`pgr_bdDijkstraCost`¶

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

_images/boost-inside.jpeg — Boost Graph Inside¶

Availability

Version 3.2.0
- New proposed signature:
  - pgr_bdDijkstraCost (Combinations)
Version 3.0.0
- Official function
Version 2.5.0
- New proposed function

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)

See Also¶

Indices and tables