pgr_dijkstra

pgr_dijkstra — Shortest path(s) using Dijkstra algorithm.

_images/boost-inside.jpeg

Boost Graph Inside

Availability

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 \(\infty\)

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

  • Running time: \(O(| start\ vids | * (V \log V + E))\)

  • Running time: \(O(| start\_vids | * (V \log V + E))\)

Signatures

Summary

pgr_dijkstra(Edges SQL, start vid, end vid  [, directed])
pgr_dijkstra(Edges SQL, start vid, end vids [, directed])
pgr_dijkstra(Edges SQL, start vids, end vid  [, directed])
pgr_dijkstra(Edges SQL, start vids, end vids [, directed])
pgr_dijkstra(Edges SQL, Combinations SQL [, directed])
RETURNS SET OF (seq, path_seq [, start vid] [, end vid], node, edge, cost, agg_cost)
OR EMPTY SET

One to One

pgr_dijkstra(Edges SQL, start vid,  end vid  [, directed])
pgr_dijkstra(Edges SQL, start vid, end vid  [, directed])
RETURNS SET OF (seq, path_seq, node, edge, cost, agg_cost)
OR EMPTY SET
Example

From vertex \(2\) to vertex \(3\) on a directed graph

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)

One to Many

pgr_dijkstra(Edges SQL, start vid, end vids [, directed])
pgr_dijkstra(Edges SQL, Combinations SQL [, directed])
RETURNS SET OF (seq, path_seq, end vid, node, edge, cost, agg_cost)
OR EMPTY SET
Example

From vertex \(2\) to vertices \(\{3, 12\}\) on a directed

SELECT * FROM pgr_Dijkstra(
  'select id, source, target, cost, reverse_cost from edge_table',
  2, ARRAY[3, 12]);
 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 |      12 |    2 |    4 |    1 |        0
   8 |        2 |      12 |    5 |    8 |    1 |        1
   9 |        3 |      12 |    6 |    9 |    1 |        2
  10 |        4 |      12 |    9 |   15 |    1 |        3
  11 |        5 |      12 |   12 |   -1 |    0 |        4
(11 rows)

Many to One

pgr_dijkstra(Edges SQL, start vids, end vids [, directed])
RETURNS SET OF (seq, path_seq, start vid, node, edge, cost, agg_cost)
OR EMPTY SET
Example

From vertices \(\{2, 7\}\) to vertex \(12\) on a directed graph

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

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

The query:

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

Return 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.

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_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 edge_table',
  ARRAY[5, 3, 4, 3, 3, 4], ARRAY[3, 5, 3, 4]);
 seq | path_seq | start_vid | end_vid | node | edge | cost | agg_cost
-----+----------+-----------+---------+------+------+------+----------
   1 |        1 |         3 |       4 |    3 |    5 |    1 |        0
   2 |        2 |         3 |       4 |    6 |    9 |    1 |        1
   3 |        3 |         3 |       4 |    9 |   16 |    1 |        2
   4 |        4 |         3 |       4 |    4 |   -1 |    0 |        3
   5 |        1 |         3 |       5 |    3 |    2 |    1 |        0
   6 |        2 |         3 |       5 |    2 |    4 |    1 |        1
   7 |        3 |         3 |       5 |    5 |   -1 |    0 |        2
   8 |        1 |         4 |       3 |    4 |    3 |    1 |        0
   9 |        2 |         4 |       3 |    3 |   -1 |    0 |        1
  10 |        1 |         4 |       5 |    4 |    3 |    1 |        0
  11 |        2 |         4 |       5 |    3 |    5 |    1 |        1
  12 |        3 |         4 |       5 |    6 |    8 |    1 |        2
  13 |        4 |         4 |       5 |    5 |   -1 |    0 |        3
  14 |        1 |         5 |       3 |    5 |    8 |    1 |        0
  15 |        2 |         5 |       3 |    6 |    9 |    1 |        1
  16 |        3 |         5 |       3 |    9 |   16 |    1 |        2
  17 |        4 |         5 |       3 |    4 |    3 |    1 |        3
  18 |        5 |         5 |       3 |    3 |   -1 |    0 |        4
  19 |        1 |         5 |       4 |    5 |    8 |    1 |        0
  20 |        2 |         5 |       4 |    6 |    9 |    1 |        1
  21 |        3 |         5 |       4 |    9 |   16 |    1 |        2
  22 |        4 |         5 |       4 |    4 |   -1 |    0 |        3
(22 rows)

Example

Making start_vids the same as end_vids.

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

Example

Manually assigned vertex combinations.

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

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

For directed graphs with cost and reverse_cost columns

_images/Fig1-originalData.png

Directed graph with cost and reverse cost columns

Example 1

Path from \(2\) to \(3\)

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)

Example 2

Path from \(2\) to \(5\)

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)

Example 3

Path from \(11\) to \(3\)

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)

Example 4

Path from \(11\) to \(5\)

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)

Example 5

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

Paths \(\{2\}\rightarrow\{3, 5\}\)

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)

Example 6

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

Paths \(\{2, 11\}\rightarrow\{5\}\)

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)

Example 7

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

Paths \(\{2, 11\}\rightarrow\{3, 5\}\)

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)

Example 8

Using Combinations to get the solution of examples 1 to 3

Paths \(\{2\}\rightarrow\{3, 5\}\cup\{11\}\rightarrow\{3\}\)

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

For undirected graphs with cost and reverse_cost columns

_images/Fig6-undirected.png

Undirected graph with cost and reverse cost columns

Example 9

Path from \(2\) to \(3\)

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)

Example 10

Path from \(2\) to \(5\)

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)

Example 11

Path from \(11\) to \(3\)

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)

Example 12

Path from \(11\) to \(5\)

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)

Example 13

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

Paths \(\{2\}\rightarrow\{3, 5\}\)

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)

Example 14

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

Paths \(\{2, 11\}\rightarrow\{5\}\)

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)

Example 15

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

Paths \(\{2, 11\}\rightarrow\{3, 5\}\)

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)

Example 16

Using Combinations to get the solution of examples 9 to 11

Paths \(\{2\}\rightarrow\{3, 5\}\cup\{11\}\rightarrow\{3\}\)

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

For directed graphs only with cost column

_images/Fig2-cost.png

Directed graph only with cost column

Example 17

Path from \(2\) to \(3\)

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

Example 18

Path from \(2\) to \(5\)

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)

Example 19

Path from \(11\) to \(3\)

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

Example 20

Path from \(11\) to \(5\)

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

Example 21

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

Paths \(\{2\}\rightarrow\{3, 5\}\)

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)

Example 22

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

Paths \(\{2, 11\}\rightarrow\{5\}\)

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)

Example 23

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

Paths \(\{2, 11\}\rightarrow\{3, 5\}\)

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)

Example 24

Using Combinations to get the solution of examples 17 to 19

Paths \(\{2\}\rightarrow\{3, 5\}\cup\{11\}\rightarrow\{3\}\)

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

For undirected graphs only with cost column

_images/Fig4-costUndirected.png

Undirected graph only with cost column

Example 25

Path from \(2\) to \(3\)

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)

Example 26

Path from \(2\) to \(5\)

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)

Example 27

Path from \(11\) to \(3\)

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)

Example 28

Path from \(11\) to \(5\)

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)

Example 29

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

Paths \(\{2\}\rightarrow\{3, 5\}\)

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)

Example 30

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

Paths \(\{2, 11\}\rightarrow\{5\}\)

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)

Example 31

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

Paths \(\{2, 11\}\rightarrow\{3, 5\}\)

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)

Example 32

Using Combinations to get the solution of examples 17 to 19

Paths \(\{2\}\rightarrow\{3, 5\}\cup\{11\}\rightarrow\{3\}\)

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

Equvalences between signatures

The following examples find the path for \(\{2\}\rightarrow\{3\}\)

Example 33

Using One to One

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)

Example 34

Using One to Many

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)

Example 35

Using Many to One

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

Example 36

Using Many to Many

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)

Example 37

Using Combinations

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

See Also

Indices and tables