# pgRouting Manual (3.0-rc1)

## pgr_aStarCost

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

Boost Graph Inside

Availability

- Version 3.0.0
  - Official function
- Version 2.4.0
  - New proposed function

Support

- Supported versions: current(3.0) 2.6
- Unsupported versions: 2.5 2.4

## Description

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

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

## Signatures

Summary

    pgr_aStarCost(edges_sql, from_vid,  to_vid   [, directed] [, heuristic] [, factor] [, epsilon])
    pgr_aStarCost(edges_sql, from_vid,  to_vids  [, directed] [, heuristic] [, factor] [, epsilon])
    pgr_aStarCost(edges_sql, from_vids, to_vid   [, directed] [, heuristic] [, factor] [, epsilon])
    pgr_aStarCost(edges_sql, from_vids, to_vids  [, 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_aStarCost(edges_sql, start_vid, end_vid)
    RETURNS SET OF (start_vid, end_vid, agg_cost)
    OR EMPTY SET

Example: | From vertex \(2\) to vertex \(12\) on a directed graph

    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, 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 \(12\) on an undirected graph using heuristic \(2\)

    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, 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 \(\{3, 12\}\) on a directed graph using heuristic \(2\)

    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, 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 \(12\) on a directed graph using heuristic \(0\)

    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, 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 \(\{3, 12\}\) on a directed graph using heuristic \(2\)

    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)

## Parameters

Parameter | Type | Description
--- | --- | ---
edges_sql | `TEXT` | edges_sql inner query.

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 query

### edges_sql

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

## Result Columns

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
- Cost - Category
- Cost Matrix - Category
- Examples use Sample Data network.

Indices and tables

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