pgr_bellmanFord - Experimental

pgr_bellmanFord — Returns the shortest path(s) using Bellman-Ford algorithm. In particular, the Bellman-Ford algorithm implemented by Boost.Graph.

Boost Graph Inside

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 3.2.0

  • New experimental function:

    • pgr_bellmanFord(Combinations)

• Version 3.0.0

  • New experimental function

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])
pgr_bellmanFord(Edges SQL, Combinations SQL [, directed]) -- Experimental on v3.2

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	TEXT		Edges query as described below.
Combinations SQL	TEXT		Combinations 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	When true Graph is considered Directed When false the graph is considered as Undirected.

Inner Queries

Edges 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

ANY-NUMERICAL

SMALLINT, INTEGER, BIGINT, REAL, FLOAT

Combinations query

Column	Type	Default	Description
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.

Where:

ANY-INTEGER

SMALLINT, INTEGER, BIGINT

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. Many to One Many to Many
end_vid	BIGINT	Identifier of the ending vertex. Returned when multiple ending vertices are in the query. One to Many Many to Many
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.

See Also

• https://en.wikipedia.org/wiki/Bellman%E2%80%93Ford_algorithm

• The queries use the Sample Data network.

Indices and tables

• Index

• Search Page