pgr_bellmanFord
— Returns the shortest path(s) using Bellman-Ford algorithm.
In particular, the Bellman-Ford algorithm implemented by Boost.Graph.
Warning
Possible server crash
Warning
Experimental functions
Availability
Support
Bellman-Ford’s algorithm, is named after Richard Bellman and Lester Ford, who first published it in 1958 and 1956, respectively.
It is a graph search algorithm that computes shortest paths from
a starting vertex (start_vid
) to an ending vertex (end_vid
) in a graph where some of the edge weights may be negative number. Though it is more versatile, it is slower than Dijkstra’s algorithm/
This implementation can be used with a directed graph and an undirected graph.
Summary
pgr_bellmanFord(edges_sql, from_vid, to_vid [, directed])
pgr_bellmanFord(edges_sql, from_vid, to_vids [, directed])
pgr_bellmanFord(edges_sql, from_vids, to_vid [, directed])
pgr_bellmanFord(edges_sql, from_vids, to_vids [, directed])
RETURNS SET OF (seq, path_seq, node, edge, cost, agg_cost)
OR EMPTY SET
Using defaults
pgr_bellmanFord(TEXT edges_sql, BIGINT start_vid, BIGINT end_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_bellmanFord(
'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)
pgr_bellmanFord(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_bellmanFord(
'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)
pgr_bellmanFord(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 \(\{ 3, 5\}\) on an undirected graph |
---|
SELECT * FROM pgr_bellmanFord(
'SELECT id, source, target, cost, reverse_cost FROM edge_table',
2, ARRAY[3,5],
FALSE
);
seq | path_seq | end_vid | node | edge | cost | agg_cost
-----+----------+---------+------+------+------+----------
1 | 1 | 3 | 2 | 2 | 1 | 0
2 | 2 | 3 | 3 | -1 | 0 | 1
3 | 1 | 5 | 2 | 4 | 1 | 0
4 | 2 | 5 | 5 | -1 | 0 | 1
(4 rows)
pgr_bellmanFord(edges_sql, from_vids, to_vid [, directed])
RETURNS SET OF (seq, path_seq, start_vid, node, edge, cost, agg_cost)
OR EMPTY SET
Example: | From vertices \(\{2, 11\}\) to vertex \(5\) on a directed graph |
---|
SELECT * FROM pgr_bellmanFord(
'SELECT id, source, target, cost, reverse_cost FROM edge_table',
ARRAY[2,11], 5
);
seq | path_seq | start_vid | node | edge | cost | agg_cost
-----+----------+-----------+------+------+------+----------
1 | 1 | 2 | 2 | 4 | 1 | 0
2 | 2 | 2 | 5 | -1 | 0 | 1
3 | 1 | 11 | 11 | 13 | 1 | 0
4 | 2 | 11 | 12 | 15 | 1 | 1
5 | 3 | 11 | 9 | 9 | 1 | 2
6 | 4 | 11 | 6 | 8 | 1 | 3
7 | 5 | 11 | 5 | -1 | 0 | 4
(7 rows)
pgr_bellmanFord(edges_sql, from_vids, to_vids [, directed])
RETURNS SET OF (seq, path_seq, start_vid, end_vid, node, edge, cost, agg_cost)
OR EMPTY SET
Example: | From vertices \(\{2, 11\}\) to vertices \(\{3, 5\}\) on an undirected graph |
---|
SELECT * FROM pgr_bellmanFord(
'SELECT id, source, target, cost, reverse_cost FROM edge_table',
ARRAY[2,11], ARRAY[3,5]
);
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 | 5 | 2 | 4 | 1 | 0
8 | 2 | 2 | 5 | 5 | -1 | 0 | 1
9 | 1 | 11 | 3 | 11 | 13 | 1 | 0
10 | 2 | 11 | 3 | 12 | 15 | 1 | 1
11 | 3 | 11 | 3 | 9 | 16 | 1 | 2
12 | 4 | 11 | 3 | 4 | 3 | 1 | 3
13 | 5 | 11 | 3 | 3 | -1 | 0 | 4
14 | 1 | 11 | 5 | 11 | 13 | 1 | 0
15 | 2 | 11 | 5 | 12 | 15 | 1 | 1
16 | 3 | 11 | 5 | 9 | 9 | 1 | 2
17 | 4 | 11 | 5 | 6 | 8 | 1 | 3
18 | 5 | 11 | 5 | 5 | -1 | 0 | 4
(18 rows)
Description of the parameters of the signatures
Parameter | Type | Default | Description |
---|---|---|---|
edges_sql | TEXT |
SQL query as described above. | |
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 |
|
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 |
Returns set of (seq, path_seq [, start_vid] [, end_vid], node, edge, cost, agg_cost)
Column | Type | Description |
---|---|---|
seq | INT |
Sequential value starting from 1. |
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 . |
Indices and tables