# pgRouting Manual (2.5)

## pgr_bdDijkstra

`pgr_bdDijkstra` — Returns the shortest path(s) using Bidirectional Dijkstra algorithm.

Boost Graph Inside

Availability:

- pgr_bdDijkstra(one to one) 2.0.0, Signature changed 2.4.0
- pgr_bdDijkstra(other signatures) 2.5.0

## Signature Summary

    pgr_bdDijkstra(edges_sql, start_vid,  end_vid)
    pgr_bdDijkstra(edges_sql, start_vid, end_vid, directed)
    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_bdDijkstra(edges_sql, start_vid, end_vids, directed)
    pgr_bdDijkstra(edges_sql, start_vids, end_vid, directed)
    pgr_bdDijkstra(edges_sql, start_vids, end_vids, directed)

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

## Signatures

### Minimal signature

    pgr_bdDijkstra(edges_sql, start_vid, end_vid)
    RETURNS SET OF (seq, path_seq, node, edge, cost, agg_cost) or EMPTY SET

The minimal signature is for a directed graph from one `start_vid` to one `end_vid`:

Example: |

    SELECT * FROM pgr_bdDijkstra(
        'SELECT id, source, target, cost, reverse_cost 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_bdDijkstra One to One

    pgr_bdDijkstra(edges_sql, start_vid, end_vid, directed)
    RETURNS SET OF (seq, path_seq, node, edge, cost, agg_cost) or EMPTY SET

This signature finds the shortest path from one `start_vid` 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`.

Example: |

    SELECT * FROM pgr_bdDijkstra(
        'SELECT id, source, target, cost, reverse_cost FROM edge_table',
        2, 3,
        false
    );
     seq | path_seq | node | edge | cost | agg_cost
    -----+----------+------+------+------+----------
       1 |        1 |    2 |    2 |    1 |        0
       2 |        2 |    3 |   -1 |    0 |        1
    (2 rows)

### pgr_bdDijkstra One to many

    pgr_bdDijkstra(edges_sql, start_vid, end_vids, directed)
    RETURNS SET OF (seq, path_seq, end_vid, node, edge, cost, agg_cost) or EMPTY SET

This signature finds the shortest 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_dijkstra 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_dijkstra.
- The extra `end_vid` in the result is used to distinguish to which path it belongs.

Example: |

    SELECT * FROM pgr_bdDijkstra(
        'SELECT id, source, target, cost, reverse_cost FROM edge_table',
        2, ARRAY[3, 11]);
     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_bdDijkstra Many to One

    pgr_bdDijkstra(edges_sql, start_vids, end_vid, directed)
    RETURNS SET OF (seq, path_seq, start_vid, node, edge, cost, 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_dijkstra where the ending vertex is fixed.

- 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.

Example: |

    SELECT * FROM pgr_bdDijkstra(
        'SELECT id, source, target, cost, reverse_cost FROM edge_table',
        ARRAY[2, 7], 3);
     seq | path_seq | start_vid | node | edge | cost | agg_cost
    -----+----------+-----------+------+------+------+----------
       1 |        1 |         2 |    2 |    4 |    1 |        0
       2 |        2 |         2 |    5 |    8 |    1 |        1
       3 |        3 |         2 |    6 |    9 |    1 |        2
       4 |        4 |         2 |    9 |   16 |    1 |        3
       5 |        5 |         2 |    4 |    3 |    1 |        4
       6 |        6 |         2 |    3 |   -1 |    0 |        5
       7 |        1 |         7 |    7 |    6 |    1 |        0
       8 |        2 |         7 |    8 |    7 |    1 |        1
       9 |        3 |         7 |    5 |    8 |    1 |        2
      10 |        4 |         7 |    6 |    9 |    1 |        3
      11 |        5 |         7 |    9 |   16 |    1 |        4
      12 |        6 |         7 |    4 |    3 |    1 |        5
      13 |        7 |         7 |    3 |   -1 |    0 |        6
    (13 rows)

### pgr_bdDijkstra Many to Many

    pgr_bdDijkstra(edges_sql, start_vids, end_vids, directed)
    RETURNS SET OF (seq, path_seq, start_vid, end_vid, node, edge, cost, 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_bdDijkstra(
        'SELECT id, source, target, cost, reverse_cost FROM edge_table',
        ARRAY[2, 7], ARRAY[3, 11]);
     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 dijkstra 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.

Where:

ANY-INTEGER: | SMALLINT, INTEGER, BIGINT
ANY-NUMERICAL: | SMALLINT, INTEGER, BIGINT, REAL, FLOAT

### Description of the parameters of the signatures

Column | Type | Default | Description
--- | --- | --- | ---
sql | `TEXT` |  | SQL query as described above.
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.

directed

`BOOLEAN`

`true`

- When `true` Graph is considered Directed
- When `false` the graph is considered as Undirected.

### 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

- The queries use the Sample Data network.
- Bidirectional Dijkstra - Family of functions
- http://www.cs.princeton.edu/courses/archive/spr06/cos423/Handouts/EPP%20shortest%20path%20algorithms.pdf
- https://en.wikipedia.org/wiki/Bidirectional_search

Indices and tables

- Index
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