pgr_maxCardinalityMatch
— Calculates a maximum cardinality matching in a graph.
Warning
Experimental functions
Availability:
Characteristics
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.
The graph can be directed or undirected.
Running time: \(O( E*V * \alpha(E,V))\)
- \(\alpha(E,V)\) is the inverse of the Ackermann function.
pgr_MaximumCardinalityMatching(edges_sql) - Proposed
pgr_MaximumCardinalityMatching(edges_sql, directed) - Proposed
RETURNS SET OF (seq, edge_id, source, target)
OR EMPTY SET
pgr_MaximumCardinalityMatching(edges_sql)
RETURNS SET OF (seq, edge_id, source, target) OR EMPTY SET
The minimal use calculates one possible maximum cardinality matching on a directed graph.
Example: |
---|
SELECT * FROM pgr_maxCardinalityMatch(
'SELECT id, source, target, cost AS going, reverse_cost AS coming FROM edge_table'
);
seq | edge | source | target
-----+------+--------+--------
1 | 1 | 1 | 2
2 | 3 | 4 | 3
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)
pgr_MaximumCardinalityMatching(edges_sql, directed)
RETURNS SET OF (seq, edge_id, source, target) OR EMPTY SET
The complete signature calculates one possible maximum cardinality matching.
Example: |
---|
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)
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, DOUBLE PRECISION
Column | Type | Description |
---|---|---|
edges_sql | TEXT |
SQL query as described above. |
directed | BOOLEAN |
(optional) Determines the type of the graph. Default TRUE. |
Column | Type | Description |
---|---|---|
seq | INT |
Sequential value starting from 1. |
edge | BIGINT |
Identifier of the edge in the original query(edges_sql). |
source | BIGINT |
Identifier of the first end point of the edge. |
target | BIGINT |
Identifier of the second end point of the edge. |