# pgRouting Manual (3.1)

## pgr_bdDijkstra

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

Boost Graph Inside

Availability:

- Version 3.0.0

  - Official function

- Version 2.5.0

  - New Proposed functions:

    - pgr_bdDijkstra(One to Many)

    - pgr_bdDijkstra(Many to One)

    - pgr_bdDijkstra(Many to Many)

- Version 2.4.0

  - Signature change on pgr_bdDijsktra(One to One)

    - Old signature no longer supported

- Version 2.0.0

  - Official pgr_bdDijkstra(One to One)

Support

- Supported versions: current(3.1) 3.0 2.6

- Unsupported versions: 2.5 2.4 2.3 2.2 2.1 2.0

## Description

The main characteristics are:

- Process is done only on edges with positive costs.

- Values are returned when there is a path.

- When the starting vertex and ending vertex are the same, there is no path.

  - The agg_cost the non included values (v, v) is 0

- When the starting vertex and ending vertex are the different and there is no path:

  - The agg_cost the non included values (u, v) is \(\infty\)

- Running time (worse case scenario): \(O((V \log V + E))\)

- For large graphs where there is a path bewtween the starting vertex and ending vertex:

  - It is expected to terminate faster than pgr_dijkstra

## Signatures

Summary

    pgr_bdDijkstra(edges_sql, start_vid,  end_vid  [, directed])
    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

Using defaults

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

Example

  From vertex \(2\) to vertex \(3\)

    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)

### 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

Example

  From vertex \(2\) to vertex \(3\) on an undirected graph

    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)

### 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

Example

  From vertex \(2\) to vertices \(\{3, 11\}\) on a directed graph

    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)

### 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

Example

  From vertices \(\{2, 7\}\) to vertex \(3\) on a directed graph

    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)

### 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

Example

  From vertices \(\{2, 7\}\) to vertices \(\{3, 11\}\) on a directed graph

    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)

## Parameters

Parameter | Type | Default | Description
--- | --- | --- | ---
Edges SQL | `TEXT` |  | Edges query 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.

directed

`BOOLEAN`

`true`

- When `true` Graph is considered Directed

- When `false` the graph is considered as Undirected.

## Inner query

### Edges query

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

## Result Columns

Returns set of `(seq, path_id, 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. Returned when multiple starting vetrices are in the query.

- Many to One

- Many to Many

end_vid

`BIGINT`

Identifier of the ending vertex. Returned when multiple ending vertices are in the query.

- One to Many

- Many to Many

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

- https://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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