   11 |    1 |        2
  10 |        4 |         6 |      17 |   12 |   13 |    1 |        3
  11 |        5 |         6 |      17 |   17 |   -1 |    0 |        4
(11 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 $\{6,1\}$ to vertices $\{10,17\}$ on an undirected graph

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

Combinations

pgr_dijkstra(Edges SQL, Combinations SQL, [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

The combinations table:

SELECT source, target FROM combinations;
 source | target
--------+--------
      5 |      6
      5 |     10
      6 |      5
      6 |     15
      6 |     14
(5 rows)

The query:

SELECT * FROM pgr_Dijkstra(
  'SELECT id, source, target, cost, reverse_cost FROM edges',
  'SELECT source, target FROM combinations',
  false);
 seq | path_seq | start_vid | end_vid | node | edge | cost | agg_cost
-----+----------+-----------+---------+------+------+------+----------
   1 |        1 |         5 |       6 |    5 |    1 |    1 |        0
   2 |        2 |         5 |       6 |    6 |   -1 |    0 |        1
   3 |        1 |         5 |      10 |    5 |    1 |    1 |        0
   4 |        2 |         5 |      10 |    6 |    2 |    1 |        1
   5 |        3 |         5 |      10 |   10 |   -1 |    0 |        2
   6 |        1 |         6 |       5 |    6 |    1 |    1 |        0
   7 |        2 |         6 |       5 |    5 |   -1 |    0 |        1
   8 |        1 |         6 |      15 |    6 |    2 |    1 |        0
   9 |        2 |         6 |      15 |   10 |    3 |    1 |        1
  10 |        3 |         6 |      15 |   15 |   -1 |    0 |        2
(10 rows)

Parameters

Column	Type	Description
Edges SQL	TEXT	Edges SQL as described below
Combinations SQL	TEXT	Combinations SQL 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.

Optional parameters

Column	Type	Default	Description
directed	BOOLEAN	true	When true the graph is considered Directed When false the graph is considered as Undirected.

Inner Queries

Edges SQL

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)
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 SQL

Parameter	Type	Description
source	ANY-INTEGER	Identifier of the departure vertex.
target	ANY-INTEGER	Identifier of the arrival vertex.

Where:

ANY-INTEGER:

SMALLINT, INTEGER, BIGINT

Result columns

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

Column	Type	Description
seq	INTEGER	Sequential value starting from 1.
path_seq	INTEGER	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. Many to One Many to Many
end_vid	BIGINT	Identifier of the ending vertex. Returned when multiple ending vertices are in the query. One to Many Many to Many
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_vid to node.

Additional Examples

Example:

Demonstration of repeated values are ignored, and result is sorted.

SELECT * FROM pgr_Dijkstra(
  'select id, source, target, cost, reverse_cost from edges',
  ARRAY[7, 10, 15, 10, 10, 15], ARRAY[10, 7, 10, 15]);
 seq | path_seq | start_vid | end_vid | node | edge | cost | agg_cost
-----+----------+-----------+---------+------+------+------+----------
   1 |        1 |         7 |      10 |    7 |    8 |    1 |        0
   2 |        2 |         7 |      10 |   11 |    9 |    1 |        1
   3 |        3 |         7 |      10 |   16 |   16 |    1 |        2
   4 |        4 |         7 |      10 |   15 |    3 |    1 |        3
   5 |        5 |         7 |      10 |   10 |   -1 |    0 |        4
   6 |        1 |         7 |      15 |    7 |    8 |    1 |        0
   7 |        2 |         7 |      15 |   11 |    9 |    1 |        1
   8 |        3 |         7 |      15 |   16 |   16 |    1 |        2
   9 |        4 |         7 |      15 |   15 |   -1 |    0 |        3
  10 |        1 |        10 |       7 |   10 |    5 |    1 |        0
  11 |        2 |        10 |       7 |   11 |    8 |    1 |        1
  12 |        3 |        10 |       7 |    7 |   -1 |    0 |        2
  13 |        1 |        10 |      15 |   10 |    5 |    1 |        0
  14 |        2 |        10 |      15 |   11 |    9 |    1 |        1
  15 |        3 |        10 |      15 |   16 |   16 |    1 |        2
  16 |        4 |        10 |      15 |   15 |   -1 |    0 |        3
  17 |        1 |        15 |       7 |   15 |   16 |    1 |        0
  18 |        2 |        15 |       7 |   16 |    9 |    1 |        1
  19 |        3 |        15 |       7 |   11 |    8 |    1 |        2
  20 |        4 |        15 |       7 |    7 |   -1 |    0 |        3
  21 |        1 |        15 |      10 |   15 |    3 |    1 |        0
  22 |        2 |        15 |      10 |   10 |   -1 |    0 |        1
(22 rows)

Example 2:

Making start_vids the same as end_vids

SELECT * FROM pgr_Dijkstra(
  'select id, source, target, cost, reverse_cost from edges',
  ARRAY[7, 10, 15], ARRAY[7, 10, 15]);
 seq | path_seq | start_vid | end_vid | node | edge | cost | agg_cost
-----+----------+-----------+---------+------+------+------+----------
   1 |        1 |         7 |      10 |    7 |    8 |    1 |        0
   2 |        2 |         7 |      10 |   11 |    9 |    1 |        1
   3 |        3 |         7 |      10 |   16 |   16 |    1 |        2
   4 |        4 |         7 |      10 |   15 |    3 |    1 |        3
   5 |        5 |         7 |      10 |   10 |   -1 |    0 |        4
   6 |        1 |         7 |      15 |    7 |    8 |    1 |        0
   7 |        2 |         7 |      15 |   11 |    9 |    1 |        1
   8 |        3 |         7 |      15 |   16 |   16 |    1 |        2
   9 |        4 |         7 |      15 |   15 |   -1 |    0 |        3
  10 |        1 |        10 |       7 |   10 |    5 |    1 |        0
  11 |        2 |        10 |       7 |   11 |    8 |    1 |        1
  12 |        3 |        10 |       7 |    7 |   -1 |    0 |        2
  13 |        1 |        10 |      15 |   10 |    5 |    1 |        0
  14 |        2 |        10 |      15 |   11 |    9 |    1 |        1
  15 |        3 |        10 |      15 |   16 |   16 |    1 |        2
  16 |        4 |        10 |      15 |   15 |   -1 |    0 |        3
  17 |        1 |        15 |       7 |   15 |   16 |    1 |        0
  18 |        2 |        15 |       7 |   16 |    9 |    1 |        1
  19 |        3 |        15 |       7 |   11 |    8 |    1 |        2
  20 |        4 |        15 |       7 |    7 |   -1 |    0 |        3
  21 |        1 |        15 |      10 |   15 |    3 |    1 |        0
  22 |        2 |        15 |      10 |   10 |   -1 |    0 |        1
(22 rows)

Example:

Manually assigned vertex combinations.

SELECT * FROM pgr_Dijkstra(
  'SELECT id, source, target, cost, reverse_cost FROM edges',
  'SELECT * FROM (VALUES (6, 10), (6, 7), (12, 10)) AS combinations (source, target)');
 seq | path_seq | start_vid | end_vid | node | edge | cost | agg_cost
-----+----------+-----------+---------+------+------+------+----------
   1 |        1 |         6 |       7 |    6 |    4 |    1 |        0
   2 |        2 |         6 |       7 |    7 |   -1 |    0 |        1
   3 |        1 |         6 |      10 |    6 |    4 |    1 |        0
   4 |        2 |         6 |      10 |    7 |    8 |    1 |        1
   5 |        3 |         6 |      10 |   11 |    9 |    1 |        2
   6 |        4 |         6 |      10 |   16 |   16 |    1 |        3
   7 |        5 |         6 |      10 |   15 |    3 |    1 |        4
   8 |        6 |         6 |      10 |   10 |   -1 |    0 |        5
   9 |        1 |        12 |      10 |   12 |   13 |    1 |        0
  10 |        2 |        12 |      10 |   17 |   15 |    1 |        1
  11 |        3 |        12 |      10 |   16 |   16 |    1 |        2
  12 |        4 |        12 |      10 |   15 |    3 |    1 |        3
  13 |        5 |        12 |      10 |   10 |   -1 |    0 |        4
(13 rows)

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

For directed graphs with cost and reverse_cost columns

Directed graph with cost and reverse cost columns

1) Path from $6$ to $10$

SELECT * FROM pgr_dijkstra(
  'SELECT id, source, target, cost, reverse_cost FROM edges',
  6, 10
);
 seq | path_seq | start_vid | end_vid | node | edge | cost | agg_cost
-----+----------+-----------+---------+------+------+------+----------
   1 |        1 |         6 |      10 |    6 |    4 |    1 |        0
   2 |        2 |         6 |      10 |    7 |    8 |    1 |        1
   3 |        3 |         6 |      10 |   11 |    9 |    1 |        2
   4 |        4 |         6 |      10 |   16 |   16 |    1 |        3
   5 |        5 |         6 |      10 |   15 |    3 |    1 |        4
   6 |        6 |         6 |      10 |   10 |   -1 |    0 |        5
(6 rows)

2) Path from $6$ to $7$

SELECT * FROM pgr_dijkstra(
  'SELECT id, source, target, cost, reverse_cost FROM edges',
  6, 7
);
 seq | path_seq | start_vid | end_vid | node | edge | cost | agg_cost
-----+----------+-----------+---------+------+------+------+----------
   1 |        1 |         6 |       7 |    6 |    4 |    1 |        0
   2 |        2 |         6 |       7 |    7 |   -1 |    0 |        1
(2 rows)

3) Path from $12$ to $10$

SELECT * FROM pgr_dijkstra(
  'SELECT id, source, target, cost, reverse_cost FROM edges',
  12, 10
);
 seq | path_seq | start_vid | end_vid | node | edge | cost | agg_cost
-----+----------+-----------+---------+------+------+------+----------
   1 |        1 |        12 |      10 |   12 |   13 |    1 |        0
   2 |        2 |        12 |      10 |   17 |   15 |    1 |        1
   3 |        3 |        12 |      10 |   16 |   16 |    1 |        2
   4 |        4 |        12 |      10 |   15 |    3 |    1 |        3
   5 |        5 |        12 |      10 |   10 |   -1 |    0 |        4
(5 rows)

4) Path from $12$ to $7$

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

5) Using One to Many to get the solution of examples 1 and 2

Paths $\{6\}\to \{10,7\}$

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

6) Using Many to One to get the solution of examples 2 and 4

Paths $\{6,12\}\to \{7\}$

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

7) Using Many to Many to get the solution of examples 1 to 4

Paths $\{6,12\}\to \{10,7\}$

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

8) Using Combinations to get the solution of examples 1 to 3

Paths $\{6\}\to \{10,7\}\cup \{12\}\to \{10\}$

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

For undirected graphs with cost and reverse_cost columns

Undirected graph with cost and reverse cost columns

9) Path from $6$ to $10$

SELECT * FROM pgr_dijkstra(
  'SELECT id, source, target, cost, reverse_cost FROM edges',
  6, 10,
  false
);
 seq | path_seq | start_vid | end_vid | node | edge | cost | agg_cost
-----+----------+-----------+---------+------+------+------+----------
   1 |        1 |         6 |      10 |    6 |    2 |    1 |        0
   2 |        2 |         6 |      10 |   10 |   -1 |    0 |        1
(2 rows)

10) Path from $6$ to $7$

SELECT * FROM pgr_dijkstra(
  'SELECT id, source, target, cost, reverse_cost FROM edges',
  6, 7,
  false
);
 seq | path_seq | start_vid | end_vid | node | edge | cost | agg_cost
-----+----------+-----------+---------+------+------+------+----------
   1 |        1 |         6 |       7 |    6 |    4 |    1 |        0
   2 |        2 |         6 |       7 |    7 |   -1 |    0 |        1
(2 rows)

11) Path from $12$ to $10$

SELECT * FROM pgr_dijkstra(
  'SELECT id, source, target, cost, reverse_cost FROM edges',
  12, 10,
  false
);
 seq | path_seq | start_vid | end_vid | node | edge | cost | agg_cost
-----+----------+-----------+---------+------+------+------+----------
   1 |        1 |        12 |      10 |   12 |   11 |    1 |        0
   2 |        2 |        12 |      10 |   11 |    5 |    1 |        1
   3 |        3 |        12 |      10 |   10 |   -1 |    0 |        2
(3 rows)

12) Path from $12$ to $7$

SELECT * FROM pgr_dijkstra(
  'SELECT id, source, target, cost, reverse_cost FROM edges',
  12, 7,
  false
);
 seq | path_seq | start_vid | end_vid | node | edge | cost | agg_cost
-----+----------+-----------+---------+------+------+------+----------
   1 |        1 |        12 |       7 |   12 |   12 |    1 |        0
   2 |        2 |        12 |       7 |    8 |   10 |    1 |        1
   3 |        3 |        12 |       7 |    7 |   -1 |    0 |        2
(3 rows)

13) Using One to Many to get the solution of examples 9 and 10

Paths $\{6\}\to \{10,7\}$

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

14) Using Many to One to get the solution of examples 10 and 12

Paths $\{6,12\}\to \{7\}$

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

15) Using Many to Many to get the solution of examples 9 to 12

Paths $\{6,12\}\to \{10,7\}$

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

16) Using Combinations to get the solution of examples 9 to 11

Paths $\{6\}\to \{10,7\}\cup \{12\}\to \{10\}$

SELECT * FROM pgr_dijkstra(
  'SELECT id, source, target, cost, reverse_cost FROM edges',
  'SELECT * FROM (VALUES (6, 10), (6, 7), (12, 10)) AS combinations (source, target)',
  false
);
 seq | path_seq | start_vid | end_vid | node | edge | cost | agg_cost
-----+----------+-----------+---------+------+------+------+----------
   1 |        1 |         6 |       7 |    6 |    4 |    1 |        0
   2 |        2 |         6 |       7 |    7 |   -1 |    0 |        1
   3 |        1 |         6 |      10 |    6 |    2 |    1 |        0
   4 |        2 |         6 |      10 |   10 |   -1 |    0 |        1
   5 |        1 |        12 |      10 |   12 |   11 |    1 |        0
   6 |        2 |        12 |      10 |   11 |    5 |    1 |        1
   7 |        3 |        12 |      10 |   10 |   -1 |    0 |        2
(7 rows)

For directed graphs only with cost column

Directed graph only with cost column

17) Path from $6$ to $10$

SELECT * FROM pgr_dijkstra(
  'SELECT id, source, target, cost FROM edges',
  6, 10
);
 seq | path_seq | start_vid | end_vid | node | edge | cost | agg_cost
-----+----------+-----------+---------+------+------+------+----------
(0 rows)

18) Path from $6$ to $7$

SELECT * FROM pgr_dijkstra(
  'SELECT id, source, target, cost FROM edges',
  6, 7
);
 seq | path_seq | start_vid | end_vid | node | edge | cost | agg_cost
-----+----------+-----------+---------+------+------+------+----------
   1 |        1 |         6 |       7 |    6 |    4 |    1 |        0
   2 |        2 |         6 |       7 |    7 |   -1 |    0 |        1
(2 rows)

19) Path from $12$ to $10$

SELECT * FROM pgr_dijkstra(
  'SELECT id, source, target, cost FROM edges',
  12, 10
);
 seq | path_seq | start_vid | end_vid | node | edge | cost | agg_cost
-----+----------+-----------+---------+------+------+------+----------
(0 rows)

20) Path from $12$ to $7$

SELECT * FROM pgr_dijkstra(
  'SELECT id, source, target, cost FROM edges',
  12, 7
);
 seq | path_seq | start_vid | end_vid | node | edge | cost | agg_cost
-----+----------+-----------+---------+------+------+------+----------
(0 rows)

21) Using One to Many to get the solution of examples 17 and 18

Paths $\{6\}\to \{10,7\}$

SELECT * FROM pgr_dijkstra(
  'SELECT id, source, target, cost FROM edges',
  6, ARRAY[10,7]
);
 seq | path_seq | start_vid | end_vid | node | edge | cost | agg_cost
-----+----------+-----------+---------+------+------+------+----------
   1 |        1 |         6 |       7 |    6 |    4 |    1 |        0
   2 |        2 |         6 |       7 |    7 |   -1 |    0 |        1
(2 rows)

22) Using Many to One to get the solution of examples 18 and 20

Paths $\{6,12\}\to \{7\}$

SELECT * FROM pgr_dijkstra(
  'SELECT id, source, target, cost FROM edges',
  ARRAY[6,12], 7
);
 seq | path_seq | start_vid | end_vid | node | edge | cost | agg_cost
-----+----------+-----------+---------+------+------+------+----------
   1 |        1 |         6 |       7 |    6 |    4 |    1 |        0
   2 |        2 |         6 |       7 |    7 |   -1 |    0 |        1
(2 rows)

23) Using Many to Many to get the solution of examples 17 to 20

Paths $\{6,12\}\to \{10,7\}$

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

24) Using Combinations to get the solution of examples 17 to 19

Paths $\{6\}\to \{10,7\}\cup \{12\}\to \{10\}$

SELECT * FROM pgr_dijkstra(
  'SELECT id, source, target, cost FROM edges',
  'SELECT * FROM (VALUES (6, 10), (6, 7), (12, 10)) AS combinations (source, target)'
);
 seq | path_seq | start_vid | end_vid | node | edge | cost | agg_cost
-----+----------+-----------+---------+------+------+------+----------
   1 |        1 |         6 |       7 |    6 |    4 |    1 |        0
   2 |        2 |         6 |       7 |    7 |   -1 |    0 |        1
(2 rows)

For undirected graphs only with cost column

Undirected graph only with cost column

25) Path from $6$ to $10$

SELECT * FROM pgr_dijkstra(
  'SELECT id, source, target, cost FROM edges',
  6, 10,
  false
);
 seq | path_seq | start_vid | end_vid | node | edge | cost | agg_cost
-----+----------+-----------+---------+------+------+------+----------
   1 |        1 |         6 |      10 |    6 |    4 |    1 |        0
   2 |        2 |         6 |      10 |    7 |    8 |    1 |        1
   3 |        3 |         6 |      10 |   11 |    5 |    1 |        2
   4 |        4 |         6 |      10 |   10 |   -1 |    0 |        3
(4 rows)

26) Path from $6$ to $7$

SELECT * FROM pgr_dijkstra(
  'SELECT id, source, target, cost FROM edges',
  6, 7,
  false
);
 seq | path_seq | start_vid | end_vid | node | edge | cost | agg_cost
-----+----------+-----------+---------+------+------+------+----------
   1 |        1 |         6 |       7 |    6 |    4 |    1 |        0
   2 |        2 |         6 |       7 |    7 |   -1 |    0 |        1
(2 rows)

27) Path from $12$ to $10$

SELECT * FROM pgr_dijkstra(
  'SELECT id, source, target, cost FROM edges',
  12, 10,
  false
);
 seq | path_seq | start_vid | end_vid | node | edge | cost | agg_cost
-----+----------+-----------+---------+------+------+------+----------
   1 |        1 |        12 |      10 |   12 |   11 |    1 |        0
   2 |        2 |        12 |      10 |   11 |    5 |    1 |        1
   3 |        3 |        12 |      10 |   10 |   -1 |    0 |        2
(3 rows)

28) Path from $12$ to $7$

SELECT * FROM pgr_dijkstra(
  'SELECT id, source, target, cost FROM edges',
  12, 7,
  false
);
 seq | path_seq | start_vid | end_vid | node | edge | cost | agg_cost
-----+----------+-----------+---------+------+------+------+----------
   1 |        1 |        12 |       7 |   12 |   12 |    1 |        0
   2 |        2 |        12 |       7 |    8 |   10 |    1 |        1
   3 |        3 |        12 |       7 |    7 |   -1 |    0 |        2
(3 rows)

29) Using One to Many to get the solution of examples 25 and 26

Paths $\{6\}\to \{10,7\}$

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

30) Using Many to One to get the solution of examples 26 and 28

Paths $\{6,12\}\to \{7\}$

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

31) Using Many to Many to get the solution of examples 25 to 28

Paths $\{6,12\}\to \{10,7\}$

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

32) Using Combinations to get the solution of examples 25 to 27

Paths $\{6\}\to \{10,7\}\cup \{12\}\to \{10\}$

SELECT * FROM pgr_dijkstra(
  'SELECT id, source, target, cost FROM edges',
  'SELECT * FROM (VALUES (6, 10), (6, 7), (12, 10)) AS combinations (source, target)',
  false
);
 seq | path_seq | start_vid | end_vid | node | edge | cost | agg_cost
-----+----------+-----------+---------+------+------+------+----------
   1 |        1 |         6 |       7 |    6 |    4 |    1 |        0
   2 |        2 |         6 |       7 |    7 |   -1 |    0 |        1
   3 |        1 |         6 |      10 |    6 |    4 |    1 |        0
   4 |        2 |         6 |      10 |    7 |    8 |    1 |        1
   5 |        3 |         6 |      10 |   11 |    5 |    1 |        2
   6 |        4 |         6 |      10 |   10 |   -1 |    0 |        3
   7 |        1 |        12 |      10 |   12 |   11 |    1 |        0
   8 |        2 |        12 |      10 |   11 |    5 |    1 |        1
   9 |        3 |        12 |      10 |   10 |   -1 |    0 |        2
(9 rows)

Equvalences between signatures

The following examples find the path for $\{6\}\to \{10\}$

33) Using One to One

SELECT * FROM pgr_dijkstra(
  'SELECT id, source, target, cost, reverse_cost FROM edges',
  6, 10
);
 seq | path_seq | start_vid | end_vid | node | edge | cost | agg_cost
-----+----------+-----------+---------+------+------+------+----------
   1 |        1 |         6 |      10 |    6 |    4 |    1 |        0
   2 |        2 |         6 |      10 |    7 |    8 |    1 |        1
   3 |        3 |         6 |      10 |   11 |    9 |    1 |        2
   4 |        4 |         6 |      10 |   16 |   16 |    1 |        3
   5 |        5 |         6 |      10 |   15 |    3 |    1 |        4
   6 |        6 |         6 |      10 |   10 |   -1 |    0 |        5
(6 rows)

34) Using One to Many

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

35) Using Many to One

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

36) Using Many to Many

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

37) Using Combinations

SELECT * FROM pgr_dijkstra(
  'SELECT id, source, target, cost, reverse_cost FROM edges',
  'SELECT * FROM (VALUES(6, 10)) AS combinations (source, target)'
);
 seq | path_seq | start_vid | end_vid | node | edge | cost | agg_cost
-----+----------+-----------+---------+------+------+------+----------
   1 |        1 |         6 |      10 |    6 |    4 |    1 |        0
   2 |        2 |         6 |      10 |    7 |    8 |    1 |        1
   3 |        3 |         6 |      10 |   11 |    9 |    1 |        2
   4 |        4 |         6 |      10 |   16 |   16 |    1 |        3
   5 |        5 |         6 |      10 |   15 |    3 |    1 |        4
   6 |        6 |         6 |      10 |   10 |   -1 |    0 |        5
(6 rows)

See Also

• https://en.wikipedia.org/wiki/Dijkstra%27s_algorithm

• The queries use the Sample Data network.

Indices and tables

• Index

• Search Page