pgr_bellmanFord - Experimental

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

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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.

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 .

See Also

Indices and tables