pgr_aStar
¶
pgr_aStar
— Shortest path using the A* algorithm.

Boost Graph Inside¶
Availability
Version 3.2.0
New proposed signature:
pgr_aStar
(Combinations)
Version 3.0.0
Official function
Version 2.4.0
New Proposed signatures:
pgr_aStar
(One to Many)pgr_aStar
(Many to One)pgr_aStar
(Many to Many)
Version 2.3.0
Signature change on
pgr_astar
(One to One)Old signature no longer supported
Version 2.0.0
Official
pgr_aStar
(One to One)
Description¶
The main characteristics are:
Default kind of graph is directed when
directed
flag is missing.directed
flag is set to true
Unless specified otherwise, ordering is:
first by
start_vid
(if exists)then by
end_vid
Values are returned when there is a path
Let \(v\) and \(u\) be nodes on the graph:
If there is no path from \(v\) to \(u\):
no corresponding row is returned
agg_cost
from \(v\) to \(u\) is \(\infty\)
There is no path when \(v = u\) therefore
no corresponding row is returned
agg_cost
from v to u is \(0\)
Edges with negative costs are not included in the graph.
When (x,y) coordinates for the same vertex identifier differ:
A random selection of the vertex’s (x,y) coordinates is used.
Running time: \(O((E + V) * \log V)\)
The results are equivalent to the union of the results of the pgr_aStar( One to One ) on the:
pgr_aStar( One to Many )
pgr_aStar( Many to One )
pgr_aStar( Many to Many )
start_vid
andend_vid
in the result is used to distinguish to which path it belongs.
Signatures¶
Summary
pgr_aStar(Edges SQL, start vid, end vid [, directed] [, heuristic] [, factor] [, epsilon]) pgr_aStar(Edges SQL, start vid, end vids [, directed] [, heuristic] [, factor] [, epsilon]) pgr_aStar(Edges SQL, start vids, end vid [, directed] [, heuristic] [, factor] [, epsilon]) pgr_aStar(Edges SQL, start vids, end vids [, directed] [, heuristic] [, factor] [, epsilon]) pgr_aStar(Edges SQL, Combinations SQL [, directed] [, heuristic] [, factor] [, epsilon]) RETURNS SET OF (seq, path_seq [, start_vid] [, end_vid], node, edge, cost, agg_cost) OR EMPTY SET
Optional parameters are named parameters and have a default value.
One to One¶
pgr_aStar(Edges SQL, start vid, end vid [, directed] [, heuristic] [, factor] [, epsilon]) RETURNS SET OF (seq, path_seq, node, edge, cost, agg_cost) OR EMPTY SET
- Example
From vertex \(2\) to vertex \(11\) on a directed graph with heuristic \(2\)
SELECT * FROM pgr_aStar(
'SELECT id, source, target, cost, reverse_cost, x1, y1, x2, y2
FROM edge_table',
2, 11,
directed => true, heuristic => 2
);
seq | path_seq | node | edge | cost | agg_cost
-----+----------+------+------+------+----------
1 | 1 | 2 | 4 | 1 | 0
2 | 2 | 5 | 8 | 1 | 1
3 | 3 | 6 | 11 | 1 | 2
4 | 4 | 11 | -1 | 0 | 3
(4 rows)
One to Many¶
pgr_aStar(Edges SQL, start vid, end vids [, directed] [, heuristic] [, factor] [, epsilon]) RETURNS SET OF (seq, path_seq, end_vid, node, edge, cost, agg_cost) OR EMPTY SET
- Example
From vertex \(2\) to vertices \(\{3, 11\}\) on a directed graph with heuristic \(3\) and factor \(3.5\)
SELECT * FROM pgr_aStar(
'SELECT id, source, target, cost, reverse_cost, x1, y1, x2, y2
FROM edge_table',
2, ARRAY[3, 11],
heuristic => 3, factor := 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 | 11 | 2 | 4 | 1 | 0
8 | 2 | 11 | 5 | 8 | 1 | 1
9 | 3 | 11 | 6 | 11 | 1 | 2
10 | 4 | 11 | 11 | -1 | 0 | 3
(10 rows)
Many to One¶
pgr_aStar(Edges SQL, start vids, end vid [, directed] [, heuristic] [, factor] [, epsilon]) RETURNS SET OF (seq, path_seq, start_vid, node, edge, cost, agg_cost) OR EMPTY SET
- Example
From vertices \(\{2, 10\}\) to vertex \(3\) on an undirected graph with heuristic \(4\)
SELECT * FROM pgr_aStar(
'SELECT id, source, target, cost, reverse_cost, x1, y1, x2, y2
FROM edge_table',
ARRAY[2, 10], 3,
false, heuristic => 4
);
seq | path_seq | start_vid | node | edge | cost | agg_cost
-----+----------+-----------+------+------+------+----------
1 | 1 | 2 | 2 | 2 | 1 | 0
2 | 2 | 2 | 3 | -1 | 0 | 1
3 | 1 | 10 | 10 | 12 | 1 | 0
4 | 2 | 10 | 11 | 11 | 1 | 1
5 | 3 | 10 | 6 | 5 | 1 | 2
6 | 4 | 10 | 3 | -1 | 0 | 3
(6 rows)
Many to Many¶
pgr_aStar(Edges SQL, start vids, end vids [, directed] [, heuristic] [, factor] [, epsilon]) RETURNS SET OF (seq, path_seq, start_vid, end_vid, node, edge, cost, agg_cost) OR EMPTY SET
- Example
From vertices \(\{2, 10\}\) to vertices \(\{3, 11\}\) on a directed graph with factor \(0.5\)
SELECT * FROM pgr_aStar(
'SELECT id, source, target, cost, reverse_cost, x1, y1, x2, y2
FROM edge_table',
ARRAY[2, 10], ARRAY[3, 11],
factor => 0.5
);
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 | 11 | 2 | 4 | 1 | 0
8 | 2 | 2 | 11 | 5 | 8 | 1 | 1
9 | 3 | 2 | 11 | 6 | 11 | 1 | 2
10 | 4 | 2 | 11 | 11 | -1 | 0 | 3
11 | 1 | 10 | 3 | 10 | 10 | 1 | 0
12 | 2 | 10 | 3 | 5 | 8 | 1 | 1
13 | 3 | 10 | 3 | 6 | 9 | 1 | 2
14 | 4 | 10 | 3 | 9 | 16 | 1 | 3
15 | 5 | 10 | 3 | 4 | 3 | 1 | 4
16 | 6 | 10 | 3 | 3 | -1 | 0 | 5
17 | 1 | 10 | 11 | 10 | 12 | 1 | 0
18 | 2 | 10 | 11 | 11 | -1 | 0 | 1
(18 rows)
Combinations¶
pgr_aStar(Edges SQL, Combinations SQL [, directed] [, heuristic] [, factor] [, epsilon]) RETURNS SET OF (seq, path_seq, start_vid, end_vid, node, edge, cost, agg_cost) OR EMPTY SET
- Example
Using a combinations table on a directed graph with factor \(0.5\).
The combinations table:
SELECT * FROM combinations_table;
source | target
--------+--------
1 | 2
1 | 3
2 | 1
2 | 4
2 | 17
(5 rows)
The query:
SELECT * FROM pgr_aStar(
'SELECT id, source, target, cost, reverse_cost, x1, y1, x2, y2
FROM edge_table',
'SELECT * FROM combinations_table',
factor => 0.5
);
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 | 4 | 1 | 1
5 | 3 | 1 | 3 | 5 | 8 | 1 | 2
6 | 4 | 1 | 3 | 6 | 9 | 1 | 3
7 | 5 | 1 | 3 | 9 | 16 | 1 | 4
8 | 6 | 1 | 3 | 4 | 3 | 1 | 5
9 | 7 | 1 | 3 | 3 | -1 | 0 | 6
10 | 1 | 2 | 1 | 2 | 1 | 1 | 0
11 | 2 | 2 | 1 | 1 | -1 | 0 | 1
12 | 1 | 2 | 4 | 2 | 4 | 1 | 0
13 | 2 | 2 | 4 | 5 | 8 | 1 | 1
14 | 3 | 2 | 4 | 6 | 9 | 1 | 2
15 | 4 | 2 | 4 | 9 | 16 | 1 | 3
16 | 5 | 2 | 4 | 4 | -1 | 0 | 4
(16 rows)
Parameters¶
Column |
Type |
Description |
---|---|---|
|
Edges SQL as described below |
|
|
Combinations SQL 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. |
Optional parameters¶
Column |
Type |
default |
Description |
---|---|---|---|
|
|
|
|
aStar optional Parameters¶
Parameter |
Type |
Default |
Description |
---|---|---|---|
|
INTEGER |
5 |
Heuristic number. Current valid values 0~5.
|
|
|
|
For units manipulation. \(factor > 0\). See Factor |
|
|
|
For less restricted results. \(epsilon >= 1\). |
Inner queries¶
Edges SQL¶
Parameter |
Type |
Default |
Description |
---|---|---|---|
|
ANY-INTEGER |
Identifier of the edge. |
|
|
ANY-INTEGER |
Identifier of the first end point vertex of the edge. |
|
|
ANY-INTEGER |
Identifier of the second end point vertex of the edge. |
|
|
ANY-NUMERICAL |
Weight of the edge (
|
|
|
ANY-NUMERICAL |
-1 |
Weight of the edge (
|
|
ANY-NUMERICAL |
X coordinate of |
|
|
ANY-NUMERICAL |
Y coordinate of |
|
|
ANY-NUMERICAL |
X coordinate of |
|
|
ANY-NUMERICAL |
Y coordinate of |
Where:
- ANY-INTEGER
SMALLINT
,INTEGER
,BIGINT
- ANY-NUMERICAL
SMALLINT
,INTEGER
,BIGINT
,REAL
,FLOAT
Combinations SQL¶
Parameter |
Type |
Description |
---|---|---|
|
ANY-INTEGER |
Identifier of the departure vertex. |
|
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 |
---|---|---|
|
|
Sequential value starting from 1. |
|
|
Relative position in the path. Has value 1 for the beginning of a path. |
|
|
Identifier of the starting vertex. Returned when multiple starting vetrices are in the query. |
|
|
Identifier of the ending vertex. Returned when multiple ending vertices are in the query. |
|
|
Identifier of the node in the path from |
|
|
Identifier of the edge used to go from |
|
|
Cost to traverse from |
|
|
Aggregate cost from |
Additional Examples¶
- Example 1
Demonstration of repeated values are ignored, and result is sorted.
SELECT * FROM pgr_aStar(
'SELECT id, source, target, cost, reverse_cost, x1, y1, x2, y2
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 2
Making
start_vids
the same asend_vids
.
SELECT * FROM pgr_aStar(
'SELECT id, source, target, cost, reverse_cost, x1, y1, x2, y2
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 3
Manually assigned vertex combinations.
SELECT * FROM pgr_aStar(
'SELECT id, source, target, cost, reverse_cost, x1, y1, x2, y2
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)
See Also¶
Indices and tables