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:  Graph is not DAG
CONTEXT:  SQL function "pgr_topologicalsort" statement 1

See Also

Indices and tables