pgr_dijkstraNear - Proposed - pgRouting Manual (3.4)

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: \(drt * Starting vids\)

One to Many

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

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

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

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 )

Dijkstra optional parameters

Near optional parameters

Edges SQL

Where:

ANY-INTEGER :

SMALLINT , INTEGER , BIGINT

ANY-NUMERICAL :

SMALLINT , INTEGER , BIGINT , REAL , FLOAT

Combinations SQL

Where:

ANY-INTEGER :

SMALLINT , INTEGER , BIGINT