pgr_biconnectedComponents - Experimental

pgr_biconnectedComponents — Return the biconnected components of an undirected graph. In particular, the algorithm implemented by Boost.Graph.

_images/boost-inside.jpeg

Boost Graph Inside

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

Synopsis

The biconnected components of an undirected graph are the maximal subsets of vertices such that the removal of a vertex from particular component will not disconnect the component. Unlike connected components, vertices may belong to multiple biconnected components. Vertices can be present in multiple biconnected components, but each edge can only be contained in a single biconnected component. So, the output only has edge version.

This implementation can only be used with an undirected graph.

Characteristics

The main Characteristics are:

  • Components are described by edges
  • The returned values are ordered:
    • component ascending
    • edge ascending
  • Running time: \(O(V + E)\)

Signatures

pgr_biconnectedComponents(edges_sql)

RETURNS SET OF (seq, component, n_seq, edge)
    OR EMPTY SET

The signature is for a undirected graph.

Example: 
SELECT * FROM pgr_biconnectedComponents(
    'SELECT id, source, target, cost, reverse_cost FROM edge_table'
);
 seq | component | n_seq | edge
-----+-----------+-------+------
   1 |         1 |     1 |    1
   2 |         2 |     1 |    2
   3 |         2 |     2 |    3
   4 |         2 |     3 |    4
   5 |         2 |     4 |    5
   6 |         2 |     5 |    8
   7 |         2 |     6 |    9
   8 |         2 |     7 |   10
   9 |         2 |     8 |   11
  10 |         2 |     9 |   12
  11 |         2 |    10 |   13
  12 |         2 |    11 |   15
  13 |         2 |    12 |   16
  14 |         6 |     1 |    6
  15 |         7 |     1 |    7
  16 |        14 |     1 |   14
  17 |        17 |     1 |   17
  18 |        18 |     1 |   18
(18 rows)
_images/bcc_sampledata.png

Description of the Signatures

Description of the edges_sql query for components functions

edges_sql:an SQL query, which should return a set of rows with the following columns:
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

Description of the parameters of the signatures

Parameter Type Default Description
edges_sql TEXT   SQL query as described above.

Description of the return values for biconnected components, connected components (edge version) and strongly connected components

Returns set of (seq, component, n_seq, edge)

Column Type Description
seq INT Sequential value starting from 1.
component BIGINT Component identifier. It is equal to the minimum edge identifier in the component.
n_seq INT It is a sequential value starting from 1 in a component.
edge BIGINT Identifier of the edge.

See Also

Indices and tables