# pgRouting Manual (3.6)

## pgr_bdAstarCost

`pgr_bdAstarCost` - Total cost of the shortest path(s) using the bidirectional A* algorithm.

Boost Graph Inside

Availability

- Version 3.2.0

  - New proposed signature:

    - `pgr_bdAstarCost` (Combinations)

- Version 3.0.0

  - Official function

- Version 2.4.0

  - New proposed function

## Description

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

The main characteristics are:

- Process works for directed and undirected graphs.

- 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 \(0\)

- 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_bdAstarCost(Edges SQL, start vid, end vid, [options])
pgr_bdAstarCost(Edges SQL, start vid, end vids, [options])
pgr_bdAstarCost(Edges SQL, start vids, end vid, [options])
pgr_bdAstarCost(Edges SQL, start vids, end vids, [options])
pgr_bdAstarCost(Edges SQL, Combinations SQL, [options])
options: `[directed, heuristic, factor, epsilon]`
Returns set of `(start_vid, end_vid, agg_cost)`
OR EMPTY SET

### One to One

pgr_bdAstarCost(Edges SQL, start vid, end vid, [options])
options: `[directed, heuristic, factor, epsilon]`
Returns set of `(start_vid, end_vid, agg_cost)`
OR EMPTY SET

Example:

  From vertex \(6\) to vertex \(12\) on a directed graph with heuristic \(2\)

    SELECT * FROM pgr_bdAstarCost(
      'SELECT id, source, target, cost, reverse_cost, x1, y1, x2, y2
      FROM edges',
      6, 12,
      directed => true, heuristic => 2
    );
     start_vid | end_vid | agg_cost
    -----------+---------+----------
             6 |      12 |        3
    (1 row)

### One to Many

pgr_bdAstarCost(Edges SQL, start vid, end vids, [options])
options: `[directed, heuristic, factor, epsilon]`
Returns set of `(start_vid, end_vid, agg_cost)`
OR EMPTY SET

Example:

  From vertex \(6\) to vertices \(\{10, 12\}\) on a directed graph with heuristic \(3\) and factor \(3.5\)

    SELECT * FROM pgr_bdAstarCost(
      'SELECT id, source, target, cost, reverse_cost, x1, y1, x2, y2
      FROM edges',
      6, ARRAY[10, 12],
      heuristic => 3, factor := 3.5
    );
     start_vid | end_vid | agg_cost
    -----------+---------+----------
             6 |      10 |        5
             6 |      12 |        3
    (2 rows)

### Many to One

pgr_bdAstarCost(Edges SQL, start vids, end vid, [options])
options: `[directed, heuristic, factor, epsilon]`
Returns set of `(start_vid, end_vid, agg_cost)`
OR EMPTY SET

Example:

  From vertices \(\{6, 8\}\) to vertex \(10\) on an undirected graph with heuristic \(4\)

    SELECT * FROM pgr_bdAstarCost(
      'SELECT id, source, target, cost, reverse_cost, x1, y1, x2, y2
      FROM edges',
      ARRAY[6, 8], 10,
      false, heuristic => 4
    );
     start_vid | end_vid | agg_cost
    -----------+---------+----------
             6 |      10 |        1
             8 |      10 |        3
    (2 rows)

### Many to Many

pgr_bdAstarCost(Edges SQL, start vids, end vids, [options])
options: `[directed, heuristic, factor, epsilon]`
Returns set of `(start_vid, end_vid, agg_cost)`
OR EMPTY SET

Example:

  From vertices \(\{6, 8\}\) to vertices \(\{10, 12\}\) on a directed graph with factor \(0.5\)

    SELECT * FROM pgr_bdAstarCost(
      'SELECT id, source, target, cost, reverse_cost, x1, y1, x2, y2
      FROM edges',
      ARRAY[6, 8], ARRAY[10, 12],
      factor => 0.5
    );
     start_vid | end_vid | agg_cost
    -----------+---------+----------
             6 |      10 |        5
             6 |      12 |        3
             8 |      10 |        5
             8 |      12 |        1
    (4 rows)

### Combinations

pgr_bdAstarCost(Edges SQL, Combinations SQL, [options])
options: `[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;
     source | target
    --------+--------
          5 |      6
          5 |     10
          6 |      5
          6 |     15
          6 |     14
    (5 rows)

The query:

    SELECT * FROM pgr_bdAstarCost(
      'SELECT id, source, target, cost, reverse_cost, x1, y1, x2, y2
      FROM edges',
      'SELECT * FROM combinations',
      factor => 0.5
    );
     start_vid | end_vid | agg_cost
    -----------+---------+----------
             5 |       6 |        1
             5 |      10 |        6
             6 |       5 |        1
             6 |      15 |        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: \(h(v) = abs(max(\Delta x, \Delta y))\)

- 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`

### 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`

## 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`.

## Additional Examples

Example 1:

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

     SELECT * FROM pgr_bdAstarCost(
      'SELECT id, source, target, cost, reverse_cost, x1, y1, x2, y2
      FROM edges',
      ARRAY[7, 10, 15, 10, 10, 15], ARRAY[10, 7, 10, 15]);
     start_vid | end_vid | agg_cost
    -----------+---------+----------
             7 |      10 |        4
             7 |      15 |        3
            10 |       7 |        2
            10 |      15 |        3
            15 |       7 |        3
            15 |      10 |        1
    (6 rows)

Example 2:

  Making start vids the same as end vids.

    SELECT * FROM pgr_bdAstarCost(
      'SELECT id, source, target, cost, reverse_cost, x1, y1, x2, y2
      FROM edges',
      ARRAY[7, 10, 15], ARRAY[7, 10, 15]);
     start_vid | end_vid | agg_cost
    -----------+---------+----------
             7 |      10 |        4
             7 |      15 |        3
            10 |       7 |        2
            10 |      15 |        3
            15 |       7 |        3
            15 |      10 |        1
    (6 rows)

Example 3:

  Manually assigned vertex combinations.

    SELECT * FROM pgr_bdAstarCost(
      'SELECT id, source, target, cost, reverse_cost, x1, y1, x2, y2
      FROM edges',
      'SELECT * FROM (VALUES (6, 10), (6, 7), (12, 10)) AS combinations (source, target)');
     start_vid | end_vid | agg_cost
    -----------+---------+----------
             6 |       7 |        1
             6 |      10 |        5
            12 |      10 |        4
    (3 rows)

## See Also

- Bidirectional A* - Family of functions

- Cost - Category

- Sample Data

Indices and tables

- Index

- Search Page