pgr_kruskal
¶
pgr_kruskal
— Minimum spanning tree of a graph using Kruskal’s algorithm.
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)
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 (
|
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¶
- Spanning Tree - Category
- Kruskal - Family of functions
- The queries use the Sample Data network.
- Boost: Kruskal’s algorithm
- Wikipedia: Kruskal’s algorithm
Indices and tables