pgr_bdDijkstraCost

pgr_bdDijkstraCost — Returns the shortest path(s)’s cost using Bidirectional Dijkstra algorithm.

_images/boost-inside.jpeg

Boost Graph Inside

Availability

Description

The pgr_bdDijkstraCost function sumarizes of the cost of the shortest path using the bidirectional Dijkstra Algorithm.

  • 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
  • It does not return a path.
  • Returns the sum of the costs of the shortest path of each pair combination of nodes requested.
  • Let be the case the values returned are stored in a table, so 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 or end vertex identifiers are ignored.
  • The returned values are ordered:
    • start_vid ascending
    • end_vid ascending

Signatures

Summary

pgr_bdDijkstraCost(Edges SQL, start vid, end vid  [, directed])
pgr_bdDijkstraCost(Edges SQL, start vid, end vids [, directed])
pgr_bdDijkstraCost(Edges SQL, start vids, end vid  [, directed])
pgr_bdDijkstraCost(Edges SQL, start vids, end vids [, directed])
pgr_bdDijkstraCost(Edges SQL, Combinations SQL [, directed])
RETURNS SET OF (start_vid, end_vid, agg_cost)
OR EMPTY SET

One to One

pgr_bdDijkstraCost(Edges SQL, start vid, end vid  [, directed])
RETURNS SET OF (start_vid, end_vid, agg_cost)
OR EMPTY SET
Example:From vertex \(6\) to vertex \(10\) on a directed graph
SELECT * FROM pgr_bdDijkstraCost(
  'SELECT id, source, target, cost, reverse_cost FROM edges',
  6, 10, true);
 start_vid | end_vid | agg_cost
-----------+---------+----------
         6 |      10 |        5
(1 row)

One to Many

pgr_bdDijkstraCost(Edges SQL, start vid, end vids [, directed])
RETURNS SET OF (start_vid, end_vid, agg_cost)
OR EMPTY SET
Example:From vertex \(6\) to vertices \(\{10, 17\}\) on a directed graph
SELECT * FROM pgr_bdDijkstraCost(
  'SELECT id, source, target, cost, reverse_cost FROM edges',
  6, ARRAY[10, 17]);
 start_vid | end_vid | agg_cost
-----------+---------+----------
         6 |      10 |        5
         6 |      17 |        4
(2 rows)

Many to One

pgr_bdDijkstraCost(Edges SQL, start vids, end vid  [, directed])
RETURNS SET OF (start_vid, end_vid, agg_cost)
OR EMPTY SET
Example:From vertices \(\{6, 1\}\) to vertex \(17\) on a directed graph
SELECT * FROM pgr_bdDijkstraCost(
  'SELECT id, source, target, cost, reverse_cost FROM edges',
  ARRAY[6, 1], 17);
 start_vid | end_vid | agg_cost
-----------+---------+----------
         1 |      17 |        5
         6 |      17 |        4
(2 rows)

Many to Many

pgr_bdDijkstraCost(Edges SQL, start vids, end vids [, directed])
RETURNS SET OF (start_vid, end_vid, agg_cost)
OR EMPTY SET
Example:From vertices \(\{6, 1\}\) to vertices \(\{10, 17\}\) on an undirected graph
SELECT * FROM pgr_bdDijkstraCost(
  'SELECT id, source, target, cost, reverse_cost FROM edges',
  ARRAY[6, 1], ARRAY[10, 17],
  directed => false);
 start_vid | end_vid | agg_cost
-----------+---------+----------
         1 |      10 |        4
         1 |      17 |        5
         6 |      10 |        1
         6 |      17 |        4
(4 rows)

Combinations

pgr_bdDijkstraCost(Edges SQL, Combinations SQL [, directed])
RETURNS SET OF (start_vid, end_vid, agg_cost)
OR EMPTY SET
Example:Using a combinations table on an undirected graph

The combinations table:

SELECT source, target FROM combinations;
 source | target
--------+--------
      5 |      6
      5 |     10
      6 |      5
      6 |     15
      6 |     14
(5 rows)

The query:

SELECT * FROM pgr_bdDijkstraCost(
  'SELECT id, source, target, cost, reverse_cost FROM edges',
  'SELECT source, target FROM combinations',
  false);
 start_vid | end_vid | agg_cost
-----------+---------+----------
         5 |       6 |        1
         5 |      10 |        2
         6 |       5 |        1
         6 |      15 |        2
(4 rows)

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.

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

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.

Additional Examples

Example 1:Demonstration of repeated values are ignored, and result is sorted.
SELECT * FROM pgr_bdDijkstraCost(
  'SELECT id, source, target, cost, reverse_cost FROM edges',
  ARRAY[7, 10, 15, 10, 10, 15], ARRAY[10, 7, 10, 15]);
 start_vid | end_vid | agg_cost
-----------+---------+----------
         7 |      10 |        4
         7 |      15 |        3
        10 |       7 |        2
        10 |      15 |        3
        15 |       7 |        3
        15 |      10 |        1
(6 rows)

Example 2:Making start vids the same as end vids.
SELECT * FROM pgr_bdDijkstraCost(
  'SELECT id, source, target, cost, reverse_cost FROM edges',
  ARRAY[7, 10, 15], ARRAY[7, 10, 15]);
 start_vid | end_vid | agg_cost
-----------+---------+----------
         7 |      10 |        4
         7 |      15 |        3
        10 |       7 |        2
        10 |      15 |        3
        15 |       7 |        3
        15 |      10 |        1
(6 rows)

Example 3:Manually assigned vertex combinations.
SELECT * FROM pgr_bdDijkstraCost(
  'SELECT id, source, target, cost, reverse_cost FROM edges',
  'SELECT * FROM (VALUES (6, 10), (6, 7), (12, 10)) AS combinations (source, target)');
 start_vid | end_vid | agg_cost
-----------+---------+----------
         6 |       7 |        1
         6 |      10 |        5
        12 |      10 |        4
(3 rows)