# pgRouting Manual (3.6)

## pgr_bdDijkstraCost

# `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 signature:

    - `pgr_bdDijkstraCost` (Combinations)

- Version 3.0.0

  - Official function

- Version 2.5.0

  - New proposed function

## Description

The `pgr_bdDijkstraCost` function sumarizes of the cost of the shortest path using the bidirectional Dijkstra Algorithm.

- Process is done only on edges with positive costs.

  - A negative value on a cost column is interpreted as the edge does not exist.

- Values are returned when there is a path.

- When there is no path:

  - When the starting vertex and ending vertex are the same.

    - The aggregate cost of the non included values \((v, v)\) is \(0\)

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

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

- For optimization purposes, any duplicated value in the starting vertices or on the ending vertices are ignored.

- 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

- It does not return a path.

- Returns the sum of the costs of the shortest path of each pair combination of nodes requested.

- Let be the case the values returned are stored in a table, so the unique index would be the pair: `(start_vid, end_vid)`.

- Depending on the function and its parameters, the results can be symmetric.

  - The aggregate cost of \((u, v)\) is the same as for \((v, u)\).

- Any duplicated value in the start or end vertex identifiers are ignored.

- The returned values are ordered:

  - `start_vid` ascending

  - `end_vid` ascending

## Signatures

Summary

pgr_bdDijkstraCost(Edges SQL, start vid, end vid , [`directed`])
pgr_bdDijkstraCost(Edges SQL, start vid, end vids, [`directed`])
pgr_bdDijkstraCost(Edges SQL, start vids, end vid , [`directed`])
pgr_bdDijkstraCost(Edges SQL, start vids, end vids, [`directed`])
pgr_bdDijkstraCost(Edges SQL, Combinations SQL, [ `directed`])
Returns set of `(start_vid, end_vid, agg_cost)`
OR EMPTY SET

### One to One

pgr_bdDijkstraCost(Edges SQL, start vid, end vid , [`directed`])
Returns set of `(start_vid, end_vid, agg_cost)`
OR EMPTY SET

Example:

  From vertex \(6\) to vertex \(10\) on a directed graph

    SELECT * FROM pgr_bdDijkstraCost(
      'SELECT id, source, target, cost, reverse_cost FROM edges',
      6, 10, true);
     start_vid | end_vid | agg_cost
    -----------+---------+----------
             6 |      10 |        5
    (1 row)

### One to Many

pgr_bdDijkstraCost(Edges SQL, start vid, end vids, [`directed`])
Returns set of `(start_vid, end_vid, agg_cost)`
OR EMPTY SET

Example:

  From vertex \(6\) to vertices \(\{10, 17\}\) on a directed graph

    SELECT * FROM pgr_bdDijkstraCost(
      'SELECT id, source, target, cost, reverse_cost FROM edges',
      6, ARRAY[10, 17]);
     start_vid | end_vid | agg_cost
    -----------+---------+----------
             6 |      10 |        5
             6 |      17 |        4
    (2 rows)

### Many to One

pgr_bdDijkstraCost(Edges SQL, start vids, end vid , [`directed`])
Returns set of `(start_vid, end_vid, agg_cost)`
OR EMPTY SET

Example:

  From vertices \(\{6, 1\}\) to vertex \(17\) on a directed graph

    SELECT * FROM pgr_bdDijkstraCost(
      'SELECT id, source, target, cost, reverse_cost FROM edges',
      ARRAY[6, 1], 17);
     start_vid | end_vid | agg_cost
    -----------+---------+----------
             1 |      17 |        5
             6 |      17 |        4
    (2 rows)

### Many to Many

pgr_bdDijkstraCost(Edges SQL, start vids, end vids, [`directed`])
Returns set of `(start_vid, end_vid, agg_cost)`
OR EMPTY SET

Example:

  From vertices \(\{6, 1\}\) to vertices \(\{10, 17\}\) on an undirected graph

    SELECT * FROM pgr_bdDijkstraCost(
      'SELECT id, source, target, cost, reverse_cost FROM edges',
      ARRAY[6, 1], ARRAY[10, 17],
      directed => false);
     start_vid | end_vid | agg_cost
    -----------+---------+----------
             1 |      10 |        4
             1 |      17 |        5
             6 |      10 |        1
             6 |      17 |        4
    (4 rows)

### Combinations

pgr_bdDijkstraCost(Edges SQL, Combinations SQL, [`directed`])
Returns set of `(start_vid, end_vid, agg_cost)`
OR EMPTY SET

Example:

  Using a combinations table on an undirected graph

The combinations table:

    SELECT source, target FROM combinations;
     source | target
    --------+--------
          5 |      6
          5 |     10
          6 |      5
          6 |     15
          6 |     14
    (5 rows)

The query:

    SELECT * FROM pgr_bdDijkstraCost(
      'SELECT id, source, target, cost, reverse_cost FROM edges',
      'SELECT source, target FROM combinations',
      false);
     start_vid | end_vid | agg_cost
    -----------+---------+----------
             5 |       6 |        1
             5 |      10 |        2
             6 |       5 |        1
             6 |      15 |        2
    (4 rows)

## Parameters

Column | Type | Description
--- | --- | ---
Edges SQL | `TEXT` | Edges SQL as described below
Combinations SQL | `TEXT` | Combinations SQL 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.

### Optional parameters

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

`directed`

`BOOLEAN`

`true`

- When `true` the graph is considered Directed

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

## Inner Queries

### Edges SQL

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`)

`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 SQL

Parameter | Type | Description
--- | --- | ---
`source` | ANY-INTEGER | Identifier of the departure vertex.
`target` | ANY-INTEGER | Identifier of the arrival vertex.

Where:

ANY-INTEGER:

  `SMALLINT`, `INTEGER`, `BIGINT`

## Result columns

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`.

## Additional Examples

Example 1:

  Demonstration of repeated values are ignored, and result is sorted.

    SELECT * FROM pgr_bdDijkstraCost(
      'SELECT id, source, target, cost, reverse_cost FROM edges',
      ARRAY[7, 10, 15, 10, 10, 15], ARRAY[10, 7, 10, 15]);
     start_vid | end_vid | agg_cost
    -----------+---------+----------
             7 |      10 |        4
             7 |      15 |        3
            10 |       7 |        2
            10 |      15 |        3
            15 |       7 |        3
            15 |      10 |        1
    (6 rows)

Example 2:

  Making start vids the same as end vids.

    SELECT * FROM pgr_bdDijkstraCost(
      'SELECT id, source, target, cost, reverse_cost FROM edges',
      ARRAY[7, 10, 15], ARRAY[7, 10, 15]);
     start_vid | end_vid | agg_cost
    -----------+---------+----------
             7 |      10 |        4
             7 |      15 |        3
            10 |       7 |        2
            10 |      15 |        3
            15 |       7 |        3
            15 |      10 |        1
    (6 rows)

Example 3:

  Manually assigned vertex combinations.

    SELECT * FROM pgr_bdDijkstraCost(
      'SELECT id, source, target, cost, reverse_cost FROM edges',
      'SELECT * FROM (VALUES (6, 10), (6, 7), (12, 10)) AS combinations (source, target)');
     start_vid | end_vid | agg_cost
    -----------+---------+----------
             6 |       7 |        1
             6 |      10 |        5
            12 |      10 |        4
    (3 rows)

## See Also

- Bidirectional Dijkstra - Family of functions

- Sample Data

- 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

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