# pgRouting Manual (3.3)

## pgr_bdAstarCost

- Supported versions: Latest (3.3) 3.2 3.1 3.0

- Unsupported versions: 2.6 2.5

# pgr_bdAstarCost

`pgr_bdAstarCost` — Returns the aggregate cost shortest path using pgr_aStar algorithm.

Boost Graph Inside

Availability

- Version 3.2.0

  - New proposed function:

    - pgr_bdAstarCost(Combinations)

- Version 3.0.0

  - Official function

- Version 2.5.0

  - New Proposed function

## Description

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

- The results are equivalent to the union of the results of the pgr_bdAstarCost( One to One ) on the:

  - pgr_bdAstarCost( One to Many )

  - pgr_bdAstarCost( Many to One )

  - pgr_bdAstarCost( Many to Many )

## Signatures

Summary

    pgr_bdAstarCost(Edges SQL, from_vid,  to_vid  [, directed] [, heuristic] [, factor] [, epsilon])
    pgr_bdAstarCost(Edges SQL, from_vid,  to_vids [, directed] [, heuristic] [, factor] [, epsilon])
    pgr_bdAstarCost(Edges SQL, from_vids, to_vid  [, directed] [, heuristic] [, factor] [, epsilon])
    pgr_bdAstarCost(Edges SQL, from_vids, to_vids [, directed] [, heuristic] [, factor] [, epsilon])
    pgr_bdAstarCost(Edges SQL, Combinations SQL [, directed] [, heuristic] [, factor] [, epsilon])

    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_bdAstarCost(Edges SQL, from_vid,  to_vid)
    RETURNS SET OF (start_vid, end_vid, agg_cost)
    OR EMPTY SET

Example

  From vertex \(2\) to vertex \(3\) on a directed graph

    SELECT * FROM pgr_bdAstarCost(
        'SELECT id, source, target, cost, reverse_cost, x1,y1,x2,y2
        FROM edge_table',
        2, 3
    );
     start_vid | end_vid | agg_cost
    -----------+---------+----------
             2 |       3 |        5
    (1 row)

### One to One

    pgr_bdAstarCost(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 \(3\) on an directed graph using heuristic \(2\)

    SELECT * FROM pgr_bdAstarCost(
        'SELECT id, source, target, cost, reverse_cost, x1,y1,x2,y2
        FROM edge_table',
        2, 3,
        true, heuristic := 2
    );
     start_vid | end_vid | agg_cost
    -----------+---------+----------
             2 |       3 |        5
    (1 row)

### One to many

    pgr_bdAstarCost(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 \(\{3, 11\}\) on a directed graph using heuristic 3 and factor \(3.5\)

    SELECT * FROM pgr_bdAstarCost(
        '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_bdAstarCost(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 \(3\) on a undirected graph using heuristic \(4\)

    SELECT * FROM pgr_bdAstarCost(
        'SELECT id, source, target, cost, reverse_cost, x1,y1,x2,y2
        FROM edge_table',
        ARRAY[2, 7], 3,
        false, heuristic := 4
    );
     start_vid | end_vid | agg_cost
    -----------+---------+----------
             2 |       3 |        1
             7 |       3 |        4
    (2 rows)

### Many to Many

    pgr_bdAstarCost(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 \(\{3, 11\}\) on a directed using heuristic \(5\) and factor \(0.5\)

    SELECT * FROM pgr_bdAstarCost(
        'SELECT id, source, target, cost, reverse_cost, x1,y1,x2,y2
        FROM edge_table',
        ARRAY[2, 7], ARRAY[3, 11],
        factor := 0.5
    );
     start_vid | end_vid | agg_cost
    -----------+---------+----------
             2 |       3 |        5
             2 |      11 |        3
             7 |       3 |        6
             7 |      11 |        4
    (4 rows)

### Combinations

    pgr_bdAstarCost(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 factor \(0.5\).

    SELECT * FROM pgr_bdAstarCost(
        'SELECT id, source, target, cost, reverse_cost, x1,y1,x2,y2
        FROM edge_table',
        'SELECT * FROM ( VALUES (2, 3), (7, 11) ) AS t(source, target)',
        factor := 0.5
    );
     start_vid | end_vid | agg_cost
    -----------+---------+----------
             2 |       3 |        5
             7 |      11 |        4
    (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:

- One to One

- One to Many

from_vids

`ARRAY[ANY-INTEGER]`

Array of starting vertices identifiers. Parameter in:

- Many to One

- Many to Many

to_vid

`ANY-INTEGER`

Ending vertex identifier. Parameter in:

- One to One

- Many to One

to_vids

`ARRAY[ANY-INTEGER]`

Array of ending vertices identifiers. Parameter in:

- One to Many

- Many to Many

### 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`.

## See Also

- Bidirectional A* - Family of functions

- Cost - Category

- Cost Matrix - Category

- Examples use Sample Data network.

Indices and tables

- Index

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