pgr_aStar — Returns the shortest path using A* algorithm.
Availability:
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 (x,y) coordinates for the same vertex identifier differ:
 A random selection of the vertex’s (x,y) coordinates is used.
 Running time: \(O((E + V) * \log V)\)
pgr_aStar(edges_sql, start_vid, end_vid)
pgr_aStar(edges_sql, start_vid, end_vid, directed, heuristic, factor, epsilon)
Warning
These are proposed functions for next mayor release.
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
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  8  1  1
3  3  6  9  1  2
4  4  9  15  1  3
5  5  12  1  0  4
(5 rows)
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  10  1  1
3  3  10  12  1  2
4  4  11  13  1  3
5  5  12  1  0  4
(5 rows)
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
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  9  1  2
10  4  12  9  15  1  3
11  5  12  12  1  0  4
(11 rows)
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
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)
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
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  2  12  2  4  1  0
8  2  2  12  5  8  1  1
9  3  2  12  6  9  1  2
10  4  2  12  9  15  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  8  1  2
22  4  7  12  6  9  1  3
23  5  7  12  9  15  1  4
24  6  7  12  12  1  0  5
(24 rows)
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 
Parameter  Type  Description 

edges_sql  TEXT  Edges SQL query as described above. 
start_vid  ANYINTEGER  Starting vertex identifier. 
end_vid  ANYINTEGER  Ending vertex identifier. 
directed  BOOLEAN 

heuristic  INTEGER  (optional). Heuristic number. Current valid values 0~5. Default 5

factor  FLOAT  (optional). For units manipulation. \(factor > 0\). Default 1. see Factor 
epsilon  FLOAT  (optional). For less restricted results. \(epsilon >= 1\). Default 1. 
Returns set of (seq, path_seq, node, edge, cost, agg_cost)
Column  Type  Description 

seq  INTEGER  Row sequence. 
path_seq  INTEGER  Path sequence that indicates the relative position on the path. 
node  BIGINT 

edge  BIGINT 

cost  FLOAT 

agg_cost  FLOAT 
