# pgr_dijkstraCost¶

## Synopsis¶

`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.

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.

## Characteristics:¶

- 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 symetric.
- 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

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

## Signature Summary¶

```
pgr_dijkstraCost(edges_sql, start_vid, end_vid);
pgr_dijkstraCost(edges_sql, start_vid, end_vid, directed);
pgr_dijkstraCost(edges_sql, start_vids, end_vid, directed);
pgr_dijkstraCost(edges_sql, start_vid, end_vids, directed);
pgr_dijkstraCost(edges_sql, start_vids, end_vids, directed);
RETURNS SET OF (start_vid, end_vid, agg_cost) or EMPTY SET
```

# Signatures¶

## Minimal signature¶

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

```
pgr_dijkstraCost(TEXT edges_sql, BIGINT start_vid, BIGINT end_vid)
RETURNS SET OF (start_vid, end_vid, agg_cost) or EMPTY SET
```

Example

```
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)
```

## pgr_dijkstraCost One to One¶

- This signature performs a Dijkstra 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`.

- on a

```
pgr_dijkstraCost(TEXT edges_sql, BIGINT start_vid, BIGINT end_vid,
BOOLEAN directed:=true);
RETURNS SET OF (start_vid, end_vid, agg_cost) or EMPTY SET
```

Example

```
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)
```

## pgr_dijkstraCost Many to One¶

```
pgr_dijkstraCost(TEXT edges_sql, array[ANY_INTEGER] start_vids, BIGINT end_vid,
BOOLEAN directed:=true);
RETURNS SET OF (start_vid, end_vid, agg_cost) or EMPTY SET
```

- This signature performs a Dijkstra 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`.

- on a

Example

```
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)
```

## pgr_dijkstraCost One to Many¶

```
pgr_dijkstraCost(TEXT edges_sql, BIGINT start_vid, array[ANY_INTEGER] end_vids,
BOOLEAN directed:=true);
RETURNS SET OF (start_vid, end_vid, agg_cost) or EMPTY SET
```

- This signature performs a Dijkstra 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`.

- on a

Example

```
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)
```

pgr_dijkstraCost Many to Many

```
pgr_dijkstraCost(TEXT edges_sql, array[ANY_INTEGER] start_vids, array[ANY_INTEGER] end_vids,
BOOLEAN directed:=true);
RETURNS SET OF (start_vid, end_vid, agg_cost) or EMPTY SET
```

- This signature performs a Dijkstra 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`.

- on a

## Example¶

```
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)
```

# Description of the Signatures¶

## Description of the edge’s SQL query¶

edges_sql: | is a TEXT that containes an SQL query, which should return a set of rows with the following columns: |
---|

Column | Type | 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), if negative: edge (source, target) does not exist, therefore it’s not part of the graph. |

reverse_cost |
ANY-NUMERICAL |
(optional) Weight of the edge (target, source), if 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 | Description |
---|---|---|

edges_sql |
TEXT |
SQL query as decribed above. |

start_vid |
BIGINT |
Identifier of the starting vertex of the path. |

end_vid |
BIGINT |
Identifier of the ending vertex of the path. |

start_vids |
array[ANY-INTEGER] |
Array of identifiers of starting vertices. |

end_vids |
array[ANY-INTEGER] |
Array of identifiers of ending vertices. |

directed |
BOOLEAN |
(optional). When false the graph is considered as Undirected. Default is true which considers the graph as Directed. |

## Description of the return values¶

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 of the shortest path from start_vid to end_vid. |

# Examples¶

Example 1: |
---|

Repeated values are ignored, and arrays are 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: |
---|

start_vids are 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)
```

The queries use the *Sample Data* network.

History

- New in version 2.2.0