pgr_dijkstraCostMatrix

pgr_dijkstraCostMatrix - Calculates a cost matrix using pgr_dijkstra.

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Availability

  • Version 3.0.0

    • Official function

  • Version 2.3.0

    • New proposed function

Description

Using Dijkstra algorithm, calculate and return a cost matrix.

Dijkstra’s algorithm, conceived by Dutch computer scientist Edsger Dijkstra in 1956. It is a graph search algorithm that solves the shortest path problem for a graph with non-negative edge path costs, producing a shortest path from a starting vertex to an ending vertex. This implementation can be used with a directed graph and an undirected graph.

The main Characteristics are:

  • Can be used as input to pgr_TSP.

    • Use directly when the resulting matrix is symmetric and there is no \(\infty\) value.

    • It will be the users responsibility to make the matrix symmetric.

      • By using geometric or harmonic average of the non symmetric values.

      • By using max or min the non symmetric values.

      • By setting the upper triangle to be the mirror image of the lower triangle.

      • By setting the lower triangle to be the mirror image of the upper triangle.

    • It is also the users responsibility to fix an \(\infty\) value.

  • Each function works as part of the family it belongs to.

  • It does not return a path.

  • Returns the sum of the costs of the shortest path for pair combination of nodes in the graph.

  • Process is done only on edges with positive costs.

  • Values are returned when there is a path.

    • When the starting vertex and ending vertex are the same, there is no path.

      • The aggregate cost in the non included values (v, v) is 0.

    • When the starting vertex and ending vertex are the different and there is no path.

      • The aggregate cost in the non included values (u, v) is \(\infty\).

  • Let be the case the values returned are stored in a table:

    • The unique index would be the pair: (start_vid, end_vid).

  • Depending on the function and its parameters, the results can be symmetric.

    • The aggregate cost of (u, v) is the same as for (v, u).

  • Any duplicated value in the start vids are ignored.

  • The returned values are ordered:

    • start_vid ascending

    • end_vid ascending

Signatures

Summary

pgr_dijkstraCost(Edges SQL, start vids [, directed])
RETURNS SET OF (start_vid, end_vid, agg_cost)
Example:

Symmetric cost matrix for vertices \(\{5, 6, 10, 15\}\) on an undirected graph

SELECT * FROM pgr_dijkstraCostMatrix(
  'SELECT id, source, target, cost, reverse_cost FROM edges',
  (SELECT array_agg(id)
    FROM vertices
    WHERE id IN (5, 6, 10, 15)),
  false);
 start_vid | end_vid | agg_cost
-----------+---------+----------
         5 |       6 |        1
         5 |      10 |        2
         5 |      15 |        3
         6 |       5 |        1
         6 |      10 |        1
         6 |      15 |        2
        10 |       5 |        2
        10 |       6 |        1
        10 |      15 |        1
        15 |       5 |        3
        15 |       6 |        2
        15 |      10 |        1
(12 rows)

Parameters

Column

Type

Description

Edges SQL

TEXT

Edges SQL as described below

start vids

ARRAY[BIGINT]

Array of identifiers of starting vertices.

Optional parameters

Column

Type

Default

Description

directed

BOOLEAN

true

  • When true the graph is considered Directed

  • When false the graph is considered as Undirected.

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

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.

Additional Examples

Example:

Use with pgr_TSP.

SELECT * FROM pgr_TSP(
  $$
  SELECT * FROM pgr_dijkstraCostMatrix(
    'SELECT id, source, target, cost, reverse_cost FROM edges',
    (SELECT array_agg(id)
      FROM vertices
      WHERE id IN (5, 6, 10, 15)),
    false)
  $$);
NOTICE:  pgr_TSP no longer solving with simulated annaeling
HINT:  Ignoring annaeling parameters
 seq | node | cost | agg_cost
-----+------+------+----------
   1 |    5 |    0 |        0
   2 |    6 |    1 |        1
   3 |   10 |    1 |        2
   4 |   15 |    1 |        3
   5 |    5 |    3 |        6
(5 rows)

See Also

Indices and tables