## pgr_dijkstraNear - Proposed

 pgr_dijkstraNear  - Using dijkstra 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.

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: $$drt = O((E + V)logV)$$

• 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  [, directed] [, cap])
pgr_dijkstraNear(Edges SQL, Start vids, End vid   [, directed] [, cap])
pgr_dijkstraNear(Edges SQL, Start vids, End vids  [, directed] [, cap], [global])
pgr_dijkstraNear(Edges SQL, Combinations SQL  [, 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 [, 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 $$2$$ find the nearest subway station.

• Using a directed graph for car routing.

• The subway stations are on the following vertices $$\{ 3, 6, 7\}$$

• The defaults used:

• directed => true

• cap => 1

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


The result shows that station at vertex $$6$$ is the nearest.

#### Many to One

pgr_dijkstraNear(Edges SQL, Start vids, End vid  [, 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 $$\{ 3, 6, 7\}$$

• 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 edge_table',
3    ARRAY[3, 6, 7], 2,
4    true,
5    cap => 2
6);
7 seq  path_seq  start_vid  end_vid  node  edge  cost  agg_cost
8-----+----------+-----------+---------+------+------+------+----------
9   1         1          3        2     3     2     1         0
10   2         2          3        2     2    -1     0         1
11   3         1          6        2     6     8     1         0
12   4         2          6        2     5     4     1         1
13   5         3          6        2     2    -1     0         2
14(5 rows)
15


The result shows that station at vertex $$3$$ is the nearest and the next best is $$6$$ .

#### Many to Many

pgr_dijkstraNear(Edges SQL, Start vids, End vids [, 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 stops are at $$\{3, 6, 7\}$$

• The second subway line stations are at $$\{4, 9\}$$

• 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 edge_table',
3    ARRAY[4, 9], ARRAY[3, 6, 7],
4    directed => false
5);
6 seq  path_seq  start_vid  end_vid  node  edge  cost  agg_cost
7-----+----------+-----------+---------+------+------+------+----------
8   1         1          4        3     4     3     1         0
9   2         2          4        3     3    -1     0         1
10(2 rows)
11


For a pedestrian the best connection is to get on/off is at vertex $$3$$ of the first subway line and at vertex $$4$$ 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  [, 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 $$\{3, 6, 7\}$$

• The second subway line stations are at $$\{4, 9\}$$

• line 3 sets the start vertices to be from the fisrt subway line and the ending vertices to be from the second subway line

• line 5 sets the start vertices to be from the first subway line and the ending vertices to be from the first subway line

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


From the results:

• making a connection from the first subway line to the second:

• $${(3 -> 9) (6 -> 9) (7 -> 9)}$$ and the best one is $$(6 -> 9)$$ with a cost of $$1$$ (lines: 12 and 13 )

• making a connection from the second subway line to the first:

• $${(4 -> 3) (9 -> 6)}$$ and both are equaly good as they have the same cost. (lines: 10 and 11 and lines: 14 and 15 )

### 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  the graph is considered Directed

• When  false  the graph is considered as Undirected .

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 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  (seq, path_seq, start_vid, end_vid, node, edge, cost, agg_cost)  OR EMPTY SET

Column

Type

Description

seq

 BIGINT 

Sequential value starting from 1.

path_seq

 BIGINT 

Sequential value starting from 1 for each $$(start\_vid \to end\_vid)$$ path.

start_vid

 BIGINT 

Identifier of the starting vertex of the path.

end_vid

 BIGINT 

Identifier of the ending vertex of the path.

node

 BIGINT 

Identifier of the node at position  path_seq  in the $$(start\_vid \to end\_vid)$$ path.

edge

 BIGINT 

Identifier of the edge used to go from node at  path_seq  to the node at  path_seq + 1  in the $$(start\_vid \to end\_vid)$$ path.

• $$-1$$ for the last node of the path.

cost

 FLOAT 

Cost to traverse from  node  using  edge  to the next node in the route sequence.

• $$0$$ for the last row of the path.

agg_cost

 FLOAT 

Total cost of traversing $$(start\_vid \to node)$$ section of the $$(start\_vid \to end\_vid)$$ path.