# pgRouting Manual (3.1)

## pgr_dijkstraCost

`pgr_dijkstraCost`

Using Dijkstra algorithm implemented by Boost.Graph, and extract only the aggregate cost of the shortest path(s) found, for the combination of vertices given.

Boost Graph Inside

Availability

- Version 3.1.0

  - New Proposed functions:

    - pgr_dijkstraCost(combinations)

- Version 2.2.0

  - New Official function

- Supported versions: current(3.1) 3.0 2.6

- Unsupported versions: 2.5 2.4 2.3 2.3

## Description

The `pgr_dijkstraCost` algorithm, is a good choice to calculate the sum of the costs of the shortest path for a subset of pairs of nodes of the graph. We make use of the Boost’s implementation of dijkstra which runs in \(O(V \log V + E)\) time.

The main characteristics are:

  - It does not return a path.

  - Returns the sum of the costs of the shortest path for pair combination of nodes in the graph.

  - Process is done only on edges with positive costs.

  - Values are returned when there is a path.

    - The returned values are in the form of a set of (start_vid, end_vid, agg_cost).

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

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

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

  - For undirected graphs, the results are symmetric.

    - The agg_cost of (u, v) is the same as for (v, u).

  - Any duplicated value in the start_vids or end_vids is ignored.

  - The returned values are ordered:

    - start_vid ascending

    - end_vid ascending

  - Running time: \(O(| start\_vids | * (V \log V + E))\)

## Signatures

Summary

    pgr_dijkstraCost(edges_sql, from_vid,  to_vid  [, directed])
    pgr_dijkstraCost(edges_sql, from_vid,  to_vids [, directed])
    pgr_dijkstraCost(edges_sql, from_vids, to_vid  [, directed])
    pgr_dijkstraCost(edges_sql, from_vids, to_vids [, directed])
    pgr_dijkstraCost(edges_sql, combinations_sql   [, directed]) -- Proposed on v3.1
    RETURNS SET OF (start_vid, end_vid, agg_cost)
    OR EMPTY SET

Using defaults

    pgr_dijkstraCost(edges_sql, from_vid,  to_vid)
    RETURNS SET OF (start_vid, end_vid, agg_cost)
    OR EMPTY SET

Example

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

    SELECT * FROM pgr_dijkstraCost(
        '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_dijkstraCost(edges_sql, from_vid,  to_vid  [, directed])
    RETURNS SET OF (start_vid, end_vid, agg_cost)
    OR EMPTY SET

Example

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

    SELECT * FROM pgr_dijkstraCost(
        '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_dijkstraCost(edges_sql, from_vid,  to_vids [, directed])
    RETURNS SET OF (start_vid, end_vid, agg_cost)
    OR EMPTY SET

Example

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

    SELECT * FROM pgr_dijkstraCost(
        '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_dijkstraCost(edges_sql, from_vids, to_vid  [, directed])
    RETURNS SET OF (start_vid, end_vid, agg_cost)
    OR EMPTY SET

Example

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

    SELECT * FROM pgr_dijkstraCost(
        '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_dijkstraCost(edges_sql, from_vids, to_vids [, directed])
    RETURNS SET OF (start_vid, end_vid, agg_cost)
    OR EMPTY SET

Example

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

    SELECT * FROM pgr_dijkstraCost(
        '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_dijkstraCost(TEXT edges_sql, TEXT combination_sql, BOOLEAN directed:=true);
    RETURNS SET OF (start_vid, end_vid, agg_cost)
    OR EMPTY SET

Example

  Using a combinations table on an undirected graph

    SELECT * FROM pgr_dijkstraCost(
        'SELECT id, source, target, cost, reverse_cost FROM edge_table',
        'SELECT source, target FROM combinations_table',
        FALSE
    );
     start_vid | end_vid | agg_cost
    -----------+---------+----------
             1 |       2 |        1
             1 |       4 |        3
             2 |       1 |        1
             2 |       4 |        2
    (4 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 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

### 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

## Return 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`.

## Additional Examples

Example 1

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

    SELECT * FROM pgr_dijkstraCost(
            'select id, source, target, cost, reverse_cost from edge_table',
                ARRAY[5, 3, 4, 3, 3, 4], ARRAY[3, 5, 3, 4]);
     start_vid | end_vid | agg_cost
    -----------+---------+----------
             3 |       4 |        3
             3 |       5 |        2
             4 |       3 |        1
             4 |       5 |        3
             5 |       3 |        4
             5 |       4 |        3
    (6 rows)

Example 2

  Making start_vids the same as end_vids

    SELECT * FROM pgr_dijkstraCost(
            'select id, source, target, cost, reverse_cost from edge_table',
                ARRAY[5, 3, 4], ARRAY[5, 3, 4]);
     start_vid | end_vid | agg_cost
    -----------+---------+----------
             3 |       4 |        3
             3 |       5 |        2
             4 |       3 |        1
             4 |       5 |        3
             5 |       3 |        4
             5 |       4 |        3
    (6 rows)

Example 3

  Four manually assigned (source, target) vertex combinations

    SELECT * FROM pgr_dijkstraCost(
        'SELECT id, source, target, cost FROM edge_table',
        'SELECT * FROM (VALUES (2, 3), (2, 5), (11, 3), (11, 5)) AS combinations (source, target)',
        FALSE
    );
     start_vid | end_vid | agg_cost
    -----------+---------+----------
             2 |       3 |        3
             2 |       5 |        1
            11 |       3 |        2
            11 |       5 |        2
    (4 rows)

## See Also

- https://en.wikipedia.org/wiki/Dijkstra%27s_algorithm

- Sample Data network.

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