pgr_aStar¶
Name¶
pgr_aStar
— Returns the shortest path using A* algorithm.
Availability:
- pgr_astar(one to one) 2.0.0, Signature changed 2.3.0
- pgr_astar(other signatures) 2.4.0
Characteristics¶
The main Characteristics are:
- Process is done only on edges with positive costs.
- Vertices of the graph are:
- positive when it belongs to the edges_sql
- 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 ∞
- When the starting vertex and ending vertex are the same, there is no path.
- When (x,y) coordinates for the same vertex identifier differ:
- A random selection of the vertex’s (x,y) coordinates is used.
- Running time: \(O((E + V) * \log V)\)
Signature Summary¶
pgr_aStar(edges_sql, start_vid, end_vid)
pgr_aStar(edges_sql, start_vid, end_vid, directed, heuristic, factor, epsilon)
Warning
Proposed functions for next mayor release.
- They are not officially in the current release.
- They will likely officially be part of the next mayor release:
- The functions make use of ANY-INTEGER and ANY-NUMERICAL
- Name might not change. (But still can)
- Signature might not change. (But still can)
- Functionality might not change. (But still can)
- pgTap tests have being done. But might need more.
- Documentation might need refinement.
pgr_aStar(edges_sql, start_vid, end_vids, directed, heuristic, factor, epsilon) -- proposed
pgr_aStar(edges_sql, starts_vid, end_vid, directed, heuristic, factor, epsilon) -- proposed
pgr_aStar(edges_sql, starts_vid, end_vids, directed, heuristic, factor, epsilon) -- proposed
RETURNS SET OF (seq, path_seq [, start_vid] [, end_vid], node, edge, cost, agg_cost)
OR EMPTY SET
Signatures¶
Minimal Signature¶
pgr_aStar(edges_sql, start_vid, end_vid)
RETURNS SET OF (seq, path_seq, node, edge, cost, agg_cost)
Example: | Using the defaults |
---|
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 | 10 | 1 | 1
3 | 3 | 10 | 12 | 1 | 2
4 | 4 | 11 | 13 | 1 | 3
5 | 5 | 12 | -1 | 0 | 4
(5 rows)
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)
Example: | Undirected 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 | 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 many¶
pgr_aStar(edges_sql, start_vid, end_vids, directed, heuristic, factor, epsilon) -- Proposed
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 eachend_vid
inend_vids
: - on a directed graph when
directed
flag is missing or is set totrue
. - on an undirected graph when
directed
flag is set tofalse
.
- on a directed graph when
Using this signature, will load once the graph and perform a one to one pgr_astar
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_astar.
- The extra
end_vid
in the result is used to distinguish to which path it belongs.
Example: |
---|
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 | 8 | 1 | 1
9 | 3 | 12 | 6 | 11 | 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, starts_vid, end_vid, directed, heuristic, factor, epsilon) -- Proposed
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
instart_vids
to oneend_vid
: - on a directed graph when
directed
flag is missing or is set totrue
. - on an undirected graph when
directed
flag is set tofalse
.
- on a directed graph when
Using this signature, will load once the graph and perform several one to one pgr_aStar where the ending vertex is fixed.
- The result is the union of the results of the one to one pgr_aStar.
- The extra
start_vid
in the result is used to distinguish to which path it belongs.
Example: |
---|
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, starts_vid, end_vids, directed, heuristic, factor, epsilon) -- Proposed
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
instart_vids
to eachend_vid
inend_vids
: - on a directed graph when
directed
flag is missing or is set totrue
. - on an undirected graph when
directed
flag is set tofalse
.
- on a directed graph when
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_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 | 7 | 3 | 7 | 6 | 1 | 0
8 | 2 | 7 | 3 | 8 | 7 | 1 | 1
9 | 3 | 7 | 3 | 5 | 8 | 1 | 2
10 | 4 | 7 | 3 | 6 | 9 | 1 | 3
11 | 5 | 7 | 3 | 9 | 16 | 1 | 4
12 | 6 | 7 | 3 | 4 | 3 | 1 | 5
13 | 7 | 7 | 3 | 3 | -1 | 0 | 6
14 | 1 | 2 | 12 | 2 | 4 | 1 | 0
15 | 2 | 2 | 12 | 5 | 10 | 1 | 1
16 | 3 | 2 | 12 | 10 | 12 | 1 | 2
17 | 4 | 2 | 12 | 11 | 13 | 1 | 3
18 | 5 | 2 | 12 | 12 | -1 | 0 | 4
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)
Description of the Signatures¶
Description of the edges_sql query for astar like functions¶
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 |
Description of the parameters of the signatures¶
Parameter | Type | Description |
---|---|---|
edges_sql | TEXT |
Edges SQL query as described above. |
start_vid | ANY-INTEGER |
Starting vertex identifier. |
end_vid | ANY-INTEGER |
Ending vertex identifier. |
directed | BOOLEAN |
|
heuristic | INTEGER |
(optional). Heuristic number. Current valid values 0~5. Default
|
factor | FLOAT |
(optional). For units manipulation. \(factor > 0\). Default 1 . see Factor |
epsilon | FLOAT |
(optional). For less restricted results. \(epsilon >= 1\). Default 1 . |
Description of the return values for a path¶
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_id | INT |
Path identifier. Has value 1 for the first of a path. Used when there are multiple paths for the same start_vid to end_vid combination. |
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 . |