pgr_dijkstra¶
pgr_dijkstra — Returns the shortest path(s) using Dijkstra algorithm. In particular, the Dijkstra algorithm implemented by Boost.Graph.
Synopsis¶
Dijkstra’s algorithm, conceived by Dutch computer scientist Edsger Dijkstra in 1956. It is a graph search algorithm that solves the shortest path problem for a graph with non-negative edge path costs, producing a shortest path from a starting vertex (start_vid) to an ending vertex (end_vid). This implementation can be used with a directed graph and an undirected graph.
Characteristics¶
- The main Characteristics are:
- Process is done only on edges with positive costs.
- Values are returned when there is a path.
- When the starting vertex and ending vertex are the same, there is no path.
- The agg_cost the non included values (v, v) is 0
- When the starting vertex and ending vertex are the different and there is no path:
- The agg_cost the non included values (u, v) is \(\infty\)
- When the starting vertex and ending vertex are the same, there is no path.
- For optimization purposes, any duplicated value in the start_vids or end_vids are ignored.
- The returned values are ordered:
- start_vid ascending
- end_vid ascending
- Running time: \(O(| start\_vids | * (V \log V + E))\)
Signature Summary¶
pgr_dijkstra(edges_sql, start_vid, end_vid)
pgr_dijkstra(edges_sql, start_vid, end_vid, directed:=true)
pgr_dijkstra(edges_sql, start_vid, end_vids, directed:=true)
pgr_dijkstra(edges_sql, start_vids, end_vid, directed:=true)
pgr_dijkstra(edges_sql, start_vids, end_vids, directed:=true)
RETURNS SET OF (seq, path_seq [, start_vid] [, end_vid], node, edge, cost, agg_cost)
OR EMPTY SET
Signatures¶
Minimal signature¶
pgr_dijkstra(TEXT edges_sql, BIGINT start_vid, BIGINT end_vid)
RETURNS SET OF (seq, path_seq, node, edge, cost, agg_cost) or EMPTY SET
The minimal signature is for a directed graph from one start_vid to one end_vid:
Example: |
---|
SELECT * FROM pgr_dijkstra(
'SELECT id, source, target, cost, reverse_cost FROM edge_table',
2, 3
);
seq | path_seq | node | edge | cost | agg_cost
-----+----------+------+------+------+----------
1 | 1 | 2 | 4 | 1 | 0
2 | 2 | 5 | 8 | 1 | 1
3 | 3 | 6 | 9 | 1 | 2
4 | 4 | 9 | 16 | 1 | 3
5 | 5 | 4 | 3 | 1 | 4
6 | 6 | 3 | -1 | 0 | 5
(6 rows)
pgr_dijkstra One to One¶
pgr_dijkstra(TEXT edges_sql, BIGINT start_vid, BIGINT end_vid,
BOOLEAN directed:=true);
RETURNS SET OF (seq, path_seq, node, edge, cost, agg_cost) or EMPTY SET
- This signature finds the shortest path from one start_vid to one end_vid:
- on a directed graph when directed flag is missing or is set to true.
- on an undirected graph when directed flag is set to false.
Example: |
---|
SELECT * FROM pgr_dijkstra(
'SELECT id, source, target, cost, reverse_cost FROM edge_table',
2, 3,
FALSE
);
seq | path_seq | node | edge | cost | agg_cost
-----+----------+------+------+------+----------
1 | 1 | 2 | 2 | 1 | 0
2 | 2 | 3 | -1 | 0 | 1
(2 rows)
pgr_dijkstra One to many¶
pgr_dijkstra(TEXT edges_sql, BIGINT start_vid, ARRAY[ANY_INTEGER] end_vids,
BOOLEAN directed:=true);
RETURNS SET OF (seq, path_seq, end_vid, node, edge, cost, agg_cost) or EMPTY SET
- This signature finds the shortest path from one start_vid to each end_vid in end_vids:
- on a directed graph when directed flag is missing or is set to true.
- on an undirected graph when directed flag is set to false.
Using this signature, will load once the graph and perform a one to one pgr_dijkstra where the starting vertex is fixed, and stop when all end_vids are reached.
- The result is equivalent to the union of the results of the one to one pgr_dijkstra.
- The extra end_vid in the result is used to distinguish to which path it belongs.
Example: |
---|
SELECT * FROM pgr_dijkstra(
'SELECT id, source, target, cost FROM edge_table',
2, ARRAY[3,5],
FALSE
);
seq | path_seq | end_vid | node | edge | cost | agg_cost
-----+----------+---------+------+------+------+----------
1 | 1 | 3 | 2 | 4 | 1 | 0
2 | 2 | 3 | 5 | 8 | 1 | 1
3 | 3 | 3 | 6 | 5 | 1 | 2
4 | 4 | 3 | 3 | -1 | 0 | 3
5 | 1 | 5 | 2 | 4 | 1 | 0
6 | 2 | 5 | 5 | -1 | 0 | 1
(6 rows)
pgr_dijkstra Many to One¶
pgr_dijkstra(TEXT edges_sql, ARRAY[ANY_INTEGER] start_vids, BIGINT end_vid,
BOOLEAN directed:=true);
RETURNS SET OF (seq, path_seq, start_vid, node, edge, cost, agg_cost) or EMPTY SET
- This signature finds the shortest path from each start_vid in start_vids to one end_vid:
- on a directed graph when directed flag is missing or is set to true.
- on an undirected graph when directed flag is set to false.
Using this signature, will load once the graph and perform several one to one pgr_dijkstra where the ending vertex is fixed.
- The result is the union of the results of the one to one pgr_dijkstra.
- The extra start_vid in the result is used to distinguish to which path it belongs.
Example: |
---|
SELECT * FROM pgr_dijkstra(
'SELECT id, source, target, cost, reverse_cost FROM edge_table',
ARRAY[2,11], 5
);
seq | path_seq | start_vid | node | edge | cost | agg_cost
-----+----------+-----------+------+------+------+----------
1 | 1 | 2 | 2 | 4 | 1 | 0
2 | 2 | 2 | 5 | -1 | 0 | 1
3 | 1 | 11 | 11 | 13 | 1 | 0
4 | 2 | 11 | 12 | 15 | 1 | 1
5 | 3 | 11 | 9 | 9 | 1 | 2
6 | 4 | 11 | 6 | 8 | 1 | 3
7 | 5 | 11 | 5 | -1 | 0 | 4
(7 rows)
pgr_dijkstra Many to Many¶
pgr_dijkstra(TEXT edges_sql, ARRAY[ANY_INTEGER] start_vids, ARRAY[ANY_INTEGER] end_vids,
BOOLEAN directed:=true);
RETURNS SET OF (seq, path_seq, start_vid, end_vid, node, edge, cost, agg_cost) or EMPTY SET
- This signature finds the shortest path from each start_vid in start_vids to each end_vid in end_vids:
- on a directed graph when directed flag is missing or is set to true.
- on an undirected graph when directed flag is set to false.
Using this signature, will load once the graph and perform several one to Many pgr_dijkstra for all start_vids.
- The result is the union of the results of the one to one pgr_dijkstra.
- The extra start_vid in the result is used to distinguish to which path it belongs.
The extra start_vid and end_vid in the result is used to distinguish to which path it belongs.
Example: |
---|
SELECT * FROM pgr_dijkstra(
'SELECT id, source, target, cost, reverse_cost FROM edge_table',
ARRAY[2,11], ARRAY[3,5],
FALSE
);
seq | path_seq | start_vid | end_vid | node | edge | cost | agg_cost
-----+----------+-----------+---------+------+------+------+----------
1 | 1 | 2 | 3 | 2 | 2 | 1 | 0
2 | 2 | 2 | 3 | 3 | -1 | 0 | 1
3 | 1 | 2 | 5 | 2 | 4 | 1 | 0
4 | 2 | 2 | 5 | 5 | -1 | 0 | 1
5 | 1 | 11 | 3 | 11 | 11 | 1 | 0
6 | 2 | 11 | 3 | 6 | 5 | 1 | 1
7 | 3 | 11 | 3 | 3 | -1 | 0 | 2
8 | 1 | 11 | 5 | 11 | 11 | 1 | 0
9 | 2 | 11 | 5 | 6 | 8 | 1 | 1
10 | 3 | 11 | 5 | 5 | -1 | 0 | 2
(10 rows)
Description of the Signatures¶
Description of the edges_sql query¶
edges_sql: | an SQL query, which should return a set of rows with the following columns: |
---|
Column | Type | Default | Description |
---|---|---|---|
id | ANY-INTEGER | Identifier of the edge. | |
source | ANY-INTEGER | Identifier of the first end point vertex of the edge. | |
target | ANY-INTEGER | Identifier of the second end point vertex of the edge. | |
cost | ANY-NUMERICAL |
|
|
reverse_cost | ANY-NUMERICAL | -1 |
|
Where:
ANY-INTEGER: | SMALLINT, INTEGER, BIGINT |
---|---|
ANY-NUMERICAL: | SMALLINT, INTEGER, BIGINT, REAL, FLOAT |
Description of the parameters of the signatures¶
Column | Type | Default | Description |
---|---|---|---|
sql | TEXT | SQL query as described above. | |
start_vid | BIGINT | Identifier of the starting vertex of the path. | |
start_vids | ARRAY[BIGINT] | Array of identifiers of starting vertices. | |
end_vid | BIGINT | Identifier of the ending vertex of the path. | |
end_vids | ARRAY[BIGINT] | Array of identifiers of ending vertices. | |
directed | BOOLEAN | true |
|
Description of the return values¶
Returns set of (seq, path_seq [, start_vid] [, end_vid], node, edge, cost, agg_cost)
Column | Type | Description |
---|---|---|
seq | INT | Sequential value starting from 1. |
path_seq | INT | Relative position in the path. Has value 1 for the beginning of a path. |
start_vid | BIGINT | Identifier of the starting vertex. Used when multiple starting vetrices are in the query. |
end_vid | BIGINT | Identifier of the ending vertex. Used when multiple ending vertices are in the query. |
node | BIGINT | Identifier of the node in the path from start_vid to end_vid. |
edge | BIGINT | Identifier of the edge used to go from node to the next node in the path sequence. -1 for the last node of the path. |
cost | FLOAT | Cost to traverse from node using edge to the next node in the path sequence. |
agg_cost | FLOAT | Aggregate cost from start_v to node. |
Additional Examples¶
The examples of this section are based on the Sample Data network.
The examples include combinations from starting vertices 2 and 11 to ending vertices 3 and 5 in a directed and undirected graph with and with out reverse_cost.
Examples for queries marked as directed with cost and reverse_cost columns¶
The examples in this section use the following Graph 1: Directed, with cost and reverse cost
SELECT * FROM pgr_dijkstra(
'SELECT id, source, target, cost, reverse_cost FROM edge_table',
2, 3
);
seq | path_seq | node | edge | cost | agg_cost
-----+----------+------+------+------+----------
1 | 1 | 2 | 4 | 1 | 0
2 | 2 | 5 | 8 | 1 | 1
3 | 3 | 6 | 9 | 1 | 2
4 | 4 | 9 | 16 | 1 | 3
5 | 5 | 4 | 3 | 1 | 4
6 | 6 | 3 | -1 | 0 | 5
(6 rows)
SELECT * FROM pgr_dijkstra(
'SELECT id, source, target, cost, reverse_cost FROM edge_table',
2, 5
);
seq | path_seq | node | edge | cost | agg_cost
-----+----------+------+------+------+----------
1 | 1 | 2 | 4 | 1 | 0
2 | 2 | 5 | -1 | 0 | 1
(2 rows)
SELECT * FROM pgr_dijkstra(
'SELECT id, source, target, cost, reverse_cost FROM edge_table',
2, ARRAY[3,5]
);
seq | path_seq | end_vid | node | edge | cost | agg_cost
-----+----------+---------+------+------+------+----------
1 | 1 | 3 | 2 | 4 | 1 | 0
2 | 2 | 3 | 5 | 8 | 1 | 1
3 | 3 | 3 | 6 | 9 | 1 | 2
4 | 4 | 3 | 9 | 16 | 1 | 3
5 | 5 | 3 | 4 | 3 | 1 | 4
6 | 6 | 3 | 3 | -1 | 0 | 5
7 | 1 | 5 | 2 | 4 | 1 | 0
8 | 2 | 5 | 5 | -1 | 0 | 1
(8 rows)
SELECT * FROM pgr_dijkstra(
'SELECT id, source, target, cost, reverse_cost FROM edge_table',
11, 3
);
seq | path_seq | node | edge | cost | agg_cost
-----+----------+------+------+------+----------
1 | 1 | 11 | 13 | 1 | 0
2 | 2 | 12 | 15 | 1 | 1
3 | 3 | 9 | 16 | 1 | 2
4 | 4 | 4 | 3 | 1 | 3
5 | 5 | 3 | -1 | 0 | 4
(5 rows)
SELECT * FROM pgr_dijkstra(
'SELECT id, source, target, cost, reverse_cost FROM edge_table',
11, 5
);
seq | path_seq | node | edge | cost | agg_cost
-----+----------+------+------+------+----------
1 | 1 | 11 | 13 | 1 | 0
2 | 2 | 12 | 15 | 1 | 1
3 | 3 | 9 | 9 | 1 | 2
4 | 4 | 6 | 8 | 1 | 3
5 | 5 | 5 | -1 | 0 | 4
(5 rows)
SELECT * FROM pgr_dijkstra(
'SELECT id, source, target, cost, reverse_cost FROM edge_table',
ARRAY[2,11], 5
);
seq | path_seq | start_vid | node | edge | cost | agg_cost
-----+----------+-----------+------+------+------+----------
1 | 1 | 2 | 2 | 4 | 1 | 0
2 | 2 | 2 | 5 | -1 | 0 | 1
3 | 1 | 11 | 11 | 13 | 1 | 0
4 | 2 | 11 | 12 | 15 | 1 | 1
5 | 3 | 11 | 9 | 9 | 1 | 2
6 | 4 | 11 | 6 | 8 | 1 | 3
7 | 5 | 11 | 5 | -1 | 0 | 4
(7 rows)
SELECT * FROM pgr_dijkstra(
'SELECT id, source, target, cost, reverse_cost FROM edge_table',
ARRAY[2, 11], ARRAY[3,5]
);
seq | path_seq | start_vid | end_vid | node | edge | cost | agg_cost
-----+----------+-----------+---------+------+------+------+----------
1 | 1 | 2 | 3 | 2 | 4 | 1 | 0
2 | 2 | 2 | 3 | 5 | 8 | 1 | 1
3 | 3 | 2 | 3 | 6 | 9 | 1 | 2
4 | 4 | 2 | 3 | 9 | 16 | 1 | 3
5 | 5 | 2 | 3 | 4 | 3 | 1 | 4
6 | 6 | 2 | 3 | 3 | -1 | 0 | 5
7 | 1 | 2 | 5 | 2 | 4 | 1 | 0
8 | 2 | 2 | 5 | 5 | -1 | 0 | 1
9 | 1 | 11 | 3 | 11 | 13 | 1 | 0
10 | 2 | 11 | 3 | 12 | 15 | 1 | 1
11 | 3 | 11 | 3 | 9 | 16 | 1 | 2
12 | 4 | 11 | 3 | 4 | 3 | 1 | 3
13 | 5 | 11 | 3 | 3 | -1 | 0 | 4
14 | 1 | 11 | 5 | 11 | 13 | 1 | 0
15 | 2 | 11 | 5 | 12 | 15 | 1 | 1
16 | 3 | 11 | 5 | 9 | 9 | 1 | 2
17 | 4 | 11 | 5 | 6 | 8 | 1 | 3
18 | 5 | 11 | 5 | 5 | -1 | 0 | 4
(18 rows)
Examples for queries marked as undirected with cost and reverse_cost columns¶
The examples in this section use the following Graph 2: Undirected, with cost and reverse cost
SELECT * FROM pgr_dijkstra(
'SELECT id, source, target, cost, reverse_cost FROM edge_table',
2, 3,
FALSE
);
seq | path_seq | node | edge | cost | agg_cost
-----+----------+------+------+------+----------
1 | 1 | 2 | 2 | 1 | 0
2 | 2 | 3 | -1 | 0 | 1
(2 rows)
SELECT * FROM pgr_dijkstra(
'SELECT id, source, target, cost, reverse_cost FROM edge_table',
2, 5,
FALSE
);
seq | path_seq | node | edge | cost | agg_cost
-----+----------+------+------+------+----------
1 | 1 | 2 | 4 | 1 | 0
2 | 2 | 5 | -1 | 0 | 1
(2 rows)
SELECT * FROM pgr_dijkstra(
'SELECT id, source, target, cost, reverse_cost FROM edge_table',
11, 3,
FALSE
);
seq | path_seq | node | edge | cost | agg_cost
-----+----------+------+------+------+----------
1 | 1 | 11 | 11 | 1 | 0
2 | 2 | 6 | 5 | 1 | 1
3 | 3 | 3 | -1 | 0 | 2
(3 rows)
SELECT * FROM pgr_dijkstra(
'SELECT id, source, target, cost, reverse_cost FROM edge_table',
11, 5,
FALSE
);
seq | path_seq | node | edge | cost | agg_cost
-----+----------+------+------+------+----------
1 | 1 | 11 | 11 | 1 | 0
2 | 2 | 6 | 8 | 1 | 1
3 | 3 | 5 | -1 | 0 | 2
(3 rows)
SELECT * FROM pgr_dijkstra(
'SELECT id, source, target, cost, reverse_cost FROM edge_table',
ARRAY[2,11], 5,
FALSE
);
seq | path_seq | start_vid | node | edge | cost | agg_cost
-----+----------+-----------+------+------+------+----------
1 | 1 | 2 | 2 | 4 | 1 | 0
2 | 2 | 2 | 5 | -1 | 0 | 1
3 | 1 | 11 | 11 | 11 | 1 | 0
4 | 2 | 11 | 6 | 8 | 1 | 1
5 | 3 | 11 | 5 | -1 | 0 | 2
(5 rows)
SELECT * FROM pgr_dijkstra(
'SELECT id, source, target, cost, reverse_cost FROM edge_table',
2, ARRAY[3,5],
FALSE
);
seq | path_seq | end_vid | node | edge | cost | agg_cost
-----+----------+---------+------+------+------+----------
1 | 1 | 3 | 2 | 2 | 1 | 0
2 | 2 | 3 | 3 | -1 | 0 | 1
3 | 1 | 5 | 2 | 4 | 1 | 0
4 | 2 | 5 | 5 | -1 | 0 | 1
(4 rows)
SELECT * FROM pgr_dijkstra(
'SELECT id, source, target, cost, reverse_cost FROM edge_table',
ARRAY[2, 11], ARRAY[3,5],
FALSE
);
seq | path_seq | start_vid | end_vid | node | edge | cost | agg_cost
-----+----------+-----------+---------+------+------+------+----------
1 | 1 | 2 | 3 | 2 | 2 | 1 | 0
2 | 2 | 2 | 3 | 3 | -1 | 0 | 1
3 | 1 | 2 | 5 | 2 | 4 | 1 | 0
4 | 2 | 2 | 5 | 5 | -1 | 0 | 1
5 | 1 | 11 | 3 | 11 | 11 | 1 | 0
6 | 2 | 11 | 3 | 6 | 5 | 1 | 1
7 | 3 | 11 | 3 | 3 | -1 | 0 | 2
8 | 1 | 11 | 5 | 11 | 11 | 1 | 0
9 | 2 | 11 | 5 | 6 | 8 | 1 | 1
10 | 3 | 11 | 5 | 5 | -1 | 0 | 2
(10 rows)
Examples for queries marked as directed with cost column¶
The examples in this section use the following Graph 3: Directed, with cost
SELECT * FROM pgr_dijkstra(
'SELECT id, source, target, cost FROM edge_table',
2, 3
);
seq | path_seq | node | edge | cost | agg_cost
-----+----------+------+------+------+----------
(0 rows)
SELECT * FROM pgr_dijkstra(
'SELECT id, source, target, cost FROM edge_table',
2, 5
);
seq | path_seq | node | edge | cost | agg_cost
-----+----------+------+------+------+----------
1 | 1 | 2 | 4 | 1 | 0
2 | 2 | 5 | -1 | 0 | 1
(2 rows)
SELECT * FROM pgr_dijkstra(
'SELECT id, source, target, cost FROM edge_table',
11, 3
);
seq | path_seq | node | edge | cost | agg_cost
-----+----------+------+------+------+----------
(0 rows)
SELECT * FROM pgr_dijkstra(
'SELECT id, source, target, cost FROM edge_table',
11, 5
);
seq | path_seq | node | edge | cost | agg_cost
-----+----------+------+------+------+----------
(0 rows)
SELECT * FROM pgr_dijkstra(
'SELECT id, source, target, cost FROM edge_table',
ARRAY[2,11], 5
);
seq | path_seq | start_vid | node | edge | cost | agg_cost
-----+----------+-----------+------+------+------+----------
1 | 1 | 2 | 2 | 4 | 1 | 0
2 | 2 | 2 | 5 | -1 | 0 | 1
(2 rows)
SELECT * FROM pgr_dijkstra(
'SELECT id, source, target, cost FROM edge_table',
2, ARRAY[3,5]
);
seq | path_seq | end_vid | node | edge | cost | agg_cost
-----+----------+---------+------+------+------+----------
1 | 1 | 5 | 2 | 4 | 1 | 0
2 | 2 | 5 | 5 | -1 | 0 | 1
(2 rows)
SELECT * FROM pgr_dijkstra(
'SELECT id, source, target, cost FROM edge_table',
ARRAY[2, 11], ARRAY[3,5]
);
seq | path_seq | start_vid | end_vid | node | edge | cost | agg_cost
-----+----------+-----------+---------+------+------+------+----------
1 | 1 | 2 | 5 | 2 | 4 | 1 | 0
2 | 2 | 2 | 5 | 5 | -1 | 0 | 1
(2 rows)
Examples for queries marked as undirected with cost column¶
The examples in this section use the following Graph 4: Undirected, with cost
SELECT * FROM pgr_dijkstra(
'SELECT id, source, target, cost FROM edge_table',
2, 3,
FALSE
);
seq | path_seq | node | edge | cost | agg_cost
-----+----------+------+------+------+----------
1 | 1 | 2 | 4 | 1 | 0
2 | 2 | 5 | 8 | 1 | 1
3 | 3 | 6 | 5 | 1 | 2
4 | 4 | 3 | -1 | 0 | 3
(4 rows)
SELECT * FROM pgr_dijkstra(
'SELECT id, source, target, cost FROM edge_table',
2, 5,
FALSE
);
seq | path_seq | node | edge | cost | agg_cost
-----+----------+------+------+------+----------
1 | 1 | 2 | 4 | 1 | 0
2 | 2 | 5 | -1 | 0 | 1
(2 rows)
SELECT * FROM pgr_dijkstra(
'SELECT id, source, target, cost FROM edge_table',
11, 3,
FALSE
);
seq | path_seq | node | edge | cost | agg_cost
-----+----------+------+------+------+----------
1 | 1 | 11 | 11 | 1 | 0
2 | 2 | 6 | 5 | 1 | 1
3 | 3 | 3 | -1 | 0 | 2
(3 rows)
SELECT * FROM pgr_dijkstra(
'SELECT id, source, target, cost FROM edge_table',
11, 5,
FALSE
);
seq | path_seq | node | edge | cost | agg_cost
-----+----------+------+------+------+----------
1 | 1 | 11 | 11 | 1 | 0
2 | 2 | 6 | 8 | 1 | 1
3 | 3 | 5 | -1 | 0 | 2
(3 rows)
SELECT * FROM pgr_dijkstra(
'SELECT id, source, target, cost FROM edge_table',
ARRAY[2,11], 5,
FALSE
);
seq | path_seq | start_vid | node | edge | cost | agg_cost
-----+----------+-----------+------+------+------+----------
1 | 1 | 2 | 2 | 4 | 1 | 0
2 | 2 | 2 | 5 | -1 | 0 | 1
3 | 1 | 11 | 11 | 11 | 1 | 0
4 | 2 | 11 | 6 | 8 | 1 | 1
5 | 3 | 11 | 5 | -1 | 0 | 2
(5 rows)
SELECT * FROM pgr_dijkstra(
'SELECT id, source, target, cost FROM edge_table',
2, ARRAY[3,5],
FALSE
);
seq | path_seq | end_vid | node | edge | cost | agg_cost
-----+----------+---------+------+------+------+----------
1 | 1 | 3 | 2 | 4 | 1 | 0
2 | 2 | 3 | 5 | 8 | 1 | 1
3 | 3 | 3 | 6 | 5 | 1 | 2
4 | 4 | 3 | 3 | -1 | 0 | 3
5 | 1 | 5 | 2 | 4 | 1 | 0
6 | 2 | 5 | 5 | -1 | 0 | 1
(6 rows)
SELECT * FROM pgr_dijkstra(
'SELECT id, source, target, cost FROM edge_table',
ARRAY[2, 11], ARRAY[3,5],
FALSE
);
seq | path_seq | start_vid | end_vid | node | edge | cost | agg_cost
-----+----------+-----------+---------+------+------+------+----------
1 | 1 | 2 | 3 | 2 | 4 | 1 | 0
2 | 2 | 2 | 3 | 5 | 8 | 1 | 1
3 | 3 | 2 | 3 | 6 | 5 | 1 | 2
4 | 4 | 2 | 3 | 3 | -1 | 0 | 3
5 | 1 | 2 | 5 | 2 | 4 | 1 | 0
6 | 2 | 2 | 5 | 5 | -1 | 0 | 1
7 | 1 | 11 | 3 | 11 | 11 | 1 | 0
8 | 2 | 11 | 3 | 6 | 5 | 1 | 1
9 | 3 | 11 | 3 | 3 | -1 | 0 | 2
10 | 1 | 11 | 5 | 11 | 11 | 1 | 0
11 | 2 | 11 | 5 | 6 | 8 | 1 | 1
12 | 3 | 11 | 5 | 5 | -1 | 0 | 2
(12 rows)
Equvalences between signatures¶
Examples: | For queries marked as directed with cost and reverse_cost columns |
---|
The examples in this section use the following:
SELECT * FROM pgr_dijkstra(
'SELECT id, source, target, cost, reverse_cost FROM edge_table',
2, 3,
TRUE
);
seq | path_seq | node | edge | cost | agg_cost
-----+----------+------+------+------+----------
1 | 1 | 2 | 4 | 1 | 0
2 | 2 | 5 | 8 | 1 | 1
3 | 3 | 6 | 9 | 1 | 2
4 | 4 | 9 | 16 | 1 | 3
5 | 5 | 4 | 3 | 1 | 4
6 | 6 | 3 | -1 | 0 | 5
(6 rows)
SELECT * FROM pgr_dijkstra(
'SELECT id, source, target, cost, reverse_cost FROM edge_table',
2,3
);
seq | path_seq | node | edge | cost | agg_cost
-----+----------+------+------+------+----------
1 | 1 | 2 | 4 | 1 | 0
2 | 2 | 5 | 8 | 1 | 1
3 | 3 | 6 | 9 | 1 | 2
4 | 4 | 9 | 16 | 1 | 3
5 | 5 | 4 | 3 | 1 | 4
6 | 6 | 3 | -1 | 0 | 5
(6 rows)
SELECT * FROM pgr_dijkstra(
'SELECT id, source, target, cost, reverse_cost FROM edge_table',
2, ARRAY[3],
TRUE
);
seq | path_seq | end_vid | node | edge | cost | agg_cost
-----+----------+---------+------+------+------+----------
1 | 1 | 3 | 2 | 4 | 1 | 0
2 | 2 | 3 | 5 | 8 | 1 | 1
3 | 3 | 3 | 6 | 9 | 1 | 2
4 | 4 | 3 | 9 | 16 | 1 | 3
5 | 5 | 3 | 4 | 3 | 1 | 4
6 | 6 | 3 | 3 | -1 | 0 | 5
(6 rows)
SELECT * FROM pgr_dijkstra(
'SELECT id, source, target, cost, reverse_cost FROM edge_table',
2, ARRAY[3]
);
seq | path_seq | end_vid | node | edge | cost | agg_cost
-----+----------+---------+------+------+------+----------
1 | 1 | 3 | 2 | 4 | 1 | 0
2 | 2 | 3 | 5 | 8 | 1 | 1
3 | 3 | 3 | 6 | 9 | 1 | 2
4 | 4 | 3 | 9 | 16 | 1 | 3
5 | 5 | 3 | 4 | 3 | 1 | 4
6 | 6 | 3 | 3 | -1 | 0 | 5
(6 rows)
SELECT * FROM pgr_dijkstra(
'SELECT id, source, target, cost, reverse_cost FROM edge_table',
ARRAY[2], ARRAY[3],
TRUE
);
seq | path_seq | start_vid | end_vid | node | edge | cost | agg_cost
-----+----------+-----------+---------+------+------+------+----------
1 | 1 | 2 | 3 | 2 | 4 | 1 | 0
2 | 2 | 2 | 3 | 5 | 8 | 1 | 1
3 | 3 | 2 | 3 | 6 | 9 | 1 | 2
4 | 4 | 2 | 3 | 9 | 16 | 1 | 3
5 | 5 | 2 | 3 | 4 | 3 | 1 | 4
6 | 6 | 2 | 3 | 3 | -1 | 0 | 5
(6 rows)
SELECT * FROM pgr_dijkstra(
'SELECT id, source, target, cost, reverse_cost FROM edge_table',
ARRAY[2], ARRAY[3]
);
seq | path_seq | start_vid | end_vid | node | edge | cost | agg_cost
-----+----------+-----------+---------+------+------+------+----------
1 | 1 | 2 | 3 | 2 | 4 | 1 | 0
2 | 2 | 2 | 3 | 5 | 8 | 1 | 1
3 | 3 | 2 | 3 | 6 | 9 | 1 | 2
4 | 4 | 2 | 3 | 9 | 16 | 1 | 3
5 | 5 | 2 | 3 | 4 | 3 | 1 | 4
6 | 6 | 2 | 3 | 3 | -1 | 0 | 5
(6 rows)
SET client_min_messages TO NOTICE;
SET
SELECT * FROM pgr_dijkstra(
'SELECT id::INTEGER, source::INTEGER, target::INTEGER, cost, reverse_cost FROM edge_table',
2, 3,
TRUE,
TRUE
);
NOTICE: Deprecated function
seq | id1 | id2 | cost
-----+-----+-----+------
0 | 2 | 4 | 1
1 | 5 | 8 | 1
2 | 6 | 9 | 1
3 | 9 | 16 | 1
4 | 4 | 3 | 1
5 | 3 | -1 | 0
(6 rows)
Examples: | For queries marked as undirected with cost and reverse_cost columns |
---|
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)
SET client_min_messages TO NOTICE;
SET
SELECT * FROM pgr_dijkstra(
'SELECT id::INTEGER, source::INTEGER, target::INTEGER, cost, reverse_cost FROM edge_table',
2, 3,
FALSE,
TRUE
);
NOTICE: Deprecated function
seq | id1 | id2 | cost
-----+-----+-----+------
0 | 2 | 2 | 1
1 | 3 | -1 | 0
(2 rows)
History
- Added functionality in version 2.1.0
- Renamed in version 2.0.0
See Also¶
- http://en.wikipedia.org/wiki/Dijkstra%27s_algorithm
- The queries use the Sample Data network.
Indices and tables