pgr_aStar¶
pgr_aStar
— Shortest path using A* algorithm.
Availability
Version 3.2.0
New proposed function:
pgr_aStar(Combinations)
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)
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, 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 

Edges query as described below. 
Combinations SQL 

Combinations query as described below. 
from_vid 

Starting vertex identifier. Parameter in: 
from_vids 

Array of starting vertices identifiers. Parameter in: 
to_vid 

Ending vertex identifier. Parameter in: 
to_vids 

Array of ending vertices identifiers. Parameter in: 
Optional Parameters¶
Parameter 
Type 
Default 
Description 

directed 



heuristic 


Heuristic number. Current valid values 0~5. Default

factor 


For units manipulation. \(factor > 0\). See Factor 
epsilon 


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 

Identifier of the edge. 

source 

Identifier of the first end point vertex of the edge. 

target 

Identifier of the second end point vertex of the edge. 

cost 

Weight of the edge (source, target)


reverse_cost 

1 
Weight of the edge (target, source),

x1 

X coordinate of source vertex. 

y1 

Y coordinate of source vertex. 

x2 

X coordinate of target vertex. 

y2 

Y coordinate of target vertex. 
Where:
 ANYINTEGER
SMALLINT, INTEGER, BIGINT
 ANYNUMERICAL
SMALLINT, INTEGER, BIGINT, REAL, FLOAT
Combinations query¶
Column 
Type 
Default 
Description 

source 

Identifier of the first end point vertex of the edge. 

target 

Identifier of the second end point vertex of the edge. 
Where:
 ANYINTEGER
SMALLINT, INTEGER, BIGINT
Result Columns¶
Returns set of (seq, path_seq [, start_vid] [, end_vid], node, edge, cost, agg_cost)
Column 
Type 
Description 

seq 

Sequential value starting from 1. 
path_seq 

Relative position in the path. Has value 1 for the beginning of a path. 
start_vid 

Identifier of the starting vertex. Returned when multiple starting vetrices are in the query. 
end_vid 

Identifier of the ending vertex. Returned when multiple ending vertices are in the query. 
node 

Identifier of the node in the path from 
edge 

Identifier of the edge used to go from 
cost 

Cost to traverse from 
agg_cost 

Aggregate cost from 
See Also¶
Indices and tables