# pgr_aStarCost¶

pgr_aStarCost — Returns the aggregate cost shortest path using pgr_aStar algorithm.

Availability

• Version 3.2.0

• New proposed function:

• pgr_aStarCost(Combinations)

• Version 3.0.0

• Official function

• Version 2.4.0

• New proposed function

## 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: $$O((E + V) * \log V)$$

## Signatures¶

Summary

pgr_aStarCost(Edges SQL, from_vid,  to_vid   [, directed] [, heuristic] [, factor] [, epsilon])
pgr_aStarCost(Edges SQL, from_vid,  to_vids  [, directed] [, heuristic] [, factor] [, epsilon])
pgr_aStarCost(Edges SQL, from_vids, to_vid   [, directed] [, heuristic] [, factor] [, epsilon])
pgr_aStarCost(Edges SQL, from_vids, to_vids  [, directed] [, heuristic] [, factor] [, epsilon])
pgr_aStarCost(Edges SQL, Combinations SQL  [, directed] [, heuristic] [, factor] [, epsilon]) -- Proposed on v3.2

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


Optional parameters are named parameters and have a default value.

Using defaults

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

Example

From vertex $$2$$ to vertex $$12$$ on a directed graph

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, from_vid,  to_vid   [, directed] [, heuristic] [, factor] [, epsilon])
RETURNS SET OF (start_vid, end_vid, agg_cost)
OR EMPTY SET

Example

From vertex $$2$$ to vertex $$12$$ on an undirected graph using heuristic $$2$$

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, from_vid,  to_vids  [, directed] [, heuristic] [, factor] [, epsilon])
RETURNS SET OF (start_vid, end_vid, agg_cost)
OR EMPTY SET

Example

From vertex $$2$$ to vertices $$\{3, 12\}$$ on a directed graph using heuristic $$2$$

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, from_vids, to_vid   [, directed] [, heuristic] [, factor] [, epsilon])
RETURNS SET OF (start_vid, end_vid, agg_cost)
OR EMPTY SET

Example

From vertices $$\{7, 2\}$$ to vertex $$12$$ on a directed graph using heuristic $$0$$

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, from_vids, to_vids  [, directed] [, heuristic] [, factor] [, epsilon])
RETURNS SET OF (start_vid, end_vid, agg_cost)
OR EMPTY SET

Example

From vertices $$\{7, 2\}$$ to vertices $$\{3, 12\}$$ on a directed graph using heuristic $$2$$

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)



### Combinations¶

pgr_aStarCost(Edges SQL, Combinations SQL  [, directed] [, heuristic] [, factor] [, epsilon])
RETURNS SET OF (start_vid, end_vid, agg_cost)
OR EMPTY SET

Example

Using a combinations table on a directed graph using heuristic $$2$$.

SELECT * FROM pgr_aStarCost(
'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);
start_vid | end_vid | agg_cost
-----------+---------+----------
2 |      12 |        4
7 |       3 |        6
(2 rows)



## Parameters¶

Parameter

Type

Description

Edges SQL

TEXT

Edges query as described below.

Combinations SQL

TEXT

Combinations query as described below.

from_vid

ANY-INTEGER

Starting vertex identifier. Parameter in:

from_vids

ARRAY[ANY-INTEGER]

Array of starting vertices identifiers. Parameter in:

to_vid

ANY-INTEGER

Ending vertex identifier. Parameter in:

to_vids

ARRAY[ANY-INTEGER]

Array of ending vertices identifiers. Parameter in:

### Optional Parameters¶

Parameter

Type

Default

Description

directed

BOOLEAN

true

• When true the graph is considered as Directed.

• When false the graph is considered as Undirected.

heuristic

INTEGER

5

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

1

For units manipulation. $$factor > 0$$. See Factor

epsilon

FLOAT

1

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

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

ANY-NUMERICAL

SMALLINT, INTEGER, BIGINT, REAL, FLOAT

### Combinations query¶

Column

Type

Default

Description

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.

Where:

ANY-INTEGER

SMALLINT, INTEGER, BIGINT

## Result Columns¶

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 from start_vid to end_vid.