pgr_bellmanFord  Experimental¶
pgr_bellmanFord
— Returns the shortest path(s) using BellmanFord algorithm.
In particular, the BellmanFord algorithm implemented by Boost.Graph.
Warning
Possible server crash
These functions might create a server crash
Warning
Experimental functions
They are not officially of the current release.
They likely will not be officially be part of the next release:
The functions might not make use of ANYINTEGER and ANYNUMERICAL
Name might change.
Signature might change.
Functionality might change.
pgTap tests might be missing.
Might need c/c++ coding.
May lack documentation.
Documentation if any might need to be rewritten.
Documentation examples might need to be automatically generated.
Might need a lot of feedback from the comunity.
Might depend on a proposed function of pgRouting
Might depend on a deprecated function of pgRouting
Availability
Version 3.2.0
New experimental function:
pgr_bellmanFord(Combinations)
Version 3.0.0
New experimental function
Description¶
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.
 The main characteristics are:
Process is valid for edges with both positive and negative edge weights.
Values are returned when there is a path.
When the start vertex and the end vertex are the same, there is no path. The agg_cost would be 0.
When the start vertex and the end vertex are different, and there exists a path between them without having a negative cycle. The agg_cost would be some finite value denoting the shortest distance between them.
When the start vertex and the end vertex are different, and there exists a path between them, but it contains a negative cycle. In such case, agg_cost for those vertices keep on decreasing furthermore, Hence agg_cost can’t be defined for them.
When the start vertex and the end vertex are different, and there is no path. The agg_cost is \(\infty\).
For optimization purposes, any duplicated value in the start_vids or end_vids are ignored.
The returned values are ordered:
start_vid ascending
end_vid ascending
Running time: \(O( start\_vids  * ( V * E))\)
Signatures¶
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])
pgr_bellmanFord(Edges SQL, Combinations SQL [, directed])
RETURNS SET OF (seq, path_seq, node, edge, cost, agg_cost)
OR EMPTY SET
Using defaults
pgr_bellmanFord(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 \(3\) 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)
One to One¶
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)
One to many¶
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)
Many to One¶
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)
Many to Many¶
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)
Combinations¶
pgr_bellmanFord(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 an undirected graph.
SELECT * FROM pgr_bellmanFord(
'SELECT id, source, target, cost, reverse_cost FROM edge_table',
'SELECT * FROM ( VALUES (2, 3), (11, 5) ) 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  11  5  11  13  1  0
8  2  11  5  12  15  1  1
9  3  11  5  9  9  1  2
10  4  11  5  6  8  1  3
11  5  11  5  5  1  0  4
(11 rows)
Parameters¶
Description of the parameters of the signatures
Parameter 
Type 
Default 
Description 

Edges SQL 

Edges query as described below. 

Combinations SQL 

Combinations query as described below. 

start_vid 

Identifier of the starting vertex of the path. 

start_vids 

Array of identifiers of starting vertices. 

end_vid 

Identifier of the ending vertex of the path. 

end_vids 

Array of identifiers of ending vertices. 

directed 



Inner Queries¶
Edges query¶
Column 
Type 
Default 
Description 

id 

Identifier of the edge. 

source 

Identifier of the first end point vertex of the edge. 

target 

Identifier of the second end point vertex of the edge. 

cost 

Weight of the edge (source, target)


reverse_cost 

1 
Weight of the edge (target, source),

Where:
 ANYINTEGER
SMALLINT, INTEGER, BIGINT
 ANYNUMERICAL
SMALLINT, INTEGER, BIGINT, REAL, FLOAT
Combinations query¶
Column 
Type 
Default 
Description 

source 

Identifier of the first end point vertex of the edge. 

target 

Identifier of the second end point vertex of the edge. 
Where:
 ANYINTEGER
SMALLINT, INTEGER, BIGINT
Results Columns¶
Returns set of (seq, path_seq [, start_vid] [, end_vid], node, edge, cost, agg_cost)
Column 
Type 
Description 

seq 

Sequential value starting from 1. 
path_seq 

Relative position in the path. Has value 1 for the beginning of a path. 
start_vid 

Identifier of the starting vertex. Returned when multiple starting vetrices are in the query. 
end_vid 

Identifier of the ending vertex. Returned when multiple ending vertices are in the query. 
node 

Identifier of the node in the path from 
edge 

Identifier of the edge used to go from 
cost 

Cost to traverse from 
agg_cost 

Aggregate cost from 
See Also¶
https://en.wikipedia.org/wiki/Bellman%E2%80%93Ford_algorithm
The queries use the Sample Data network.
Indices and tables