pgr_dijkstra - pgRouting Manual (3.0)
pgr_dijkstra
pgr_dijkstra
- Returns the shortest path(s) using Dijkstra algorithm.
In particular, the Dijkstra algorithm implemented by Boost.Graph.
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 |
|
Inner SQL query as described below. |
|
|
start_vid |
|
Identifier of the starting vertex of the path. |
|
|
start_vids |
|
Array of identifiers of starting vertices. |
|
|
end_vid |
|
Identifier of the ending vertex of the path. |
|
|
end_vids |
|
Array of identifiers of ending vertices. |
|
|
directed |
|
|
|
Inner query
|
Column |
Type |
Default |
Description |
|---|---|---|---|
|
id |
|
Identifier of the edge. |
|
|
source |
|
Identifier of the first end point vertex of the edge. |
|
|
target |
|
Identifier of the second end point vertex of the edge. |
|
|
cost |
|
Weight of the edge (source, target)
|
|
|
reverse_cost |
|
-1 |
Weight of the edge (target, source) ,
|
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 |
|
Sequential value starting from 1 . |
|
path_id |
|
Path identifier. Has value
1
for the first of a path. Used when there are multiple paths for the same
|
|
path_seq |
|
Relative position in the path. Has value 1 for the beginning of a path. |
|
start_vid |
|
Identifier of the starting vertex. Returned when multiple starting vetrices are in the query. |
|
end_vid |
|
Identifier of the ending vertex. Returned when multiple ending vertices are in the query. |
|
node |
|
Identifier of the node in the path from
|
|
edge |
|
Identifier of the edge used to go from
|
|
cost |
|
Cost to traverse from
|
|
agg_cost |
|
Aggregate cost from
|
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
directedwithcostandreverse_costcolumns
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
undirectedwithcostandreverse_costcolumns
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
directedwithcostcolumn
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
undirectedwithcostcolumn
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
directedwithcostandreverse_costcolumns
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
undirectedwithcostandreverse_costcolumns
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)