pgr_topologicalSort - Experimental

pgr_topologicalSort - Linear ordering of the vertices for directed acyclic graphs (DAG).

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

Description

The topological sort algorithm creates a linear ordering of the vertices such that if edge \((u,v)\) appears in the graph, then \(v\) comes before \(u\) in the ordering.

The main characteristics are:

  • Process is valid for directed acyclic graphs only. otherwise it will throw warnings.

  • For optimization purposes, if there are more than one answer, the function

    will return one of them.

  • The returned values are ordered in topological order:

  • Running time: \(O(V + E)\)

Signatures

Summary

pgr_topologicalSort( Edges SQL )
RETURNS SET OF (seq, sorted_v)
OR EMPTY SET
Example :

Topologically sorting the graph 

SELECT * FROM pgr_topologicalsort(
  $$SELECT id, source, target, cost
  FROM edges WHERE cost >= 0
  UNION
  SELECT id, target, source, reverse_cost
  FROM edges WHERE cost < 0$$);
 seq  sorted_v
-----+----------
   1         1
   2         5
   3         2
   4         4
   5         3
   6        13
   7        14
   8        15
   9        10
  10         6
  11         7
  12         8
  13         9
  14        11
  15        16
  16        12
  17        17
(17 rows)

Parameters

Parameter

Type

Description

Edges SQL

TEXT

Edges SQL as described below.

Inner Queries

Edges SQL

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 )

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 set of (seq, sorted_v)

Column

Type

Description

seq

INTEGER

Sequential value starting from \(1\)

sorted_v

BIGINT

Linear topological ordering of the vertices

Additional examples

Example :

Topologically sorting the one way segments 

SELECT * FROM pgr_topologicalsort(
  $$SELECT id, source, target, cost, -1 AS reverse_cost
  FROM edges WHERE cost >= 0
  UNION
  SELECT id, source, target, -1, reverse_cost
  FROM edges WHERE cost < 0$$);
 seq  sorted_v
-----+----------
   1         5
   2         2
   3         4
   4        13
   5        14
   6         1
   7         3
   8        15
   9        10
  10         6
  11         7
  12         8
  13         9
  14        11
  15        12
  16        16
  17        17
(17 rows)
Example :

Graph is not a DAG 

SELECT * FROM pgr_topologicalsort(
  $$SELECT id, source, target, cost, reverse_cost FROM edges$$);
ERROR:  The graph must be a DAG.
HINT:  Working with Directed Graph

CONTEXT:  SQL function "pgr_topologicalsort" statement 1

See Also

Indices and tables