pgr_bellmanFord
— Returns the shortest path(s) using BellmanFord algorithm.
In particular, the BellmanFord algorithm implemented by Boost.Graph.
Warning
Possible server crash
Warning
Experimental functions
Availability
Support
BellmanFord’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  ANYINTEGER 
Identifier of the edge.  
source  ANYINTEGER 
Identifier of the first end point vertex of the edge.  
target  ANYINTEGER 
Identifier of the second end point vertex of the edge.  
cost  ANYNUMERICAL 
Weight of the edge (source, target)


reverse_cost  ANYNUMERICAL 
1  Weight of the edge (target, source),

Where:
ANYINTEGER:  SMALLINT, INTEGER, BIGINT 

ANYNUMERICAL:  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