pgr_bdDijkstra

pgr_bdDijkstra — Returns the shortest path(s) using Bidirectional Dijkstra algorithm.

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Boost Graph Inside

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Description

The main characteristics are:

  • 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

Signatures

Summary

pgr_bdDijkstra(Edges SQL, start vid, end vid  [, directed])
pgr_bdDijkstra(Edges SQL, start vid, end vids [, directed])
pgr_bdDijkstra(Edges SQL, start vids, end vid  [, directed])
pgr_bdDijkstra(Edges SQL, start vids, end vids [, directed])
pgr_bdDijkstra(Edges SQL, Combinations SQL [, directed])
RETURNS (seq, path_seq [, start_vid] [, end_vid], node, edge, cost, agg_cost)
 OR EMPTY SET

One to One

pgr_bdDijkstra(Edges SQL, start vid, end vid  [, directed])
RETURNS (seq, path_seq, node, edge, cost, agg_cost)
OR EMPTY SET
Example:From vertex \(6\) to vertex \(10\) on a directed graph
SELECT * FROM pgr_bdDijkstra(
  'select id, source, target, cost, reverse_cost from edges',
  6, 10, true);
 seq | path_seq | node | edge | cost | agg_cost
-----+----------+------+------+------+----------
   1 |        1 |    6 |    4 |    1 |        0
   2 |        2 |    7 |    8 |    1 |        1
   3 |        3 |   11 |    9 |    1 |        2
   4 |        4 |   16 |   16 |    1 |        3
   5 |        5 |   15 |    3 |    1 |        4
   6 |        6 |   10 |   -1 |    0 |        5
(6 rows)

One to Many

pgr_bdDijkstra(Edges SQL, start vid, end vids [, directed])
RETURNS (seq, path_seq, end_vid, node, edge, cost, agg_cost)
OR EMPTY SET
Example:From vertex \(6\) to vertices \(\{10, 17\}\) on a directed graph
SELECT * FROM pgr_bdDijkstra(
  'select id, source, target, cost, reverse_cost from edges',
  6, ARRAY[10, 17]);
 seq | path_seq | end_vid | node | edge | cost | agg_cost
-----+----------+---------+------+------+------+----------
   1 |        1 |      10 |    6 |    4 |    1 |        0
   2 |        2 |      10 |    7 |    8 |    1 |        1
   3 |        3 |      10 |   11 |    9 |    1 |        2
   4 |        4 |      10 |   16 |   16 |    1 |        3
   5 |        5 |      10 |   15 |    3 |    1 |        4
   6 |        6 |      10 |   10 |   -1 |    0 |        5
   7 |        1 |      17 |    6 |    4 |    1 |        0
   8 |        2 |      17 |    7 |    8 |    1 |        1
   9 |        3 |      17 |   11 |   11 |    1 |        2
  10 |        4 |      17 |   12 |   13 |    1 |        3
  11 |        5 |      17 |   17 |   -1 |    0 |        4
(11 rows)

Many to One

pgr_bdDijkstra(Edges SQL, start vids, end vid  [, directed])
RETURNS (seq, path_seq, start_vid, node, edge, cost, agg_cost)
OR EMPTY SET
Example:From vertices \(\{6, 1\}\) to vertex \(17\) on a directed graph
SELECT * FROM pgr_bdDijkstra(
  'select id, source, target, cost, reverse_cost from edges',
  ARRAY[6, 1], 17);
 seq | path_seq | start_vid | node | edge | cost | agg_cost
-----+----------+-----------+------+------+------+----------
   1 |        1 |         1 |    1 |    6 |    1 |        0
   2 |        2 |         1 |    3 |    7 |    1 |        1
   3 |        3 |         1 |    7 |    8 |    1 |        2
   4 |        4 |         1 |   11 |   11 |    1 |        3
   5 |        5 |         1 |   12 |   13 |    1 |        4
   6 |        6 |         1 |   17 |   -1 |    0 |        5
   7 |        1 |         6 |    6 |    4 |    1 |        0
   8 |        2 |         6 |    7 |    8 |    1 |        1
   9 |        3 |         6 |   11 |   11 |    1 |        2
  10 |        4 |         6 |   12 |   13 |    1 |        3
  11 |        5 |         6 |   17 |   -1 |    0 |        4
(11 rows)

Many to Many

pgr_bdDijkstra(Edges SQL, start vids, end vids [, directed])
RETURNS (seq, path_seq, start_vid, end_vid, node, edge, cost, agg_cost)
OR EMPTY SET
Example:From vertices \(\{6, 1\}\) to vertices \(\{10, 17\}\) on an undirected graph
SELECT * FROM pgr_bdDijkstra(
  'select id, source, target, cost, reverse_cost from edges',
  ARRAY[6, 1], ARRAY[10, 17],
  directed => false);
 seq | path_seq | start_vid | end_vid | node | edge | cost | agg_cost
-----+----------+-----------+---------+------+------+------+----------
   1 |        1 |         1 |      10 |    1 |    6 |    1 |        0
   2 |        2 |         1 |      10 |    3 |    7 |    1 |        1
   3 |        3 |         1 |      10 |    7 |    4 |    1 |        2
   4 |        4 |         1 |      10 |    6 |    2 |    1 |        3
   5 |        5 |         1 |      10 |   10 |   -1 |    0 |        4
   6 |        1 |         1 |      17 |    1 |    6 |    1 |        0
   7 |        2 |         1 |      17 |    3 |    7 |    1 |        1
   8 |        3 |         1 |      17 |    7 |    8 |    1 |        2
   9 |        4 |         1 |      17 |   11 |   11 |    1 |        3
  10 |        5 |         1 |      17 |   12 |   13 |    1 |        4
  11 |        6 |         1 |      17 |   17 |   -1 |    0 |        5
  12 |        1 |         6 |      10 |    6 |    2 |    1 |        0
  13 |        2 |         6 |      10 |   10 |   -1 |    0 |        1
  14 |        1 |         6 |      17 |    6 |    2 |    1 |        0
  15 |        2 |         6 |      17 |   10 |    5 |    1 |        1
  16 |        3 |         6 |      17 |   11 |   11 |    1 |        2
  17 |        4 |         6 |      17 |   12 |   13 |    1 |        3
  18 |        5 |         6 |      17 |   17 |   -1 |    0 |        4
(18 rows)

Combinations

pgr_bdDijkstra(Edges SQL, Combinations SQL [, directed])
RETURNS (seq, path_seq, start_vid, end_vid, node, edge, cost, 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_bdDijkstra(
  'SELECT id, source, target, cost, reverse_cost FROM edges',
  'SELECT source, target FROM combinations',
  false);
 seq | path_seq | start_vid | end_vid | node | edge | cost | agg_cost
-----+----------+-----------+---------+------+------+------+----------
   1 |        1 |         5 |       6 |    5 |    1 |    1 |        0
   2 |        2 |         5 |       6 |    6 |   -1 |    0 |        1
   3 |        1 |         5 |      10 |    5 |    1 |    1 |        0
   4 |        2 |         5 |      10 |    6 |    2 |    1 |        1
   5 |        3 |         5 |      10 |   10 |   -1 |    0 |        2
   6 |        1 |         6 |       5 |    6 |    1 |    1 |        0
   7 |        2 |         6 |       5 |    5 |   -1 |    0 |        1
   8 |        1 |         6 |      15 |    6 |    2 |    1 |        0
   9 |        2 |         6 |      15 |   10 |    3 |    1 |        1
  10 |        3 |         6 |      15 |   15 |   -1 |    0 |        2
(10 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

Returns set of (seq, path_seq [, start_vid] [, end_vid], node, edge, cost, agg_cost)

Column Type Description
seq INTEGER Sequential value starting from 1.
path_seq INTEGER Relative position in the path. Has value 1 for the beginning of a path.
start_vid BIGINT

Identifier of the starting vertex. Returned when multiple starting vetrices are in the query.

end_vid BIGINT

Identifier of the ending vertex. Returned when multiple ending vertices are in the query.

node BIGINT Identifier of the node in the path from start_vid to end_vid.
edge BIGINT Identifier of the edge used to go from node to the next node in the path sequence. -1 for the last node of the path.
cost FLOAT Cost to traverse from node using edge to the next node in the path sequence.
agg_cost FLOAT Aggregate cost from start_vid to node.

Additional Examples

Example 1:Demonstration of repeated values are ignored, and result is sorted.
SELECT * FROM pgr_bdDijkstra(
  'select id, source, target, cost, reverse_cost from edges',
  ARRAY[7, 10, 15, 10, 10, 15], ARRAY[10, 7, 10, 15]);
 seq | path_seq | start_vid | end_vid | node | edge | cost | agg_cost
-----+----------+-----------+---------+------+------+------+----------
   1 |        1 |         7 |      10 |    7 |    8 |    1 |        0
   2 |        2 |         7 |      10 |   11 |    9 |    1 |        1
   3 |        3 |         7 |      10 |   16 |   16 |    1 |        2
   4 |        4 |         7 |      10 |   15 |    3 |    1 |        3
   5 |        5 |         7 |      10 |   10 |   -1 |    0 |        4
   6 |        1 |         7 |      15 |    7 |    8 |    1 |        0
   7 |        2 |         7 |      15 |   11 |    9 |    1 |        1
   8 |        3 |         7 |      15 |   16 |   16 |    1 |        2
   9 |        4 |         7 |      15 |   15 |   -1 |    0 |        3
  10 |        1 |        10 |       7 |   10 |    2 |    1 |        0
  11 |        2 |        10 |       7 |    6 |    4 |    1 |        1
  12 |        3 |        10 |       7 |    7 |   -1 |    0 |        2
  13 |        1 |        10 |      15 |   10 |    5 |    1 |        0
  14 |        2 |        10 |      15 |   11 |    9 |    1 |        1
  15 |        3 |        10 |      15 |   16 |   16 |    1 |        2
  16 |        4 |        10 |      15 |   15 |   -1 |    0 |        3
  17 |        1 |        15 |       7 |   15 |    3 |    1 |        0
  18 |        2 |        15 |       7 |   10 |    2 |    1 |        1
  19 |        3 |        15 |       7 |    6 |    4 |    1 |        2
  20 |        4 |        15 |       7 |    7 |   -1 |    0 |        3
  21 |        1 |        15 |      10 |   15 |    3 |    1 |        0
  22 |        2 |        15 |      10 |   10 |   -1 |    0 |        1
(22 rows)

Example 2:Making start vids the same as end vids.
SELECT * FROM pgr_bdDijkstra(
  'select id, source, target, cost, reverse_cost from edges',
  ARRAY[7, 10, 15], ARRAY[7, 10, 15]);
 seq | path_seq | start_vid | end_vid | node | edge | cost | agg_cost
-----+----------+-----------+---------+------+------+------+----------
   1 |        1 |         7 |      10 |    7 |    8 |    1 |        0
   2 |        2 |         7 |      10 |   11 |    9 |    1 |        1
   3 |        3 |         7 |      10 |   16 |   16 |    1 |        2
   4 |        4 |         7 |      10 |   15 |    3 |    1 |        3
   5 |        5 |         7 |      10 |   10 |   -1 |    0 |        4
   6 |        1 |         7 |      15 |    7 |    8 |    1 |        0
   7 |        2 |         7 |      15 |   11 |    9 |    1 |        1
   8 |        3 |         7 |      15 |   16 |   16 |    1 |        2
   9 |        4 |         7 |      15 |   15 |   -1 |    0 |        3
  10 |        1 |        10 |       7 |   10 |    2 |    1 |        0
  11 |        2 |        10 |       7 |    6 |    4 |    1 |        1
  12 |        3 |        10 |       7 |    7 |   -1 |    0 |        2
  13 |        1 |        10 |      15 |   10 |    5 |    1 |        0
  14 |        2 |        10 |      15 |   11 |    9 |    1 |        1
  15 |        3 |        10 |      15 |   16 |   16 |    1 |        2
  16 |        4 |        10 |      15 |   15 |   -1 |    0 |        3
  17 |        1 |        15 |       7 |   15 |    3 |    1 |        0
  18 |        2 |        15 |       7 |   10 |    2 |    1 |        1
  19 |        3 |        15 |       7 |    6 |    4 |    1 |        2
  20 |        4 |        15 |       7 |    7 |   -1 |    0 |        3
  21 |        1 |        15 |      10 |   15 |    3 |    1 |        0
  22 |        2 |        15 |      10 |   10 |   -1 |    0 |        1
(22 rows)

Example 3:Manually assigned vertex combinations.
SELECT * FROM pgr_bdDijkstra(
  'SELECT id, source, target, cost, reverse_cost FROM edges',
  'SELECT * FROM (VALUES (6, 10), (6, 7), (12, 10)) AS combinations (source, target)');
 seq | path_seq | start_vid | end_vid | node | edge | cost | agg_cost
-----+----------+-----------+---------+------+------+------+----------
   1 |        1 |         6 |       7 |    6 |    4 |    1 |        0
   2 |        2 |         6 |       7 |    7 |   -1 |    0 |        1
   3 |        1 |         6 |      10 |    6 |    4 |    1 |        0
   4 |        2 |         6 |      10 |    7 |    8 |    1 |        1
   5 |        3 |         6 |      10 |   11 |    9 |    1 |        2
   6 |        4 |         6 |      10 |   16 |   16 |    1 |        3
   7 |        5 |         6 |      10 |   15 |    3 |    1 |        4
   8 |        6 |         6 |      10 |   10 |   -1 |    0 |        5
   9 |        1 |        12 |      10 |   12 |   13 |    1 |        0
  10 |        2 |        12 |      10 |   17 |   15 |    1 |        1
  11 |        3 |        12 |      10 |   16 |   16 |    1 |        2
  12 |        4 |        12 |      10 |   15 |    3 |    1 |        3
  13 |        5 |        12 |      10 |   10 |   -1 |    0 |        4
(13 rows)