# pgRouting Manual (3.3)

## pgr_bdDijkstraCost

- Supported versions: Latest (3.3) 3.2 3.1 3.0

- Unsupported versions: 2.6 2.5

# pgr_bdDijkstraCost

`pgr_bdDijkstraCost` — Returns the shortest path(s)’s cost using Bidirectional Dijkstra algorithm.

Boost Graph Inside

Availability:

- Version 3.2.0

  - New proposed function:

    - pgr_bdDijkstraCost(Combinations)

- Version 3.0.0

  - Official function

- Version 2.5.0

  - New proposed function

## 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_bdDijkstraCost(Edges SQL, from_vid,  to_vid  [, directed])
    pgr_bdDijkstraCost(Edges SQL, from_vid,  to_vids [, directed])
    pgr_bdDijkstraCost(Edges SQL, from_vids, to_vid  [, directed])
    pgr_bdDijkstraCost(Edges SQL, from_vids, to_vids [, directed])
    pgr_bdDijkstraCost(Edges SQL, Combinations SQL [, directed])

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

Using default

    pgr_bdDijkstraCost(Edges SQL, from_vid,  to_vid)
    RETURNS SET OF (seq, path_seq, node, edge, cost, agg_cost)
    OR EMPTY SET

Example

  From vertex \(2\) to vertex \(3\) on a directed graph

    SELECT * FROM pgr_bdDijkstraCost(
        'SELECT id, source, target, cost, reverse_cost FROM edge_table',
        2, 3
    );
     start_vid | end_vid | agg_cost
    -----------+---------+----------
             2 |       3 |        5
    (1 row)

### One to One

    pgr_bdDijkstraCost(Edges SQL, from_vid,  to_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_bdDijkstraCost(
        'SELECT id, source, target, cost, reverse_cost FROM edge_table',
        2, 3,
        false
    );
     start_vid | end_vid | agg_cost
    -----------+---------+----------
             2 |       3 |        1
    (1 row)

### One to Many

    pgr_bdDijkstraCost(Edges SQL, from_vid,  to_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_bdDijkstraCost(
        'SELECT id, source, target, cost, reverse_cost FROM edge_table',
        2, ARRAY[3, 11]);
     start_vid | end_vid | agg_cost
    -----------+---------+----------
             2 |       3 |        5
             2 |      11 |        3
    (2 rows)

### Many to One

    pgr_bdDijkstraCost(Edges SQL, from_vids, to_vids [, 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_bdDijkstraCost(
        'SELECT id, source, target, cost, reverse_cost FROM edge_table',
        ARRAY[2, 7], 3);
     start_vid | end_vid | agg_cost
    -----------+---------+----------
             2 |       3 |        5
             7 |       3 |        6
    (2 rows)

### Many to Many

    pgr_bdDijkstraCost(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_bdDijkstraCost(
        'SELECT id, source, target, cost, reverse_cost FROM edge_table',
        ARRAY[2, 7], ARRAY[3, 11]);
     start_vid | end_vid | agg_cost
    -----------+---------+----------
             2 |       3 |        5
             2 |      11 |        3
             7 |       3 |        6
             7 |      11 |        4
    (4 rows)

### Combinations

    pgr_bdDijkstra(Edges SQL, Combinations SQL [, directed])
    RETURNS SET OF (seq, path_seq, start_vid, end_vid, node, edge, cost, agg_cost)
    OR EMPTY SET

Example

  Using a combinations table on a directed graph.

    SELECT * FROM pgr_bdDijkstraCost(
        'SELECT id, source, target, cost, reverse_cost FROM edge_table',
        'SELECT * FROM ( VALUES (2, 3), (7, 11) ) AS t(source, target)');
     start_vid | end_vid | agg_cost
    -----------+---------+----------
             2 |       3 |        5
             7 |      11 |        4
    (2 rows)

## Parameters

Parameter | Type | Default | Description
--- | --- | --- | ---
Edges SQL | `TEXT` |  | Edges query as described below
Combinations SQL | `TEXT` |  | Combinations 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 queries

### 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

### Combinations query

Column | Type | Default | Description
--- | --- | --- | ---
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.

Where:

ANY-INTEGER

  SMALLINT, INTEGER, BIGINT

## Result Columns

Returns SET OF `(start_vid, end_vid, agg_cost)`

Column | Type | Description
--- | --- | ---
start_vid | `BIGINT` | Identifier of the starting vertex.
end_vid | `BIGINT` | Identifier of the ending vertex.
agg_cost | `FLOAT` | Aggregate cost from `start_vid` to `end_vid`.

## See Also

- The queries use the Sample Data network.

- pgr_bdDijkstra

- 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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