# pgRouting Manual (2.5)

## pgr_aStarCost – proposed

## Name

`pgr_aStarCost` — Returns the aggregate cost shortest path using aStar - Family of functions algorithm.

Boost Graph Inside

Availability: 2.4.0

## Signature Summary

Warning

Proposed functions for next mayor release.

- They are not officially in the current release.
- They will likely officially be part of the next mayor release:
  - The functions make use of ANY-INTEGER and ANY-NUMERICAL
  - Name might not change. (But still can)
  - Signature might not change. (But still can)
  - Functionality might not change. (But still can)
  - pgTap tests have being done. But might need more.
  - Documentation might need refinement.

    pgr_aStarCost(edges_sql, start_vid, end_vid) -- Proposed
    pgr_aStarCost(edges_sql, start_vid, end_vid, directed, heuristic, factor, epsilon) -- Proposed
    pgr_aStarCost(edges_sql, start_vid, end_vids, directed, heuristic, factor, epsilon) -- Proposed
    pgr_aStarCost(edges_sql, starts_vid, end_vid, directed, heuristic, factor, epsilon) -- Proposed
    pgr_aStarCost(edges_sql, starts_vid, end_vids, directed, heuristic, factor, epsilon) -- Proposed

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

## Signatures

### Minimal Signature

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

Example: | Using the defaults

    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, start_vid, end_vid, directed, heuristic, factor, epsilon)
    RETURNS SET OF (start_vid, end_vid, agg_cost) OR EMPTY SET

Example: | Setting a Heuristic

    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, start_vid, end_vids, directed, heuristic, factor, epsilon) -- Proposed
    RETURNS SET OF (start_vid, end_vid, agg_cost) OR EMPTY SET

This signature finds a path from one `start_vid` to each `end_vid` in `end_vids`:
  - on a directed graph when `directed` flag is missing or is set to `true`.
  - on an undirected graph when `directed` flag is set to `false`.

Using this signature, will load once the graph and perform a one to one pgr_astar where the starting vertex is fixed, and stop when all `end_vids` are reached.

- The result is equivalent to the union of the results of the one to one pgr_astar.
- The extra `end_vid` column in the result is used to distinguish to which path it belongs.

Example: |

    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, starts_vid, end_vid, directed, heuristic, factor, epsilon) -- Proposed
    RETURNS SET OF (start_vid, end_vid, agg_cost) OR EMPTY SET

This signature finds the shortest path from each `start_vid` in `start_vids` to one `end_vid`:
  - on a directed graph when `directed` flag is missing or is set to `true`.
  - on an undirected graph when `directed` flag is set to `false`.

Using this signature, will load once the graph and perform several one to one pgr_aStar where the ending vertex is fixed.

- The result is the union of the results of the one to one pgr_aStar.
- The extra `start_vid` column in the result is used to distinguish to which path it belongs.

Example: |

    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, starts_vid, end_vids, directed, heuristic, factor, epsilon) -- Proposed
    RETURNS SET OF (start_vid, end_vid, agg_cost) OR EMPTY SET

This signature finds the shortest path from each `start_vid` in `start_vids` to each `end_vid` in `end_vids`:
  - on a directed graph when `directed` flag is missing or is set to `true`.
  - on an undirected graph when `directed` flag is set to `false`.

Using this signature, will load once the graph and perform several one to Many pgr_dijkstra for all `start_vids`.

- The result is the union of the results of the one to one pgr_dijkstra.
- The extra `start_vid` in the result is used to distinguish to which path it belongs.

The extra `start_vid` and `end_vid` in the result is used to distinguish to which path it belongs.

Example: |

    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)

## Description of the Signatures

### Description of the edges_sql query for astar like functions

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

### Description of the parameters of the signatures

Parameter | Type | Description
--- | --- | ---
edges_sql | `TEXT` | Edges SQL query as described above.
start_vid | `ANY-INTEGER` | Starting vertex identifier.
end_vid | `ANY-INTEGER` | Ending vertex identifier.

directed

`BOOLEAN`

- Optional.
  - When `false` the graph is considered as Undirected.
  - Default is `true` which considers the graph as Directed.

heuristic

`INTEGER`

(optional). 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` | (optional). For units manipulation. \(factor > 0\). Default `1`. See Factor
epsilon | `FLOAT` | (optional). For less restricted results. \(epsilon >= 1\). Default `1`.

### Description of the return values for a Cost function

Returns set of `(start_vid, end_vid, agg_cost)`

Column | Type | Description
--- | --- | ---
start_vid | `BIGINT` | Identifier of the starting vertex. Used when multiple starting vetrices are in the query.
end_vid | `BIGINT` | Identifier of the ending vertex. Used when multiple ending vertices are in the query.
agg_cost | `FLOAT` | Aggregate cost from `start_vid` to `end_vid`.

## See Also

- aStar - Family of functions.
- Sample Data network.
- http://www.boost.org/libs/graph/doc/astar_search.html
- http://en.wikipedia.org/wiki/A*_search_algorithm

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