pgr_bdDijkstraCost¶
pgr_bdDijkstraCost
— Returns the shortest path(s)’s cost using Bidirectional Dijkstra algorithm.
Availability:
- Version 3.0.0
- Official function
- Version 2.5.0
- New proposed function
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_bdDijkstraCost(edges_sql, from_vid, to_vid [, directed])
pgr_bdDijkstraCost(edges_sql, from_vid, to_vids [, directed])
pgr_bdDijkstraCost(edges_sql, from_vids, to_vid [, directed])
pgr_bdDijkstraCost(edges_sql, from_vids, to_vids [, directed])
RETURNS SET OF (start_vid, end_vid, agg_cost)
OR EMPTY SET
Using default
pgr_bdDijkstraCost(edges_sql, from_vid, to_vid)
RETURNS SET OF (seq, path_seq, node, edge, cost, agg_cost)
OR EMPTY SET
Example: | From vertex \(2\) to vertex \(3\) on a directed graph |
---|
SELECT * FROM pgr_bdDijkstraCost(
'SELECT id, source, target, cost, reverse_cost FROM edge_table',
2, 3
);
start_vid | end_vid | agg_cost
-----------+---------+----------
2 | 3 | 5
(1 row)
One to One¶
pgr_bdDijkstraCost(edges_sql, from_vid, to_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_bdDijkstraCost(edges_sql, from_vid, to_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_bdDijkstraCost(
'SELECT id, source, target, cost, reverse_cost FROM edge_table',
2, ARRAY[3, 11]);
start_vid | end_vid | agg_cost
-----------+---------+----------
2 | 3 | 5
2 | 11 | 3
(2 rows)
Many to One¶
pgr_bdDijkstraCost(edges_sql, from_vids, to_vids [, 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 |
|
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)
|
|
reverse_cost | ANY-NUMERICAL |
-1 | Weight of the edge (target, source),
|
Where:
ANY-INTEGER: | SMALLINT, INTEGER, BIGINT |
---|---|
ANY-NUMERICAL: | SMALLINT, INTEGER, BIGINT, REAL, FLOAT |
Result Columns¶
Returns SET OF (start_vid, end_vid, agg_cost)
Column | Type | Description |
---|---|---|
start_vid | BIGINT |
Identifier of the starting vertex. Used when multiple starting vetrices are in the query. |
end_vid | BIGINT |
Identifier of the ending vertex. Used when multiple ending vertices are in the query. |
agg_cost | FLOAT |
Aggregate cost from start_vid to end_vid . |
See Also¶
- The queries use the Sample Data network.
- pgr_bdDijkstra
- https://www.cs.princeton.edu/courses/archive/spr06/cos423/Handouts/EPP%20shortest%20path%20algorithms.pdf
- https://en.wikipedia.org/wiki/Bidirectional_search
Indices and tables