# pgr_bdDijkstra¶

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

Availability:

• 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)

Support

## 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])

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)



## Parameters¶

Parameter Type Default Description
edges_sql TEXT   Inner SQL 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 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 SMALLINT, INTEGER, BIGINT, REAL, FLOAT

## 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.