# pgr_bellmanFord - Experimental¶

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

• 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 ANY-INTEGER and ANY-NUMERICAL
• 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 3.0.0
• New experimental function

Support

• Supported versions: current(3.0)

## Description¶

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.

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])

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)



### 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)



## Parameters¶

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
• 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

## Results Columns¶

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.