pgr_transitiveClosure - Experimental

pgr_transitiveClosure — Returns the transitive closure graph of the input graph. In particular, the transitive closure algorithm implemented by Boost.Graph.

_images/boost-inside.jpeg

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 3.0.0
    • New experimental function

Support

  • Supported versions: current(3.0)

Description

The transitive_closure() function transforms the input graph g into the transitive closure graph tc.

This implementation can only be used with a directed graph with no cycles i.e. directed acyclic graph.

The main characteristics are:
  • Process is valid for directed acyclic graphs only. otherwise it will throw warnings.
  • The returned values are not ordered:
  • Running time: \(O(|V||E|)\)

Signatures

Summary

The pgr_transitiveClosure function has the following signature:

pgr_transitiveClosure(Edges SQL)
RETURNS SETOF (id, vid, target_array)
Example:Complete Graph of 3 vertexs
SELECT * FROM pgr_transitiveclosure(
  'SELECT id,source,target,cost,reverse_cost FROM edge_table1'
);
 seq | vid | target_array
-----+-----+--------------
   1 |   0 | {1,3,2}
   2 |   1 | {3,2}
   3 |   3 | {2}
   4 |   2 | {}
(4 rows)

Parameters

Column Type Description
Edges SQL TEXT SQL query as described in Inner query

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
ANY-NUMERICAL:SMALLINT, INTEGER, BIGINT, REAL, FLOAT

Result Columns

RETURNS SETOF (seq, vid, target_array)

The function returns a single row. The columns of the row are:

Column Type Description
seq INTEGER Sequential value starting from 1.
vid BIGINT Identifier of the vertex.
target_array ARRAY[BIGINT] Array of identifiers of the vertices that are reachable from vertex v.

Additional Examples

Example:Some sub graphs of the sample data
SELECT * FROM pgr_transitiveclosure(
  'SELECT id,source,target,cost,reverse_cost FROM edge_table where id=2'
);
 seq | vid | target_array
-----+-----+--------------
   1 |   2 | {}
   2 |   3 | {2}
(2 rows)

SELECT * FROM pgr_transitiveclosure(
  'SELECT id,source,target,cost,reverse_cost FROM edge_table where id=3'
);
 seq | vid | target_array
-----+-----+--------------
   1 |   3 | {}
   2 |   4 | {3}
(2 rows)

SELECT * FROM pgr_transitiveclosure(
  'SELECT id,source,target,cost,reverse_cost FROM edge_table where id=2 or id=3'
);
 seq | vid | target_array
-----+-----+--------------
   1 |   2 | {}
   2 |   3 | {2}
   3 |   4 | {3,2}
(3 rows)

SELECT * FROM pgr_transitiveclosure(
  'SELECT id,source,target,cost,reverse_cost FROM edge_table where id=11'
);
 seq | vid | target_array
-----+-----+--------------
   1 |   6 | {11}
   2 |  11 | {}
(2 rows)

-- q3
SELECT * FROM pgr_transitiveclosure(
  'SELECT id,source,target,cost,reverse_cost FROM edge_table where cost=-1 or reverse_cost=-1'
);
 seq | vid | target_array
-----+-----+---------------
   1 |   2 | {}
   2 |   3 | {11,12,6,2}
   3 |   4 | {11,12,3,6,2}
   4 |   6 | {11,12}
   5 |  11 | {12}
   6 |  10 | {11,12}
   7 |  12 | {}
(7 rows)

See Also

Indices and tables