# pgRouting Manual (2.5)

## pgr_bdAstar

## Name

`pgr_bdAstar` — Returns the shortest path using A* algorithm.

Boost Graph Inside

Availability:

- pgr_bdAstar(one to one) 2.0.0, Signature change on 2.5.0
- pgr_bdAstar(other signatures) 2.5.0

## Signature Summary

    pgr_bdAstar(edges_sql, start_vid, end_vid)
    pgr_bdAstar(edges_sql, start_vid, end_vid, directed [, heuristic, factor, epsilon])
    RETURNS SET OF (seq, path_seq , node, edge, cost, agg_cost)
      OR EMPTY SET

Warning

Experimental functions

- They are not officially of the current release.
- They likely will not be officially be part of the next release:
  - The functions might not make use of ANY-INTEGER and ANY-NUMERICAL
  - Name might change.
  - Signature might change.
  - Functionality might change.
  - pgTap tests might be missing.
  - Might need c/c++ coding.
  - May lack documentation.
  - Documentation if any might need to be rewritten.
  - Documentation examples might need to be automatically generated.
  - Might need a lot of feedback from the comunity.
  - Might depend on a proposed function of pgRouting
  - Might depend on a deprecated function of pgRouting

    pgr_bdAstar(edges_sql, start_vid, end_vids [, directed, heuristic, factor, epsilon])
    pgr_bdAstar(edges_sql, start_vids, end_vid [, directed, heuristic, factor, epsilon])
    pgr_bdAstar(edges_sql, start_vids, end_vids [, directed, heuristic, factor, epsilon])

    RETURNS SET OF (seq, path_seq [, start_vid] [, end_vid], node, edge, cost, agg_cost)
    OR EMPTY SET

Using these signatures, will load once the graph and perform several one to one pgr_bdAstar

- The result is the union of the results of the one to one pgr_bdAStar.
- The extra `start_vid` and/or `end_vid` in the result is used to distinguish to which path it belongs.

Avaliability

- pgr_bdAstar(one to one) 2.0, signature change on 2.5
- pgr_bdAstar(other signatures) 2.5

## Signatures

### Minimal Signature

    pgr_bdAstar(edges_sql, start_vid, end_vid)
    RETURNS SET OF (seq, path_seq, node, edge, cost, agg_cost)

This usage finds the shortest path from the `start_vid` to the `end_vid`
  - on a directed graph
  - with heuristic’s value 5
  - with factor’s value 1
  - with epsilon’s value 1

Example: | Using the defaults

    SELECT * FROM pgr_bdAstar(
        'SELECT id, source, target, cost, reverse_cost, x1,y1,x2,y2
        FROM edge_table',
        2, 3
    );
     seq | path_seq | node | edge | cost | agg_cost
    -----+----------+------+------+------+----------
       1 |        1 |    2 |    4 |    1 |        0
       2 |        2 |    5 |    8 |    1 |        1
       3 |        3 |    6 |    9 |    1 |        2
       4 |        4 |    9 |   16 |    1 |        3
       5 |        5 |    4 |    3 |    1 |        4
       6 |        6 |    3 |   -1 |    0 |        5
    (6 rows)

### pgr_bdAstar One to One

    pgr_bdAstar(edges_sql, start_vid, end_vid, directed [, heuristic, factor, epsilon])
    RETURNS SET OF (seq, path_seq, node, edge, cost, agg_cost)

This usage finds the shortest path from the `start_vid` to the `end_vid` allowing the user to choose
  - heuristic,
  - and/or factor
  - and/or epsilon.

Note

In the One to One signature, because of the deprecated signature existence, it is compulsory to indicate if the graph is directed or undirected.

Example: | Directed using Heuristic 2

    SELECT * FROM pgr_bdAstar(
        'SELECT id, source, target, cost, reverse_cost, x1,y1,x2,y2
        FROM edge_table',
        2, 3,
        true, heuristic := 2
    );
     seq | path_seq | node | edge | cost | agg_cost
    -----+----------+------+------+------+----------
       1 |        1 |    2 |    4 |    1 |        0
       2 |        2 |    5 |    8 |    1 |        1
       3 |        3 |    6 |    9 |    1 |        2
       4 |        4 |    9 |   16 |    1 |        3
       5 |        5 |    4 |    3 |    1 |        4
       6 |        6 |    3 |   -1 |    0 |        5
    (6 rows)

### pgr_bdAstar One to many

    pgr_bdAstar(edges_sql, start_vid, end_vids [, directed, heuristic, factor, epsilon])
    RETURNS SET OF (seq, path_seq, end_vid, node, edge, cost, agg_cost) or EMPTY SET

This usage finds the shortest path from the `start_vid` to each `end_vid` in `end_vids` allowing the user to choose
  - if the graph is directed or undirected
  - and/or heuristic,
  - and/or factor
  - and/or epsilon.

Example: | Directed using Heuristic 3 and a factor of 3.5

    SELECT * FROM pgr_bdAstar(
        'SELECT id, source, target, cost, reverse_cost, x1,y1,x2,y2
        FROM edge_table',
        2, ARRAY[3, 11],
        heuristic := 3, factor := 3.5
    );
     seq | path_seq | end_vid | node | edge | cost | agg_cost
    -----+----------+---------+------+------+------+----------
       1 |        1 |       3 |    2 |    4 |    1 |        0
       2 |        2 |       3 |    5 |    8 |    1 |        1
       3 |        3 |       3 |    6 |    9 |    1 |        2
       4 |        4 |       3 |    9 |   16 |    1 |        3
       5 |        5 |       3 |    4 |    3 |    1 |        4
       6 |        6 |       3 |    3 |   -1 |    0 |        5
       7 |        1 |      11 |    2 |    4 |    1 |        0
       8 |        2 |      11 |    5 |    8 |    1 |        1
       9 |        3 |      11 |    6 |   11 |    1 |        2
      10 |        4 |      11 |   11 |   -1 |    0 |        3
    (10 rows)

### pgr_bdAstar Many to One

    pgr_bdAstar(edges_sql, start_vids, end_vid [, directed, heuristic, factor, epsilon])
    RETURNS SET OF (seq, path_seq, start_vid, node, edge, cost, agg_cost) or EMPTY SET

This usage finds the shortest path from each `start_vid` in `start_vids` to the `end_vid` allowing the user to choose
  - if the graph is directed or undirected
  - and/or heuristic,
  - and/or factor
  - and/or epsilon.

Example: | Undirected graph with Heuristic 4

    SELECT * FROM pgr_bdAstar(
        'SELECT id, source, target, cost, reverse_cost, x1,y1,x2,y2
        FROM edge_table',
        ARRAY[2, 7], 3,
        false, heuristic := 4
    );
     seq | path_seq | start_vid | node | edge | cost | agg_cost
    -----+----------+-----------+------+------+------+----------
       1 |        1 |         2 |    2 |    2 |    1 |        0
       2 |        2 |         2 |    3 |   -1 |    0 |        1
       3 |        1 |         7 |    7 |    6 |    1 |        0
       4 |        2 |         7 |    8 |    7 |    1 |        1
       5 |        3 |         7 |    5 |    4 |    1 |        2
       6 |        4 |         7 |    2 |    2 |    1 |        3
       7 |        5 |         7 |    3 |   -1 |    0 |        4
    (7 rows)

### pgr_bdAstar Many to Many

    pgr_bdAstar(edges_sql, start_vids, end_vids [, directed, heuristic, factor, epsilon])
    RETURNS SET OF (seq, path_seq, start_vid, end_vid, node, edge, cost, agg_cost) or EMPTY SET

This usage finds the shortest path from each `start_vid` in `start_vids` to each `end_vid` in `end_vids` allowing the user to choose
  - if the graph is directed or undirected
  - and/or heuristic,
  - and/or factor
  - and/or epsilon.

Example: | Directed graph with a factor of 0.5

    SELECT * FROM pgr_bdAstar(
        'SELECT id, source, target, cost, reverse_cost, x1,y1,x2,y2
        FROM edge_table',
        ARRAY[2, 7], ARRAY[3, 11],
        factor := 0.5
    );
     seq | path_seq | start_vid | end_vid | node | edge | cost | agg_cost
    -----+----------+-----------+---------+------+------+------+----------
       1 |        1 |         2 |       3 |    2 |    4 |    1 |        0
       2 |        2 |         2 |       3 |    5 |    8 |    1 |        1
       3 |        3 |         2 |       3 |    6 |    9 |    1 |        2
       4 |        4 |         2 |       3 |    9 |   16 |    1 |        3
       5 |        5 |         2 |       3 |    4 |    3 |    1 |        4
       6 |        6 |         2 |       3 |    3 |   -1 |    0 |        5
       7 |        1 |         2 |      11 |    2 |    4 |    1 |        0
       8 |        2 |         2 |      11 |    5 |    8 |    1 |        1
       9 |        3 |         2 |      11 |    6 |   11 |    1 |        2
      10 |        4 |         2 |      11 |   11 |   -1 |    0 |        3
      11 |        1 |         7 |       3 |    7 |    6 |    1 |        0
      12 |        2 |         7 |       3 |    8 |    7 |    1 |        1
      13 |        3 |         7 |       3 |    5 |    8 |    1 |        2
      14 |        4 |         7 |       3 |    6 |    9 |    1 |        3
      15 |        5 |         7 |       3 |    9 |   16 |    1 |        4
      16 |        6 |         7 |       3 |    4 |    3 |    1 |        5
      17 |        7 |         7 |       3 |    3 |   -1 |    0 |        6
      18 |        1 |         7 |      11 |    7 |    6 |    1 |        0
      19 |        2 |         7 |      11 |    8 |    7 |    1 |        1
      20 |        3 |         7 |      11 |    5 |   10 |    1 |        2
      21 |        4 |         7 |      11 |   10 |   12 |    1 |        3
      22 |        5 |         7 |      11 |   11 |   -1 |    0 |        4
    (22 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.
start_vids | `ARRAY[ANY-INTEGER]` | Starting vertices identifierers.
end_vid | `ANY-INTEGER` | Ending vertex identifier.
end_vids | `ARRAY[ANY-INTEGER]` | Ending vertices identifiers.

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 path

Returns set of `(seq, path_seq [, start_vid] [, end_vid], node, edge, cost, agg_cost)`

Column | Type | Description
--- | --- | ---
seq | `INT` | Sequential value starting from 1.
path_id | `INT` | Path identifier. Has value 1 for the first of a path. Used when there are multiple paths for the same `start_vid` to `end_vid` combination.
path_seq | `INT` | Relative position in the path. Has value 1 for the beginning of a path.
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.
node | `BIGINT` | Identifier of the node in the path from `start_vid` to `end_vid`.
edge | `BIGINT` | Identifier of the edge used to go from `node` to the next node in the path sequence. `-1` for the last node of the path.
cost | `FLOAT` | Cost to traverse from `node` using `edge` to the next node in the path sequence.
agg_cost | `FLOAT` | Aggregate cost from `start_v` to `node`.

## See Also

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

Indices and tables

- Index
- Search Page