pgr_bdAstar
¶
pgr_bdAstar
— Shortest path using the bidirectional A* algorithm.
Availability
- Version 3.2.0
- New proposed signature:
pgr_bdAstar
(Combinations)
- New proposed signature:
- Version 3.0.0
- Official function
- Version 2.5.0
- New Proposed signatures:
pgr_bdAstar
(One to Many)pgr_bdAstar
(Many to One)pgr_bdAstar
(Many to Many)
- Signature change on
pgr_bdAstar
(One to One)- Old signature no longer supported
- New Proposed signatures:
- Version 2.0.0
- Official
pgr_bdAstar
(One to One)
- Official
Description¶
The main characteristics are:
- Process works for directed and undirected graphs.
- 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 \(u\):
- 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_bdAStar(
One to One ) on the:
- pgr_bdAstar( One to Many )
- pgr_bdAstar( Many to One )
- pgr_bdAstar( Many to Many )
start_vid
andend_vid
in the result is used to distinguish to which path it belongs.
Signatures¶
Summary
pgr_bdAstar(Edges SQL, start vid, end vid [, directed] [, heuristic] [, factor] [, epsilon]) pgr_bdAstar(Edges SQL, start vid, end vids [, directed] [, heuristic] [, factor] [, epsilon]) pgr_bdAstar(Edges SQL, start vids, end vid [, directed] [, heuristic] [, factor] [, epsilon]) pgr_bdAstar(Edges SQL, start vids, end vids [, directed] [, heuristic] [, factor] [, epsilon]) pgr_bdAstar(Edges SQL, Combinations SQL [, directed] [, heuristic] [, factor] [, epsilon]) RETURNS (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_bdAstar(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 \(6\) to vertex \(12\) on a directed graph with heuristic \(2\) |
---|
SELECT * FROM pgr_bdAstar(
'SELECT id, source, target, cost, reverse_cost, x1, y1, x2, y2
FROM edges',
6, 12,
directed => true, heuristic => 2
);
seq | path_seq | node | edge | cost | agg_cost
-----+----------+------+------+------+----------
1 | 1 | 6 | 4 | 1 | 0
2 | 2 | 7 | 10 | 1 | 1
3 | 3 | 8 | 12 | 1 | 2
4 | 4 | 12 | -1 | 0 | 3
(4 rows)
One to Many¶
pgr_bdAstar(Edges SQL, start vid, end vids [, directed] [, heuristic] [, factor] [, epsilon]) RETURNS (seq, path_seq, end_vid, node, edge, cost, agg_cost) OR EMPTY SET
Example: | From vertex \(6\) to vertices \(\{10, 12\}\) on a directed graph with heuristic \(3\) and factor \(3.5\) |
---|
SELECT * FROM pgr_bdAstar(
'SELECT id, source, target, cost, reverse_cost, x1, y1, x2, y2
FROM edges',
6, ARRAY[10, 12],
heuristic => 3, factor := 3.5
);
seq | path_seq | end_vid | node | edge | cost | agg_cost
-----+----------+---------+------+------+------+----------
1 | 1 | 10 | 6 | 4 | 1 | 0
2 | 2 | 10 | 7 | 8 | 1 | 1
3 | 3 | 10 | 11 | 9 | 1 | 2
4 | 4 | 10 | 16 | 16 | 1 | 3
5 | 5 | 10 | 15 | 3 | 1 | 4
6 | 6 | 10 | 10 | -1 | 0 | 5
7 | 1 | 12 | 6 | 4 | 1 | 0
8 | 2 | 12 | 7 | 8 | 1 | 1
9 | 3 | 12 | 11 | 11 | 1 | 2
10 | 4 | 12 | 12 | -1 | 0 | 3
(10 rows)
Many to One¶
pgr_bdAstar(Edges SQL, start vids, end vid [, directed] [, heuristic] [, factor] [, epsilon]) RETURNS (seq, path_seq, start_vid, node, edge, cost, agg_cost) OR EMPTY SET
Example: | From vertices \(\{6, 8\}\) to vertex \(10\) on an undirected graph with heuristic \(4\) |
---|
SELECT * FROM pgr_bdAstar(
'SELECT id, source, target, cost, reverse_cost, x1, y1, x2, y2
FROM edges',
ARRAY[6, 8], 10,
false, heuristic => 4
);
seq | path_seq | start_vid | node | edge | cost | agg_cost
-----+----------+-----------+------+------+------+----------
1 | 1 | 6 | 6 | 2 | 1 | 0
2 | 2 | 6 | 10 | -1 | 0 | 1
3 | 1 | 8 | 8 | 12 | 1 | 0
4 | 2 | 8 | 12 | 11 | 1 | 1
5 | 3 | 8 | 11 | 5 | 1 | 2
6 | 4 | 8 | 10 | -1 | 0 | 3
(6 rows)
Many to Many¶
pgr_bdAstar(Edges SQL, start vids, end vids [, directed] [, heuristic] [, factor] [, epsilon]) RETURNS (seq, path_seq, start_vid, end_vid, node, edge, cost, agg_cost) OR EMPTY SET
Example: | From vertices \(\{6, 8\}\) to vertices \(\{10, 12\}\) on a directed graph with factor \(0.5\) |
---|
SELECT * FROM pgr_bdAstar(
'SELECT id, source, target, cost, reverse_cost, x1, y1, x2, y2
FROM edges',
ARRAY[6, 8], ARRAY[10, 12],
factor => 0.5
);
seq | path_seq | start_vid | end_vid | node | edge | cost | agg_cost
-----+----------+-----------+---------+------+------+------+----------
1 | 1 | 6 | 10 | 6 | 4 | 1 | 0
2 | 2 | 6 | 10 | 7 | 8 | 1 | 1
3 | 3 | 6 | 10 | 11 | 9 | 1 | 2
4 | 4 | 6 | 10 | 16 | 16 | 1 | 3
5 | 5 | 6 | 10 | 15 | 3 | 1 | 4
6 | 6 | 6 | 10 | 10 | -1 | 0 | 5
7 | 1 | 6 | 12 | 6 | 4 | 1 | 0
8 | 2 | 6 | 12 | 7 | 10 | 1 | 1
9 | 3 | 6 | 12 | 8 | 12 | 1 | 2
10 | 4 | 6 | 12 | 12 | -1 | 0 | 3
11 | 1 | 8 | 10 | 8 | 10 | 1 | 0
12 | 2 | 8 | 10 | 7 | 8 | 1 | 1
13 | 3 | 8 | 10 | 11 | 9 | 1 | 2
14 | 4 | 8 | 10 | 16 | 16 | 1 | 3
15 | 5 | 8 | 10 | 15 | 3 | 1 | 4
16 | 6 | 8 | 10 | 10 | -1 | 0 | 5
17 | 1 | 8 | 12 | 8 | 12 | 1 | 0
18 | 2 | 8 | 12 | 12 | -1 | 0 | 1
(18 rows)
Combinations¶
pgr_bdAstar(Edges SQL, Combinations SQL [, directed] [, heuristic] [, factor] [, epsilon]) RETURNS (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;
source | target
--------+--------
5 | 6
5 | 10
6 | 5
6 | 15
6 | 14
(5 rows)
The query:
SELECT * FROM pgr_bdAstar(
'SELECT id, source, target, cost, reverse_cost, x1, y1, x2, y2
FROM edges',
'SELECT * FROM combinations',
factor => 0.5
);
seq | path_seq | start_vid | end_vid | node | edge | cost | agg_cost
-----+----------+-----------+---------+------+------+------+----------
1 | 1 | 5 | 6 | 5 | 1 | 1 | 0
2 | 2 | 5 | 6 | 6 | -1 | 0 | 1
3 | 1 | 5 | 10 | 5 | 1 | 1 | 0
4 | 2 | 5 | 10 | 6 | 4 | 1 | 1
5 | 3 | 5 | 10 | 7 | 8 | 1 | 2
6 | 4 | 5 | 10 | 11 | 9 | 1 | 3
7 | 5 | 5 | 10 | 16 | 16 | 1 | 4
8 | 6 | 5 | 10 | 15 | 3 | 1 | 5
9 | 7 | 5 | 10 | 10 | -1 | 0 | 6
10 | 1 | 6 | 5 | 6 | 1 | 1 | 0
11 | 2 | 6 | 5 | 5 | -1 | 0 | 1
12 | 1 | 6 | 15 | 6 | 4 | 1 | 0
13 | 2 | 6 | 15 | 7 | 8 | 1 | 1
14 | 3 | 6 | 15 | 11 | 9 | 1 | 2
15 | 4 | 6 | 15 | 16 | 16 | 1 | 3
16 | 5 | 6 | 15 | 15 | -1 | 0 | 4
(16 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 |
|
aStar optional Parameters¶
Parameter | Type | Default | Description |
---|---|---|---|
heuristic |
INTEGER |
5 | Heuristic number. Current valid values 0~5.
|
factor |
FLOAT |
1 |
For units manipulation. \(factor > 0\). |
epsilon |
FLOAT |
1 |
For less restricted results. \(epsilon >= 1\). |
See heuristics available and factor handling.
Inner Queries¶
Edges SQL¶
Parameter | 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 (
|
|
reverse_cost |
ANY-NUMERICAL | -1 | Weight of the edge (
|
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 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 |
---|
Result 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 1: | Demonstration of repeated values are ignored, and result is sorted. |
---|
SELECT * FROM pgr_bdAstar(
'SELECT id, source, target, cost, reverse_cost, x1, y1, x2, y2
FROM edges',
ARRAY[7, 10, 15, 10, 10, 15], ARRAY[10, 7, 10, 15]);
seq | path_seq | start_vid | end_vid | node | edge | cost | agg_cost
-----+----------+-----------+---------+------+------+------+----------
1 | 1 | 7 | 10 | 7 | 8 | 1 | 0
2 | 2 | 7 | 10 | 11 | 9 | 1 | 1
3 | 3 | 7 | 10 | 16 | 16 | 1 | 2
4 | 4 | 7 | 10 | 15 | 3 | 1 | 3
5 | 5 | 7 | 10 | 10 | -1 | 0 | 4
6 | 1 | 7 | 15 | 7 | 8 | 1 | 0
7 | 2 | 7 | 15 | 11 | 9 | 1 | 1
8 | 3 | 7 | 15 | 16 | 16 | 1 | 2
9 | 4 | 7 | 15 | 15 | -1 | 0 | 3
10 | 1 | 10 | 7 | 10 | 5 | 1 | 0
11 | 2 | 10 | 7 | 11 | 8 | 1 | 1
12 | 3 | 10 | 7 | 7 | -1 | 0 | 2
13 | 1 | 10 | 15 | 10 | 5 | 1 | 0
14 | 2 | 10 | 15 | 11 | 9 | 1 | 1
15 | 3 | 10 | 15 | 16 | 16 | 1 | 2
16 | 4 | 10 | 15 | 15 | -1 | 0 | 3
17 | 1 | 15 | 7 | 15 | 16 | 1 | 0
18 | 2 | 15 | 7 | 16 | 9 | 1 | 1
19 | 3 | 15 | 7 | 11 | 8 | 1 | 2
20 | 4 | 15 | 7 | 7 | -1 | 0 | 3
21 | 1 | 15 | 10 | 15 | 3 | 1 | 0
22 | 2 | 15 | 10 | 10 | -1 | 0 | 1
(22 rows)
Example 2: | Making start vids the same as end vids. |
---|
SELECT * FROM pgr_bdAstar(
'SELECT id, source, target, cost, reverse_cost, x1, y1, x2, y2
FROM edges',
ARRAY[7, 10, 15], ARRAY[7, 10, 15]);
seq | path_seq | start_vid | end_vid | node | edge | cost | agg_cost
-----+----------+-----------+---------+------+------+------+----------
1 | 1 | 7 | 10 | 7 | 8 | 1 | 0
2 | 2 | 7 | 10 | 11 | 9 | 1 | 1
3 | 3 | 7 | 10 | 16 | 16 | 1 | 2
4 | 4 | 7 | 10 | 15 | 3 | 1 | 3
5 | 5 | 7 | 10 | 10 | -1 | 0 | 4
6 | 1 | 7 | 15 | 7 | 8 | 1 | 0
7 | 2 | 7 | 15 | 11 | 9 | 1 | 1
8 | 3 | 7 | 15 | 16 | 16 | 1 | 2
9 | 4 | 7 | 15 | 15 | -1 | 0 | 3
10 | 1 | 10 | 7 | 10 | 5 | 1 | 0
11 | 2 | 10 | 7 | 11 | 8 | 1 | 1
12 | 3 | 10 | 7 | 7 | -1 | 0 | 2
13 | 1 | 10 | 15 | 10 | 5 | 1 | 0
14 | 2 | 10 | 15 | 11 | 9 | 1 | 1
15 | 3 | 10 | 15 | 16 | 16 | 1 | 2
16 | 4 | 10 | 15 | 15 | -1 | 0 | 3
17 | 1 | 15 | 7 | 15 | 16 | 1 | 0
18 | 2 | 15 | 7 | 16 | 9 | 1 | 1
19 | 3 | 15 | 7 | 11 | 8 | 1 | 2
20 | 4 | 15 | 7 | 7 | -1 | 0 | 3
21 | 1 | 15 | 10 | 15 | 3 | 1 | 0
22 | 2 | 15 | 10 | 10 | -1 | 0 | 1
(22 rows)
Example 3: | Manually assigned vertex combinations. |
---|
SELECT * FROM pgr_bdAstar(
'SELECT id, source, target, cost, reverse_cost, x1, y1, x2, y2
FROM edges',
'SELECT * FROM (VALUES (6, 10), (6, 7), (12, 10)) AS combinations (source, target)');
seq | path_seq | start_vid | end_vid | node | edge | cost | agg_cost
-----+----------+-----------+---------+------+------+------+----------
1 | 1 | 6 | 7 | 6 | 4 | 1 | 0
2 | 2 | 6 | 7 | 7 | -1 | 0 | 1
3 | 1 | 6 | 10 | 6 | 4 | 1 | 0
4 | 2 | 6 | 10 | 7 | 8 | 1 | 1
5 | 3 | 6 | 10 | 11 | 9 | 1 | 2
6 | 4 | 6 | 10 | 16 | 16 | 1 | 3
7 | 5 | 6 | 10 | 15 | 3 | 1 | 4
8 | 6 | 6 | 10 | 10 | -1 | 0 | 5
9 | 1 | 12 | 10 | 12 | 13 | 1 | 0
10 | 2 | 12 | 10 | 17 | 15 | 1 | 1
11 | 3 | 12 | 10 | 16 | 16 | 1 | 2
12 | 4 | 12 | 10 | 15 | 3 | 1 | 3
13 | 5 | 12 | 10 | 10 | -1 | 0 | 4
(13 rows)