pgr_dijkstraNearCost - Proposed

pgr_dijkstraNearCost — 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.

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_dijkstraNearCost(Edges SQL, start vid, end vids, [options A])

pgr_dijkstraNearCost(Edges SQL, start vids, end vid, [options A])

pgr_dijkstraNearCost(Edges SQL, start vids, end vids, [options B])

pgr_dijkstraNearCost(Edges SQL, Combinations SQL, [options B])

options A: [directed, cap]

options B: [directed, cap, global]

Returns set of (start_vid, end_vid, agg_cost)

OR EMPTY SET

One to Many

pgr_dijkstraNearCost(Edges SQL, start vid, end vids, [options])

options: [directed, cap]

Returns set of (start_vid, end_vid, 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

SELECT * FROM pgr_dijkstraNearCost(
  'SELECT id, source, target, cost, reverse_cost FROM edges',
  6, ARRAY[10, 11, 1]);
 start_vid | end_vid | agg_cost
-----------+---------+----------
         6 |      11 |        2
(1 row)

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

Many to One

pgr_dijkstraNearCost(Edges SQL, start vids, end vid, [options])

options: [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 \(6\)

• 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

SELECT * FROM pgr_dijkstraNearCost(
  'SELECT id, source, target, cost, reverse_cost FROM edges',
  ARRAY[10, 11, 1], 6,
  true,
  cap => 2) ORDER BY agg_cost;
 start_vid | end_vid | agg_cost
-----------+---------+----------
        10 |       6 |        1
        11 |       6 |        2
(2 rows)

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

Many to Many

pgr_dijkstraNearCost(Edges SQL, start vids, end vids, [options])

options: [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 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

SELECT * FROM pgr_dijkstraNearCost(
  'SELECT id, source, target, cost, reverse_cost FROM edges',
  ARRAY[15, 16], ARRAY[10, 11, 1],
  directed => false);
 start_vid | end_vid | agg_cost
-----------+---------+----------
        15 |      10 |        1
(1 row)

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_dijkstraNearCost(Edges SQL, Combinations SQL, [options])

options: [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 \(\{1, 10, 11\}\)

• 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 fisrt 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

SELECT * FROM pgr_dijkstraNearCost(
  'SELECT id, source, target, cost, reverse_cost FROM edges',
  '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',
  global => false);
 start_vid | end_vid | agg_cost
-----------+---------+----------
        11 |      16 |        1
        15 |      10 |        1
        16 |      11 |        1
        10 |      16 |        2
         1 |      16 |        4
(5 rows)

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: 1)

• 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: 12 and 13)

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

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 from start_vid to end_vid.

See Also

• Dijkstra - Family of functions

• pgr_dijkstraNear - 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