# pgr_aStarCost – proposed¶

## Name¶

pgr_aStarCost — Returns the aggregate cost shortest path using aStar - Family of functions algorithm.

Availability: 2.4.0

## Signature Summary¶

Warning

These are 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_aStarCost(edges_sql, start_vid, end_vid) -- Proposed
pgr_aStarCost(edges_sql, start_vid, end_vid, directed, heuristic, factor, epsilon) -- Proposed
pgr_aStarCost(edges_sql, start_vid, end_vids, directed, heuristic, factor, epsilon) -- Proposed
pgr_aStarCost(edges_sql, starts_vid, end_vid, directed, heuristic, factor, epsilon) -- Proposed
pgr_aStarCost(edges_sql, starts_vid, end_vids, directed, heuristic, factor, epsilon) -- Proposed

RETURNS SET OF (start_vid, end_vid, agg_cost) OR EMPTY SET


## Signatures¶

### Minimal Signature¶

pgr_aStarCost(edges_sql, start_vid, end_vid)
RETURNS SET OF (start_vid, end_vid, agg_cost) OR EMPTY SET

Example: Using the defaults
SELECT * FROM pgr_aStarCost(
'SELECT id, source, target, cost, reverse_cost, x1, y1, x2, y2 FROM edge_table',
2, 12);
start_vid | end_vid | agg_cost
-----------+---------+----------
2 |      12 |        4
(1 row)



### One to One¶

pgr_aStarCost(edges_sql, start_vid, end_vid, directed, heuristic, factor, epsilon)
RETURNS SET OF (start_vid, end_vid, agg_cost) OR EMPTY SET

Example: Setting a Heuristic
SELECT * FROM pgr_aStarCost(
'SELECT id, source, target, cost, reverse_cost, x1, y1, x2, y2 FROM edge_table',
2, 12,
directed := false, heuristic := 2);
start_vid | end_vid | agg_cost
-----------+---------+----------
2 |      12 |        4
(1 row)



### One to many¶

pgr_aStarCost(edges_sql, start_vid, end_vids, directed, heuristic, factor, epsilon) -- Proposed
RETURNS SET OF (start_vid, end_vid, agg_cost) OR EMPTY SET

This signature finds a path from one start_vid to each end_vid in end_vids:
• on a directed graph when directed flag is missing or is set to true.
• on an undirected graph when directed flag is set to false.

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 column in the result is used to distinguish to which path it belongs.
SELECT * FROM pgr_aStarCost(
'SELECT id, source, target, cost, reverse_cost, x1, y1, x2, y2 FROM edge_table',
2, ARRAY[3, 12], heuristic := 2);
start_vid | end_vid | agg_cost
-----------+---------+----------
2 |       3 |        5
2 |      12 |        4
(2 rows)



### Many to One¶

pgr_aStarCost(edges_sql, starts_vid, end_vid, directed, heuristic, factor, epsilon) -- Proposed
RETURNS SET OF (start_vid, end_vid, agg_cost) OR EMPTY SET

This signature finds the shortest path from each start_vid in start_vids to one end_vid:
• on a directed graph when directed flag is missing or is set to true.
• on an undirected graph when directed flag is set to false.

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 column in the result is used to distinguish to which path it belongs.
SELECT * FROM pgr_aStarCost(
'SELECT id, source, target, cost, reverse_cost, x1, y1, x2, y2 FROM edge_table',
ARRAY[7, 2], 12, heuristic := 0);
start_vid | end_vid | agg_cost
-----------+---------+----------
2 |      12 |        4
7 |      12 |        5
(2 rows)



### Many to Many¶

pgr_aStarCost(edges_sql, starts_vid, end_vids, directed, heuristic, factor, epsilon) -- Proposed
RETURNS SET OF (start_vid, end_vid, agg_cost) OR EMPTY SET

This signature finds the shortest path from each start_vid in start_vids to each end_vid in end_vids:
• on a directed graph when directed flag is missing or is set to true.
• on an undirected graph when directed flag is set to false.

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.

SELECT * FROM pgr_aStarCost(
'SELECT id, source, target, cost, reverse_cost, x1, y1, x2, y2 FROM edge_table',
ARRAY[7, 2], ARRAY[3, 12], heuristic := 2);
start_vid | end_vid | agg_cost
-----------+---------+----------
2 |       3 |        5
2 |      12 |        4
7 |       3 |        6
7 |      12 |        5
(4 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)

• When negative: edge (source, target) does not exist, therefore it’s not part of the graph.
reverse_cost ANY-NUMERICAL -1

Weight of the edge (target, source),

• When negative: edge (target, source) does not exist, therefore it’s not part of the graph.
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 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
• Optional.
• When false the graph is considered as Undirected.
• Default is true which considers the graph as Directed.
heuristic INTEGER

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

• 0: h(v) = 0 (Use this value to compare with pgr_dijkstra)
• 1: h(v) abs(max(dx, dy))
• 2: h(v) abs(min(dx, dy))
• 3: h(v) = dx * dx + dy * dy
• 4: h(v) = sqrt(dx * dx + dy * dy)
• 5: h(v) = abs(dx) + abs(dy)
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¶

Returns set of (start_vid, end_vid, agg_cost)

Column Type Description
start_vid BIGINT Identifier of the starting vertex.
end_vid BIGINT Identifier of the ending vertex.
agg_cost FLOAT Aggregate cost of the shortest path from start_vid to end_vid.