pgr_kruskal

pgr_kruskal — Minimum spanning tree of a graph using Kruskal’s algorithm.

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Availability

  • Version 3.0.0

    • New Official function

Description

This algorithm finds the minimum spanning forest in a possibly disconnected graph using Kruskal’s algorithm.

The main Characteristics are:

  • It’s implementation is only on undirected graph.

  • Process is done only on edges with positive costs.

  • When the graph is connected

    • The resulting edges make up a tree

  • When the graph is not connected,

    • Finds a minimum spanning tree for each connected component.

    • The resulting edges make up a forest.

  • The total weight of all the edges in the tree or forest is minimized.

  • Kruskal’s running time: \(O(E * log E)\)

  • EMPTY SET is returned when there are no edges in the graph.

Signatures

Summary

pgr_kruskal(Edges SQL)
RETURNS SET OF (edge, cost)
OR EMPTY SET
Example:

Minimum spanning forest

SELECT * FROM pgr_kruskal(
  'SELECT id, source, target, cost, reverse_cost
  FROM edges ORDER BY id'
) ORDER BY edge;
 edge | cost
------+------
    1 |    1
    2 |    1
    3 |    1
    6 |    1
    7 |    1
   10 |    1
   11 |    1
   12 |    1
   13 |    1
   14 |    1
   15 |    1
   16 |    1
   17 |    1
   18 |    1
(14 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 (edge, cost)

Column

Type

Description

edge

BIGINT

Identifier of the edge.

cost

FLOAT

Cost to traverse the edge.

See Also

Indices and tables