pgr_aStar¶
pgr_aStar
— Shortest path using A* algorithm.
Availability
- Version 3.2.0
- New proposed function:
- pgr_aStar(Combinations)
- New proposed function:
- Version 3.0.0
- Official function
- Version 2.4.0
- New Proposed functions:
- pgr_aStar(One to Many)
- pgr_aStar(Many to One)
- pgr_aStar(Many to Many)
- New Proposed functions:
- Version 2.3.0
- Signature change on pgr_astar(One to One)
- Old signature no longer supported
- Signature change on pgr_astar(One to One)
- 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
- first by
- 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 \(0\)
- If there is no path from \(v\) to \(u\):
- 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, from_vid, to_vid [, directed] [, heuristic] [, factor] [, epsilon])
pgr_aStar(Edges SQL, from_vid, to_vids [, directed] [, heuristic] [, factor] [, epsilon])
pgr_aStar(Edges SQL, from_vids, to_vid [, directed] [, heuristic] [, factor] [, epsilon])
pgr_aStar(Edges SQL, from_vids, to_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.
Using defaults
pgr_aStar(Edges SQL, from_vid, to_vid)
RETURNS SET OF (seq, path_seq, node, edge, cost, agg_cost)
OR EMPTY SET
Example: | From vertex \(2\) to vertex \(12\) on a directed graph |
---|
SELECT * FROM pgr_astar(
'SELECT id, source, target, cost, reverse_cost, x1, y1, x2, y2 FROM edge_table',
2, 12);
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 | 13 | 1 | 3
5 | 5 | 12 | -1 | 0 | 4
(5 rows)
One to One¶
pgr_aStar(Edges SQL, from_vid, to_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 \(12\) on an undirected graph using heuristic \(2\) |
---|
SELECT * FROM pgr_astar(
'SELECT id, source, target, cost, reverse_cost, x1, y1, x2, y2 FROM edge_table',
2, 12,
directed := false, heuristic := 2);
seq | path_seq | node | edge | cost | agg_cost
-----+----------+------+------+------+----------
1 | 1 | 2 | 2 | 1 | 0
2 | 2 | 3 | 3 | 1 | 1
3 | 3 | 4 | 16 | 1 | 2
4 | 4 | 9 | 15 | 1 | 3
5 | 5 | 12 | -1 | 0 | 4
(5 rows)
One to many¶
pgr_aStar(Edges SQL, from_vid, to_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 \(\{3, 12\}\) on a directed graph using heuristic \(2\) |
---|
SELECT * FROM pgr_astar(
'SELECT id, source, target, cost, reverse_cost, x1, y1, x2, y2 FROM edge_table',
2, ARRAY[3, 12], heuristic := 2);
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 | 10 | 1 | 1
9 | 3 | 12 | 10 | 12 | 1 | 2
10 | 4 | 12 | 11 | 13 | 1 | 3
11 | 5 | 12 | 12 | -1 | 0 | 4
(11 rows)
Many to One¶
pgr_aStar(Edges SQL, from_vids, to_vid [, directed] [, heuristic] [, factor] [, epsilon])
RETURNS SET OF (seq, path_seq, start_vid, node, edge, cost, agg_cost)
OR EMPTY SET
Example: | From vertices \(\{7, 2\}\) to vertex \(12\) on a directed graph using heuristic \(0\) |
---|
SELECT * FROM pgr_astar(
'SELECT id, source, target, cost, reverse_cost, x1, y1, x2, y2 FROM edge_table',
ARRAY[7, 2], 12, heuristic := 0);
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_aStar(Edges SQL, from_vids, to_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 \(\{7, 2\}\) to vertices \(\{3, 12\}\) on a directed graph using heuristic \(2\) |
---|
SELECT * FROM pgr_astar(
'SELECT id, source, target, cost, reverse_cost, x1, y1, x2, y2 FROM edge_table',
ARRAY[7, 2], ARRAY[3, 12], heuristic := 2);
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 | 12 | 2 | 4 | 1 | 0
8 | 2 | 2 | 12 | 5 | 10 | 1 | 1
9 | 3 | 2 | 12 | 10 | 12 | 1 | 2
10 | 4 | 2 | 12 | 11 | 13 | 1 | 3
11 | 5 | 2 | 12 | 12 | -1 | 0 | 4
12 | 1 | 7 | 3 | 7 | 6 | 1 | 0
13 | 2 | 7 | 3 | 8 | 7 | 1 | 1
14 | 3 | 7 | 3 | 5 | 8 | 1 | 2
15 | 4 | 7 | 3 | 6 | 9 | 1 | 3
16 | 5 | 7 | 3 | 9 | 16 | 1 | 4
17 | 6 | 7 | 3 | 4 | 3 | 1 | 5
18 | 7 | 7 | 3 | 3 | -1 | 0 | 6
19 | 1 | 7 | 12 | 7 | 6 | 1 | 0
20 | 2 | 7 | 12 | 8 | 7 | 1 | 1
21 | 3 | 7 | 12 | 5 | 10 | 1 | 2
22 | 4 | 7 | 12 | 10 | 12 | 1 | 3
23 | 5 | 7 | 12 | 11 | 13 | 1 | 4
24 | 6 | 7 | 12 | 12 | -1 | 0 | 5
(24 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 using heuristic \(2\). |
---|
SELECT * FROM pgr_astar(
'SELECT id, source, target, cost, reverse_cost, x1, y1, x2, y2 FROM edge_table',
'SELECT * FROM ( VALUES (7, 3), (2, 12) ) AS t(source, target)',
heuristic := 2);
seq | path_seq | start_vid | end_vid | node | edge | cost | agg_cost
-----+----------+-----------+---------+------+------+------+----------
1 | 1 | 2 | 12 | 2 | 4 | 1 | 0
2 | 2 | 2 | 12 | 5 | 10 | 1 | 1
3 | 3 | 2 | 12 | 10 | 12 | 1 | 2
4 | 4 | 2 | 12 | 11 | 13 | 1 | 3
5 | 5 | 2 | 12 | 12 | -1 | 0 | 4
6 | 1 | 7 | 3 | 7 | 6 | 1 | 0
7 | 2 | 7 | 3 | 8 | 7 | 1 | 1
8 | 3 | 7 | 3 | 5 | 8 | 1 | 2
9 | 4 | 7 | 3 | 6 | 9 | 1 | 3
10 | 5 | 7 | 3 | 9 | 16 | 1 | 4
11 | 6 | 7 | 3 | 4 | 3 | 1 | 5
12 | 7 | 7 | 3 | 3 | -1 | 0 | 6
(12 rows)
Parameters¶
Parameter | Type | Description |
---|---|---|
Edges SQL | TEXT |
Edges query as described below. |
Combinations SQL | TEXT |
Combinations query as described below. |
from_vid | ANY-INTEGER |
Starting vertex identifier. Parameter in: |
from_vids | ARRAY[ANY-INTEGER] |
Array of starting vertices identifiers. Parameter in: |
to_vid | ANY-INTEGER |
Ending vertex identifier. Parameter in: |
to_vids | ARRAY[ANY-INTEGER] |
Array of ending vertices identifiers. Parameter in: |
Optional Parameters¶
Parameter | Type | Default | Description |
---|---|---|---|
directed | BOOLEAN |
true |
|
heuristic | INTEGER |
5 |
Heuristic number. Current valid values 0~5. Default
|
factor | FLOAT |
1 |
For units manipulation. \(factor > 0\). See Factor |
epsilon | FLOAT |
1 |
For less restricted results. \(epsilon >= 1\). |
Inner queries¶
Edges 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 |
Weight of the edge (source, target)
|
|
reverse_cost | ANY-NUMERICAL |
-1 | Weight of the edge (target, source),
|
x1 | ANY-NUMERICAL |
X coordinate of source vertex. | |
y1 | ANY-NUMERICAL |
Y coordinate of source vertex. | |
x2 | ANY-NUMERICAL |
X coordinate of target vertex. | |
y2 | ANY-NUMERICAL |
Y coordinate of target vertex. |
Where:
ANY-INTEGER: | SMALLINT, INTEGER, BIGINT |
---|---|
ANY-NUMERICAL: | SMALLINT, INTEGER, BIGINT, REAL, FLOAT |
Combinations query¶
Column | Type | Default | Description |
---|---|---|---|
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. |
Where:
ANY-INTEGER: | SMALLINT, INTEGER, BIGINT |
---|
Result Columns¶
Returns set of (seq, path_seq [, start_vid] [, end_vid], node, edge, cost, agg_cost)
Column | Type | Description |
---|---|---|
seq | 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. 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_v to node . |