# pgRouting Manual (3.1)

## pgr_topologicalSort - Experimental

`pgr_topologicalSort` — Returns the linear ordering of the vertices(s) for weighted directed acyclic graphs(DAG). In particular, the topological sort algorithm implemented by Boost.Graph.

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(3.1) 3.0

- TBD

## 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.

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.

  - 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

  For a directed graph

    SELECT * FROM pgr_topologicalsort(
      'SELECT id,source,target,cost,reverse_cost FROM edge_table1'
    );
     seq | sorted_v
    -----+----------
       1 |        0
       2 |        1
       3 |        3
       4 |        2
    (4 rows)

## Parameters

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

## Inner query

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

## Result Columns

Returns set of `(seq, sorted_v)`

Column | Type | Description
--- | --- | ---
seq | `INT` | Sequential value starting from 1.
sorted_v | `BIGINT` | Linear ordering of the vertices(ordered in topological order)

## See Also

- https://en.wikipedia.org/wiki/Topological_sorting

- The queries use the Sample Data network.

Indices and tables

- Index

- Search Page