# pgr_aStarCost¶

pgr_aStarCost - Total cost of the shortest path(s) using the A* algorithm.

Availability

• Version 3.2.0

• New proposed signature:

• Version 3.0.0

• Official function

• Version 2.4.0

• New proposed function

## Description¶

The pgr_aStarCost function sumarizes of the cost of the shortest path(s) using the A* algorithm.

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

• It does not return a path.

• Returns the sum of the costs of the shortest path of each pair combination of nodes requested.

• Let be the case the values returned are stored in a table, so the unique index would be the pair: (start_vid, end_vid)

• For undirected graphs, the results are symmetric.

• The agg_cost of (u, v) is the same as for (v, u).

• The returned values are ordered in ascending order:

• start_vid ascending

• end_vid ascending

## Signatures¶

Summary

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

### 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

From vertex $$2$$ to vertex $$11$$ on a directed graph with heuristic $$2$$

SELECT * FROM pgr_aStarCost(
'SELECT id, source, target, cost, reverse_cost, x1, y1, x2, y2
FROM edge_table',
2, 11,
directed => true, heuristic => 2
);
start_vid | end_vid | agg_cost
-----------+---------+----------
2 |      11 |        3
(1 row)



### One to Many¶

pgr_aStarCost(Edges SQL, start vid, end vids [, directed] [, heuristic] [, factor] [, epsilon])
RETURNS SET OF (start_vid, end_vid, agg_cost)
OR EMPTY SET
Example

From vertex $$2$$ to vertices $$\{3, 11\}$$ on a directed graph with heuristic $$3$$ and factor $$3.5$$

SELECT * FROM pgr_aStarCost(
'SELECT id, source, target, cost, reverse_cost, x1, y1, x2, y2
FROM edge_table',
2, ARRAY[3, 11],
heuristic => 3, factor := 3.5
);
start_vid | end_vid | agg_cost
-----------+---------+----------
2 |       3 |        5
2 |      11 |        3
(2 rows)



### Many to One¶

pgr_aStarCost(Edges SQL, start vids, end vid [, directed] [, heuristic] [, factor] [, epsilon])
RETURNS SET OF (start_vid, end_vid, agg_cost)
OR EMPTY SET
Example

From vertices $$\{2, 10\}$$ to vertex $$3$$ on an undirected graph with heuristic $$4$$

SELECT * FROM pgr_aStarCost(
'SELECT id, source, target, cost, reverse_cost, x1, y1, x2, y2
FROM edge_table',
ARRAY[2, 10], 3,
false, heuristic => 4
);
start_vid | end_vid | agg_cost
-----------+---------+----------
2 |       3 |        1
10 |       3 |        3
(2 rows)



### Many to Many¶

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

From vertices $$\{2, 10\}$$ to vertices $$\{3, 11\}$$ on a directed graph with factor $$0.5$$

SELECT * FROM pgr_aStarCost(
'SELECT id, source, target, cost, reverse_cost, x1, y1, x2, y2
FROM edge_table',
ARRAY[2, 10], ARRAY[3, 11],
factor => 0.5
);
start_vid | end_vid | agg_cost
-----------+---------+----------
2 |       3 |        5
2 |      11 |        3
10 |       3 |        5
10 |      11 |        1
(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 with factor $$0.5$$.

The combinations table:

SELECT * FROM combinations_table;
source | target
--------+--------
1 |      2
1 |      3
2 |      1
2 |      4
2 |     17
(5 rows)



The query:

SELECT * FROM pgr_aStarCost(
'SELECT id, source, target, cost, reverse_cost, x1, y1, x2, y2
FROM edge_table',
'SELECT * FROM combinations_table',
factor => 0.5
);
start_vid | end_vid | agg_cost
-----------+---------+----------
1 |       2 |        1
1 |       3 |        6
2 |       1 |        1
2 |       4 |        4
(4 rows)



## Parameters¶

Column

Type

Description

Edges SQL

TEXT

Edges SQL as described below

Combinations SQL

TEXT

Combinations SQL as described below

start vid

BIGINT

Identifier of the starting vertex of the path.

start vids

ARRAY[BIGINT]

Array of identifiers of starting vertices.

end vid

BIGINT

Identifier of the ending vertex of the path.

end vids

ARRAY[BIGINT]

Array of identifiers of ending vertices.

### Optional parameters¶

Column

Type

default

Description

directed

BOOLEAN

true

• When true the graph is considered Directed

• When false the graph is considered as Undirected.

### aStar optional Parameters¶

Parameter

Type

Default

Description

heuristic

INTEGER

5

Heuristic number. Current valid values 0~5.

• 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 SQL¶

Parameter

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 SQL¶

Parameter

Type

Description

source

ANY-INTEGER

Identifier of the departure vertex.

target

ANY-INTEGER

Identifier of the arrival vertex.

Where:

ANY-INTEGER

SMALLINT, INTEGER, BIGINT

## Return Columns¶

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.

Example 1

Demonstration of repeated values are ignored, and result is sorted.

 SELECT * FROM pgr_aStarCost(
'SELECT id, source, target, cost, reverse_cost, x1, y1, x2, y2
FROM edge_table',
ARRAY[5, 3, 4, 3, 3, 4], ARRAY[3, 5, 3, 4]);
start_vid | end_vid | agg_cost
-----------+---------+----------
3 |       4 |        3
3 |       5 |        2
4 |       3 |        1
4 |       5 |        3
5 |       3 |        4
5 |       4 |        3
(6 rows)


Example 2

Making start_vids the same as end_vids.

SELECT * FROM pgr_aStarCost(
'SELECT id, source, target, cost, reverse_cost, x1, y1, x2, y2
FROM edge_table',
ARRAY[5, 3, 4], ARRAY[5, 3, 4]);
start_vid | end_vid | agg_cost
-----------+---------+----------
3 |       4 |        3
3 |       5 |        2
4 |       3 |        1
4 |       5 |        3
5 |       3 |        4
5 |       4 |        3
(6 rows)


Example 3

Manually assigned vertex combinations.

SELECT * FROM pgr_aStarCost(
'SELECT id, source, target, cost, reverse_cost, x1, y1, x2, y2
FROM edge_table',
'SELECT * FROM (VALUES (2, 3), (2, 5), (11, 3)) AS combinations (source, target)');
start_vid | end_vid | agg_cost
-----------+---------+----------
2 |       3 |        5
2 |       5 |        1
11 |       3 |        4
(3 rows)