# pgRouting Manual (3.6)

## pgr_dijkstraNear - Proposed

# `pgr_dijkstraNear` - Proposed

`pgr_dijkstraNear` — Using Dijkstra’s algorithm, finds the route that leads to the nearest vertex.

Warning

Proposed functions for next mayor release.

- They are not officially in the current release.

- They will likely officially be part of the next mayor release:

  - The functions make use of ANY-INTEGER and ANY-NUMERICAL

  - Name might not change. (But still can)

  - Signature might not change. (But still can)

  - Functionality might not change. (But still can)

  - pgTap tests have being done. But might need more.

  - Documentation might need refinement.

Boost Graph Inside

Availability

- Version 3.3.0

  - Promoted to proposed function

- Version 3.2.0

  - New experimental function

## Description

Given a graph, a starting vertex and a set of ending vertices, this function finds the shortest path from the starting vertex to the nearest ending vertex.

### Characteristics

- Uses Dijkstra algorithm.

- Works for directed and undirected graphs.

- When there are more than one path to the same vertex with same cost:

  - The algorithm will return just one path

- Optionally allows to find more than one path.

  - When more than one path is to be returned:

    - Results are sorted in increasing order of:

      - aggregate cost

      - Within the same value of aggregate costs:

        - results are sorted by (source, target)

- Running time: Dijkstra running time: \(drt = O((|E| + |V|)log|V|)\)

  - One to Many; \(drt\)

  - Many to One: \(drt\)

  - Many to Many: \(drt * |Starting vids|\)

  - Combinations: \(drt * |Starting vids|\)

## Signatures

Summary

pgr_dijkstraNear(Edges SQL, start vid, end vids, [options A])
pgr_dijkstraNear(Edges SQL, start vids, end vid, [options A])
pgr_dijkstraNear(Edges SQL, start vids, end vids, [options B])
pgr_dijkstraNear(Edges SQL, Combinations SQL, [options B])
options A: `[directed, cap]`
options B: `[directed, cap, global]`
Returns set of `(seq, path_seq, start_vid, end_vid, node, edge, cost, agg_cost)`
OR EMPTY SET

### One to Many

pgr_dijkstraNear(Edges SQL, start vid, end vids, [options])
options: `[directed, cap]`
Returns set of `(seq, path_seq, start_vid, end_vid, node, edge, cost, agg_cost)`
OR EMPTY SET

Example:

  Departing on car from vertex \(6\) find the nearest subway station.

- Using a directed graph for car routing.

- The subway stations are on the following vertices \(\{1, 10, 11\}\)

- The defaults used:

  - directed => true

  - cap => 1

     1SELECT * FROM pgr_dijkstraNear(
     2  'SELECT id, source, target, cost, reverse_cost FROM edges',
     3  6, ARRAY[10, 11, 1]);
     4 seq | path_seq | start_vid | end_vid | node | edge | cost | agg_cost
     5-----+----------+-----------+---------+------+------+------+----------
     6   1 |        1 |         6 |      11 |    6 |    4 |    1 |        0
     7   2 |        2 |         6 |      11 |    7 |    8 |    1 |        1
     8   3 |        3 |         6 |      11 |   11 |   -1 |    0 |        2
     9(3 rows)
    10

The result shows that station at vertex \(11\) is the nearest.

### Many to One

pgr_dijkstraNear(Edges SQL, start vids, end vid, [options])
options: `[directed, cap]`
Returns set of `(seq, path_seq, start_vid, end_vid, node, edge, cost, agg_cost)`
OR EMPTY SET

Example:

  Departing on a car from a subway station find the nearest two stations to vertex \(2\)

- Using a directed graph for car routing.

- The subway stations are on the following vertices \(\{1, 10, 11\}\)

- On line 4: using the positional parameter: directed set to `true`

- In line 5: using named parameter cap => 2

     1SELECT * FROM pgr_dijkstraNear(
     2  'SELECT id, source, target, cost, reverse_cost FROM edges',
     3  ARRAY[10, 11, 1], 6,
     4  true,
     5  cap => 2);
     6 seq | path_seq | start_vid | end_vid | node | edge | cost | agg_cost
     7-----+----------+-----------+---------+------+------+------+----------
     8   1 |        1 |        10 |       6 |   10 |    2 |    1 |        0
     9   2 |        2 |        10 |       6 |    6 |   -1 |    0 |        1
    10   3 |        1 |        11 |       6 |   11 |    8 |    1 |        0
    11   4 |        2 |        11 |       6 |    7 |    4 |    1 |        1
    12   5 |        3 |        11 |       6 |    6 |   -1 |    0 |        2
    13(5 rows)
    14

The result shows that station at vertex \(10\) is the nearest and the next best is \(11\).

### Many to Many

pgr_dijkstraNear(Edges SQL, start vids, end vids, [options])
options: `[directed, cap, global]`
Returns set of `(seq, path_seq, start_vid, end_vid, node, edge, cost, agg_cost)`
OR EMPTY SET

Example:

  Find the best pedestrian connection between two lines of buses

- Unsing an undirected graph for pedestrian routing

- The first subway line stations are at \(\{15, 16\}\)

- The second subway line stations stops are at \(\{1, 10, 11\}\)

- On line 4: using the named parameter: directed => false

- The defaults used:

  - cap => 1

  - global => true

     1SELECT * FROM pgr_dijkstraNear(
     2  'SELECT id, source, target, cost, reverse_cost FROM edges',
     3  ARRAY[15, 16], ARRAY[10, 11, 1],
     4  directed => false);
     5 seq | path_seq | start_vid | end_vid | node | edge | cost | agg_cost
     6-----+----------+-----------+---------+------+------+------+----------
     7   1 |        1 |        15 |      10 |   15 |    3 |    1 |        0
     8   2 |        2 |        15 |      10 |   10 |   -1 |    0 |        1
     9(2 rows)
    10

For a pedestrian the best connection is to get on/off is at vertex \(15\) of the first subway line and at vertex \(10\) of the second subway line.

Only one route is returned because global is `true` and cap is `1`

### Combinations

pgr_dijkstraNear(Edges SQL, Combinations SQL, [options])
options: `[directed, cap, global]`
Returns set of `(seq, path_seq, start_vid, end_vid, node, edge, cost, agg_cost)`
OR EMPTY SET

Example:

  Find the best car connection between all the stations of two subway lines

- Using a directed graph for car routing.

- The first subway line stations stops are at \(\{1, 10, 11\}\)

- The second subway line stations are at \(\{15, 16\}\)

The combinations contents:

    SELECT unnest(ARRAY[10, 11, 1]) as source, target
    FROM (SELECT unnest(ARRAY[15, 16]) AS target) a
      UNION
    SELECT unnest(ARRAY[15, 16]), target
    FROM (SELECT unnest(ARRAY[10, 11, 1]) AS target) b ORDER BY source, target;
     source | target
    --------+--------
          1 |     15
          1 |     16
         10 |     15
         10 |     16
         11 |     15
         11 |     16
         15 |      1
         15 |     10
         15 |     11
         16 |      1
         16 |     10
         16 |     11
    (12 rows)

The query:

- lines 3~4 sets the start vertices to be from the first subway line and the ending vertices to be from the second subway line

- lines 6~7 sets the start vertices to be from the first subway line and the ending vertices to be from the first subway line

- On line 8: using the named parameter is global => false

- The defaults used:

  - directed => true

  - cap => 1

     1SELECT * FROM pgr_dijkstraNear(
     2  'SELECT id, source, target, cost, reverse_cost FROM edges',
     3  'SELECT unnest(ARRAY[10, 11, 1]) as source, target
     4  FROM (SELECT unnest(ARRAY[15, 16]) AS target) a
     5  UNION
     6  SELECT unnest(ARRAY[15, 16]), target
     7  FROM (SELECT unnest(ARRAY[10, 11, 1]) AS target) b',
     8  global => false);
     9 seq | path_seq | start_vid | end_vid | node | edge | cost | agg_cost
    10-----+----------+-----------+---------+------+------+------+----------
    11   1 |        1 |        11 |      16 |   11 |    9 |    1 |        0
    12   2 |        2 |        11 |      16 |   16 |   -1 |    0 |        1
    13   3 |        1 |        15 |      10 |   15 |    3 |    1 |        0
    14   4 |        2 |        15 |      10 |   10 |   -1 |    0 |        1
    15   5 |        1 |        16 |      11 |   16 |    9 |    1 |        0
    16   6 |        2 |        16 |      11 |   11 |   -1 |    0 |        1
    17   7 |        1 |        10 |      16 |   10 |    5 |    1 |        0
    18   8 |        2 |        10 |      16 |   11 |    9 |    1 |        1
    19   9 |        3 |        10 |      16 |   16 |   -1 |    0 |        2
    20  10 |        1 |         1 |      16 |    1 |    6 |    1 |        0
    21  11 |        2 |         1 |      16 |    3 |    7 |    1 |        1
    22  12 |        3 |         1 |      16 |    7 |    8 |    1 |        2
    23  13 |        4 |         1 |      16 |   11 |    9 |    1 |        3
    24  14 |        5 |         1 |      16 |   16 |   -1 |    0 |        4
    25(14 rows)
    26

From the results:

- making a connection from the first subway line \(\{1, 10, 11\}\) to the second \(\{15, 16\}\):

  - The best connections from all the stations from the first line are: \({(1 \rightarrow 16) (10 \rightarrow 16) (11 \rightarrow 16)}\)

  - The best one is \((11 \rightarrow 16)\) with a cost of \(1\) (lines: 11 and 12)

- making a connection from the second subway line \(\{15, 16\}\) to the first \(\{1, 10, 11\}\):

  - The best connections from all the stations from the second line are: \({(15 \rightarrow 10) (16 \rightarrow 11)}\)

  - Both are equaly good as they have the same cost. (lines: 13 and 14 and lines: 15 and 16)

## 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.

### Dijkstra optional parameters

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

`directed`

`BOOLEAN`

`true`

- When `true` the graph is considered Directed

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

### Near optional parameters

Parameter | Type | Default | Description
--- | --- | --- | ---
`cap` | `BIGINT` | `1` | Find at most `cap` number of nearest shortest paths

`global`

`BOOLEAN`

`true`

- When `true`: only `cap` limit results will be returned

- When `false`: `cap` limit per `Start vid` will be returned

## 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

Returns `(seq, path_seq, start_vid, end_vid, node, edge, cost, agg_cost)`

Column | Type | Description
--- | --- | ---
`seq` | `INTEGER` | Sequential value starting from 1.
`path_seq` | `INTEGER` | Relative position in the path. Has value 1 for the beginning of a path.
`start_vid` | `BIGINT` | Identifier of the starting vertex of the current path.
`end_vid` | `BIGINT` | Identifier of the ending vertex of the current path.
`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_vid` to `node`.

## See Also

- Dijkstra - Family of functions

- pgr_dijkstraNearCost - Proposed

- Sample Data network.

- boost: https://www.boost.org/libs/graph/doc/table_of_contents.html

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

Indices and tables

- Index

- Search Page