# pgr_bdDijkstra¶

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

Boost Graph Inside

Availability:

• Version 3.2.0

• New proposed function:

• pgr_bdDijkstra(Combinations)

• Version 3.0.0

• Official function

• Version 2.5.0

• New Proposed functions:

• pgr_bdDijkstra(One to Many)

• pgr_bdDijkstra(Many to One)

• pgr_bdDijkstra(Many to Many)

• Version 2.4.0

• Signature change on pgr_bdDijsktra(One to One)

• Old signature no longer supported

• Version 2.0.0

• Official pgr_bdDijkstra(One to One)

## Description¶

The main characteristics are:

• 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 agg_cost the non included values (v, v) is 0

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

• The agg_cost the non included values (u, v) is $$\infty$$

• 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]) -- Proposed on v3.2

RETURNS SET OF (seq, path_seq [, start_vid] [, end_vid], node, edge, cost, agg_cost)
OR EMPTY SET


Using defaults

pgr_bdDijkstra(Edges SQL, start_vid, end_vid)
RETURNS SET OF (seq, path_seq, node, edge, cost, agg_cost)
OR EMPTY SET

Example

From vertex $$2$$ to vertex $$3$$

SELECT * FROM pgr_bdDijkstra(
'SELECT id, source, target, cost, reverse_cost FROM edge_table',
2, 3
);
seq | path_seq | node | edge | cost | agg_cost
-----+----------+------+------+------+----------
1 |        1 |    2 |    4 |    1 |        0
2 |        2 |    5 |    8 |    1 |        1
3 |        3 |    6 |    9 |    1 |        2
4 |        4 |    9 |   16 |    1 |        3
5 |        5 |    4 |    3 |    1 |        4
6 |        6 |    3 |   -1 |    0 |        5
(6 rows)



### One to One¶

pgr_bdDijkstra(Edges SQL, start_vid, end_vid [, directed])
RETURNS SET OF (seq, path_seq, node, edge, cost, agg_cost)
OR EMPTY SET

Example

From vertex $$2$$ to vertex $$3$$ on an undirected graph

SELECT * FROM pgr_bdDijkstra(
'SELECT id, source, target, cost, reverse_cost FROM edge_table',
2, 3,
false
);
seq | path_seq | node | edge | cost | agg_cost
-----+----------+------+------+------+----------
1 |        1 |    2 |    2 |    1 |        0
2 |        2 |    3 |   -1 |    0 |        1
(2 rows)



### One to many¶

pgr_bdDijkstra(Edges SQL, start_vid, end_vids [, directed])
RETURNS SET OF (seq, path_seq, end_vid, node, edge, cost, agg_cost)
OR EMPTY SET

Example

From vertex $$2$$ to vertices $$\{3, 11\}$$ on a directed graph

SELECT * FROM pgr_bdDijkstra(
'SELECT id, source, target, cost, reverse_cost FROM edge_table',
2, ARRAY[3, 11]);
seq | path_seq | end_vid | node | edge | cost | agg_cost
-----+----------+---------+------+------+------+----------
1 |        1 |       3 |    2 |    4 |    1 |        0
2 |        2 |       3 |    5 |    8 |    1 |        1
3 |        3 |       3 |    6 |    9 |    1 |        2
4 |        4 |       3 |    9 |   16 |    1 |        3
5 |        5 |       3 |    4 |    3 |    1 |        4
6 |        6 |       3 |    3 |   -1 |    0 |        5
7 |        1 |      11 |    2 |    4 |    1 |        0
8 |        2 |      11 |    5 |    8 |    1 |        1
9 |        3 |      11 |    6 |   11 |    1 |        2
10 |        4 |      11 |   11 |   -1 |    0 |        3
(10 rows)



### Many to One¶

pgr_bdDijkstra(Edges SQL, start_vids, end_vid [, directed])
RETURNS SET OF (seq, path_seq, start_vid, node, edge, cost, agg_cost)
OR EMPTY SET

Example

From vertices $$\{2, 7\}$$ to vertex $$3$$ on a directed graph

SELECT * FROM pgr_bdDijkstra(
'SELECT id, source, target, cost, reverse_cost FROM edge_table',
ARRAY[2, 7], 3);
seq | path_seq | start_vid | node | edge | cost | agg_cost
-----+----------+-----------+------+------+------+----------
1 |        1 |         2 |    2 |    4 |    1 |        0
2 |        2 |         2 |    5 |    8 |    1 |        1
3 |        3 |         2 |    6 |    9 |    1 |        2
4 |        4 |         2 |    9 |   16 |    1 |        3
5 |        5 |         2 |    4 |    3 |    1 |        4
6 |        6 |         2 |    3 |   -1 |    0 |        5
7 |        1 |         7 |    7 |    6 |    1 |        0
8 |        2 |         7 |    8 |    7 |    1 |        1
9 |        3 |         7 |    5 |    8 |    1 |        2
10 |        4 |         7 |    6 |    9 |    1 |        3
11 |        5 |         7 |    9 |   16 |    1 |        4
12 |        6 |         7 |    4 |    3 |    1 |        5
13 |        7 |         7 |    3 |   -1 |    0 |        6
(13 rows)



### Many to Many¶

pgr_bdDijkstra(Edges SQL, start_vids, end_vids [, directed])
RETURNS SET OF (seq, path_seq, start_vid, end_vid, node, edge, cost, agg_cost)
OR EMPTY SET

Example

From vertices $$\{2, 7\}$$ to vertices $$\{3, 11\}$$ on a directed graph

SELECT * FROM pgr_bdDijkstra(
'SELECT id, source, target, cost, reverse_cost FROM edge_table',
ARRAY[2, 7], ARRAY[3, 11]);
seq | path_seq | start_vid | end_vid | node | edge | cost | agg_cost
-----+----------+-----------+---------+------+------+------+----------
1 |        1 |         2 |       3 |    2 |    4 |    1 |        0
2 |        2 |         2 |       3 |    5 |    8 |    1 |        1
3 |        3 |         2 |       3 |    6 |    9 |    1 |        2
4 |        4 |         2 |       3 |    9 |   16 |    1 |        3
5 |        5 |         2 |       3 |    4 |    3 |    1 |        4
6 |        6 |         2 |       3 |    3 |   -1 |    0 |        5
7 |        1 |         2 |      11 |    2 |    4 |    1 |        0
8 |        2 |         2 |      11 |    5 |    8 |    1 |        1
9 |        3 |         2 |      11 |    6 |   11 |    1 |        2
10 |        4 |         2 |      11 |   11 |   -1 |    0 |        3
11 |        1 |         7 |       3 |    7 |    6 |    1 |        0
12 |        2 |         7 |       3 |    8 |    7 |    1 |        1
13 |        3 |         7 |       3 |    5 |    8 |    1 |        2
14 |        4 |         7 |       3 |    6 |    9 |    1 |        3
15 |        5 |         7 |       3 |    9 |   16 |    1 |        4
16 |        6 |         7 |       3 |    4 |    3 |    1 |        5
17 |        7 |         7 |       3 |    3 |   -1 |    0 |        6
18 |        1 |         7 |      11 |    7 |    6 |    1 |        0
19 |        2 |         7 |      11 |    8 |    7 |    1 |        1
20 |        3 |         7 |      11 |    5 |   10 |    1 |        2
21 |        4 |         7 |      11 |   10 |   12 |    1 |        3
22 |        5 |         7 |      11 |   11 |   -1 |    0 |        4
(22 rows)



### Combinations¶

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

Example

Using a combinations table on a directed graph.

SELECT * FROM pgr_bdDijkstra(
'SELECT id, source, target, cost, reverse_cost FROM edge_table',
'SELECT * FROM ( VALUES (2, 3), (7, 11) ) AS t(source, target)');
seq | path_seq | start_vid | end_vid | node | edge | cost | agg_cost
-----+----------+-----------+---------+------+------+------+----------
1 |        1 |         2 |       3 |    2 |    4 |    1 |        0
2 |        2 |         2 |       3 |    5 |    8 |    1 |        1
3 |        3 |         2 |       3 |    6 |    9 |    1 |        2
4 |        4 |         2 |       3 |    9 |   16 |    1 |        3
5 |        5 |         2 |       3 |    4 |    3 |    1 |        4
6 |        6 |         2 |       3 |    3 |   -1 |    0 |        5
7 |        1 |         7 |      11 |    7 |    6 |    1 |        0
8 |        2 |         7 |      11 |    8 |    7 |    1 |        1
9 |        3 |         7 |      11 |    5 |   10 |    1 |        2
10 |        4 |         7 |      11 |   10 |   12 |    1 |        3
11 |        5 |         7 |      11 |   11 |   -1 |    0 |        4
(11 rows)



## Parameters¶

Parameter

Type

Default

Description

Edges SQL

TEXT

Edges query as described below

Combinations SQL

TEXT

Combinations query 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.

directed

BOOLEAN

true

• When true Graph is considered Directed

• When false the graph is considered as Undirected.

## Inner queries¶

### Edges query¶

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)

• When negative: edge (source, target) does not exist, therefore it’s not part of the graph.

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 query¶

Column

Type

Default

Description

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.

Where:

ANY-INTEGER

SMALLINT, INTEGER, BIGINT

## Result Columns¶

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

Column

Type

Description

seq

INT

Sequential value starting from 1.

path_id

INT

Path identifier. Has value 1 for the first of a path. Used when there are multiple paths for the same start_vid to end_vid combination.

path_seq

INT

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_v to node.