# pgr_bdAstarCostMatrix¶

pgr_bdAstarCostMatrix - Calculates the a cost matrix using pgr_aStar.

Availability

• Version 3.0.0

• Official function

• Version 2.5.0

• New proposed function

## Description¶

The main characteristics are:

• Using internaly the pgr_bdAstar algorithm

• Returns a cost matrix.

• No ordering is performed

• let v and u are nodes on the graph:

• when there is no path from v to u:

• no corresponding row is returned

• cost from v to u is $$\inf$$

• when $$v = u$$ then

• no corresponding row is returned

• cost from v to u is $$0$$

• When the graph is undirected the cost matrix is symmetric

## Signatures¶

Summary

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

Symmetric cost matrix for vertices $$\{5, 6, 10, 15\}$$ on an undirected graph using heuristic $$2$$

SELECT * FROM pgr_bdAstarCostMatrix(
'SELECT id, source, target, cost, reverse_cost, x1, y1, x2, y2 FROM edges',
(SELECT array_agg(id) FROM vertices WHERE id IN (5, 6, 10, 15)),
directed => false, heuristic => 2
);
start_vid | end_vid | agg_cost
-----------+---------+----------
5 |       6 |        1
5 |      10 |        2
5 |      15 |        3
6 |       5 |        1
6 |      10 |        1
6 |      15 |        2
10 |       5 |        2
10 |       6 |        1
10 |      15 |        1
15 |       5 |        3
15 |       6 |        2
15 |      10 |        1
(12 rows)



## Parameters¶

Column

Type

Description

Edges SQL

TEXT

Edges SQL as described below

start vids

ARRAY[BIGINT]

Array of identifiers of starting 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: $$h(v) = abs(max(\Delta x, \Delta y))$$

• 2: $$h(v) = abs(min(\Delta x, \Delta y))$$

• 3: $$h(v) = \Delta x * \Delta x + \Delta y * \Delta y$$

• 4: $$h(v) = sqrt(\Delta x * \Delta x + \Delta y * \Delta y)$$

• 5: $$h(v) = abs(\Delta x) + abs(\Delta y)$$

factor

FLOAT

1

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

epsilon

FLOAT

1

For less restricted results. $$epsilon >= 1$$.

See heuristics available and factor handling.

## 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

## Result 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:

Use with pgr_TSP

SELECT * FROM pgr_TSP(
$$SELECT * FROM pgr_bdAstarCostMatrix( 'SELECT id, source, target, cost, reverse_cost, x1, y1, x2, y2 FROM edges', (SELECT array_agg(id) FROM vertices WHERE id IN (5, 6, 10, 15)), directed=> false, heuristic => 2 )$$
);
NOTICE:  pgr_TSP no longer solving with simulated annaeling
HINT:  Ignoring annaeling parameters
seq | node | cost | agg_cost
-----+------+------+----------
1 |    5 |    0 |        0
2 |    6 |    1 |        1
3 |   10 |    1 |        2
4 |   15 |    1 |        3
5 |    5 |    3 |        6
(5 rows)