pgr_maxCardinalityMatch

pgr_maxCardinalityMatch — Calculates a maximum cardinality matching in a graph.

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Availability

  • Version 3.0.0
    • Official function
  • Version 2.5.0
    • Renamed from pgr_maximumCardinalityMatching
    • Proposed function
  • Version 2.3.0
    • New Experimental function

Support

Description

The main characteristics are:

  • A matching or independent edge set in a graph is a set of edges without common vertices.
  • A maximum matching is a matching that contains the largest possible number of edges.
    • There may be many maximum matchings.
    • Calculates one possible maximum cardinality matching in a graph.
  • The graph can be directed or undirected.
  • Running time: \(O( E*V * \alpha(E,V))\)

Signatures

pgr_maxCardinalityMatch(Edges SQL [, directed])

RETURNS SET OF (seq, edge_id, source, target)
OR EMPTY SET
Example:For an undirected graph 
SELECT * FROM pgr_maxCardinalityMatch(
    'SELECT id, source, target, cost AS going, reverse_cost AS coming FROM edge_table',
    directed := false
);
 seq | edge | source | target
-----+------+--------+--------
   1 |    1 |      1 |      2
   2 |    3 |      3 |      4
   3 |    9 |      6 |      9
   4 |    6 |      7 |      8
   5 |   14 |     10 |     13
   6 |   13 |     11 |     12
   7 |   17 |     14 |     15
   8 |   18 |     16 |     17
(8 rows)

Parameters

Parameter Type Default Description
edges_sql TEXT   SQL query as described above.
directed BOOLEAN true Determines the type of the graph. - When true Graph is considered Directed - When false the graph is considered as Undirected.

Inner query

Edges SQL:an SQL query, which should return a set of rows with the following columns:
Column Type 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.
going ANY-NUMERIC A positive value represents the existence of the edge (source, target).
coming ANY-NUMERIC A positive value represents the existence of the edge (target, source).

Where:

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

Result Columns

Column Type Description
seq INT Sequential value starting from 1.
edge BIGINT Identifier of the edge in the original query.
source BIGINT Identifier of the first end point of the edge.
target BIGINT Identifier of the second end point of the edge.