pgr_bdDijkstraCostMatrix - pgRouting Manual (3.3)

Description

Using bidirectional Dijkstra algorithm, calculate and return a cost matrix.

• Process is done only on edges with positive costs.

  • A negative value on a cost column is interpreted as the edge does not exist.

• Values are returned when there is a path.

• When there is no path:

  • When the starting vertex and ending vertex are the same.

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

• For optimization purposes, any duplicated value in the starting vertices or on the ending vertices are ignored.

• Running time (worse case scenario): \(O((V \log V + E))\)

• For large graphs where there is a path bewtween the starting vertex and ending vertex:

  • It is expected to terminate faster than pgr_dijkstra

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

Example :

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

SELECT * FROM pgr_bdDijkstraCostMatrix(
  '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

Inner Queries

Result Columns

Set of (start_vid, end_vid, agg_cost)

Additional Examples

Example :

Use with pgr_TSP .

SELECT * FROM pgr_TSP(
  $$
  SELECT * FROM pgr_bdDijkstraCostMatrix(
    'SELECT id, source, target, cost, reverse_cost FROM edges',
    (SELECT array_agg(id)
      FROM vertices
      WHERE id IN (5, 6, 10, 15)),
    false)
  $$);
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

• Bidirectional Dijkstra - Family of functions

• Cost Matrix - Category

• Traveling Sales Person - Family of functions

• Sample Data

Indices and tables

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