pgr_dijkstraNearCost - Proposed - pgRouting Manual (3.3)

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

pgr_dijkstraNearCost(Edges SQL, Start vid,  End vids [, directed] [, cap])
RETURNS SET OF (start_vid, end_vid, 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_dijkstraNearCost(
2    'SELECT id, source, target, cost, reverse_cost FROM edge_table',
3    2, ARRAY[3, 6, 7]
4);
5 start_vid  end_vid  agg_cost
6-----------+---------+----------
7         2        6         2
8(1 row)
9

The result shows that station at vertex \(6\) is the nearest.

Many to One

pgr_dijkstraNearCost(Edges SQL, Start vids, End vid  [, directed] [, cap])
RETURNS SET OF (start_vid, end_vid, 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_dijkstraNearCost(
 2    'SELECT id, source, target, cost, reverse_cost FROM edge_table',
 3    ARRAY[3, 6, 7], 2,
 4    true,
 5    cap => 2
 6);
 7 start_vid  end_vid  agg_cost
 8-----------+---------+----------
 9         3        2         1
10         6        2         2
11(2 rows)
12

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

Many to Many

pgr_dijkstraNearCost(Edges SQL, Start vids, End vids [, directed] [, cap], [global])
RETURNS SET OF (start_vid, end_vid, 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_dijkstraNearCost(
 2    'SELECT id, source, target, cost, reverse_cost FROM edge_table',
 3    ARRAY[4, 9], ARRAY[3, 6, 7],
 4    directed => false
 5);
 6 start_vid  end_vid  agg_cost
 7-----------+---------+----------
 8         4        3         1
 9(1 row)
10

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_dijkstraNearCost(Edges SQL, Combinations SQL  [, directed] [, cap], [global])
RETURNS SET OF (start_vid, end_vid, 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_dijkstraNearCost(
 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 start_vid  end_vid  agg_cost
 9-----------+---------+----------
10         4        3         1
11         6        9         1
12         9        6         1
13         3        9         2
14         7        9         4
15(5 rows)
16

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 \(1\) (line: 11 )

• 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 12 )

Edges query

Where:

ANY-INTEGER :

SMALLINT, INTEGER, BIGINT

ANY-NUMERICAL :

SMALLINT, INTEGER, BIGINT, REAL, FLOAT

Combinations query

Where:

ANY-INTEGER :

SMALLINT, INTEGER, BIGINT