pgr_aStar
— Shortest path using A* algorithm.
Availability
Support
The main characteristics are:
directed
flag is missing.directed
flag is set to truestart_vid
(if exists)end_vid
agg_cost
from \(v\) to \(u\) is \(\infty\)agg_cost
from v to u is \(0\)start_vid
and end_vid
in the result is used to distinguish to which path it belongs.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])
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)
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)
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)
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)
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)
Parameter  Type  Description 

edges_sql  TEXT 
edges_sql inner query. 
from_vid  ANYINTEGER 
Starting vertex identifier. Parameter in: 
from_vids  ARRAY[ANYINTEGER] 
Array of starting vertices identifiers. Parameter in: 
to_vid  ANYINTEGER 
Ending vertex identifier. Parameter in: 
to_vids  ARRAY[ANYINTEGER] 
Array of ending vertices identifiers. Parameter in: 
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. \(epsilon >= 1\). 
edges_sql:  an SQL query, which should return a set of rows with the following columns: 

Column  Type  Default  Description 

id  ANYINTEGER 
Identifier of the edge.  
source  ANYINTEGER 
Identifier of the first end point vertex of the edge.  
target  ANYINTEGER 
Identifier of the second end point vertex of the edge.  
cost  ANYNUMERICAL 
Weight of the edge (source, target)


reverse_cost  ANYNUMERICAL 
1  Weight of the edge (target, source),

x1  ANYNUMERICAL 
X coordinate of source vertex.  
y1  ANYNUMERICAL 
Y coordinate of source vertex.  
x2  ANYNUMERICAL 
X coordinate of target vertex.  
y2  ANYNUMERICAL 
Y coordinate of target vertex. 
Where:
ANYINTEGER:  SMALLINT, INTEGER, BIGINT 

ANYNUMERICAL:  SMALLINT, INTEGER, BIGINT, REAL, FLOAT 
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 . 