pgr_kruskalBFS¶
pgr_kruskalBFS
— Prim algorithm for Minimum Spanning Tree with Depth First
Search ordering.
Availability
- Version 3.0.0
- New Official function
Support
Description¶
Visits and extracts the nodes information in Breath First Search ordering of the Minimum Spanning Tree created using Prims’s algorithm.
The main Characteristics are:
- It’s implementation is only on undirected graph.
- Process is done only on edges with positive costs.
- The total weight of all the edges in the tree or forest is minimized.
- 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.
- Kruskal’s running time: \(O(E * log E)\)
- Returned tree nodes from a root vertex are on Breath First Search order
- Breath First Search Running time: \(O(E + V)\)
Signatures¶
pgr_kruskalBFS(Edges SQL, Root vid [, max_depth])
pgr_kruskalBFS(Edges SQL, Root vids [, max_depth])
RETURNS SET OF (seq, depth, start_vid, node, edge, cost, agg_cost)
Single vertex¶
pgr_kruskalBFS(Edges SQL, Root vid [, max_depth])
RETURNS SET OF (seq, depth, start_vid, node, edge, cost, agg_cost)
Example: | The Minimum Spanning Tree having as root vertex \(2\) |
---|
SELECT * FROM pgr_kruskalBFS(
'SELECT id, source, target, cost, reverse_cost FROM edge_table ORDER BY id',
2
);
seq | depth | start_vid | node | edge | cost | agg_cost
-----+-------+-----------+------+------+------+----------
1 | 0 | 2 | 2 | -1 | 0 | 0
2 | 1 | 2 | 1 | 1 | 1 | 1
3 | 1 | 2 | 3 | 2 | 1 | 1
4 | 2 | 2 | 4 | 3 | 1 | 2
5 | 3 | 2 | 9 | 16 | 1 | 3
6 | 4 | 2 | 12 | 15 | 1 | 4
7 | 5 | 2 | 11 | 13 | 1 | 5
8 | 6 | 2 | 6 | 11 | 1 | 6
9 | 6 | 2 | 10 | 12 | 1 | 6
10 | 7 | 2 | 5 | 10 | 1 | 7
11 | 7 | 2 | 13 | 14 | 1 | 7
12 | 8 | 2 | 8 | 7 | 1 | 8
13 | 9 | 2 | 7 | 6 | 1 | 9
(13 rows)
Multiple vertices¶
pgr_kruskalBFS(Edges SQL, Root vids [, max_depth])
RETURNS SET OF (seq, depth, start_vid, node, edge, cost, agg_cost)
Example: | The Minimum Spanning Tree starting on vertices \(\{13, 2\}\) with \(depth <= 3\) |
---|
SELECT * FROM pgr_kruskalBFS(
'SELECT id, source, target, cost, reverse_cost FROM edge_table ORDER BY id',
ARRAY[13,2], max_depth := 3
);
seq | depth | start_vid | node | edge | cost | agg_cost
-----+-------+-----------+------+------+------+----------
1 | 0 | 2 | 2 | -1 | 0 | 0
2 | 1 | 2 | 1 | 1 | 1 | 1
3 | 1 | 2 | 3 | 2 | 1 | 1
4 | 2 | 2 | 4 | 3 | 1 | 2
5 | 3 | 2 | 9 | 16 | 1 | 3
6 | 0 | 13 | 13 | -1 | 0 | 0
7 | 1 | 13 | 10 | 14 | 1 | 1
8 | 2 | 13 | 5 | 10 | 1 | 2
9 | 2 | 13 | 11 | 12 | 1 | 2
10 | 3 | 13 | 8 | 7 | 1 | 3
11 | 3 | 13 | 6 | 11 | 1 | 3
12 | 3 | 13 | 12 | 13 | 1 | 3
(12 rows)
Parameters¶
Parameter | Type | Description |
---|---|---|
Edges SQL | TEXT |
SQL query described in Inner query. |
Root vid | BIGINT |
Identifier of the root vertex of the tree.
|
Root vids | ARRAY[ANY-INTEGER] |
Array of identifiers of the root vertices.
|
Optional Parameters¶
Parameter | Type | Default | Description |
---|---|---|---|
max_depth | BIGINT |
\(9223372036854775807\) | Upper limit for depth of node in the tree
|
Inner query¶
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),
|
Where:
ANY-INTEGER: | SMALLINT, INTEGER, BIGINT |
---|---|
ANY-NUMERICAL: | SMALLINT, INTEGER, BIGINT, REAL, FLOAT |
Result Columns¶
Returns SET OF (seq, depth, start_vid, node, edge, cost, agg_cost)
Column | Type | Description |
---|---|---|
seq | BIGINT |
Sequential value starting from \(1\). |
depth | BIGINT |
Depth of the
|
start_vid | BIGINT |
Identifier of the root vertex.
|
node | BIGINT |
Identifier of node reached using edge . |
edge | BIGINT |
Identifier of the
|
cost | FLOAT |
Cost to traverse edge . |
agg_cost | FLOAT |
Aggregate cost from start_vid to node . |
See Also¶
- Spanning Tree - Category
- Kruskal - Family of functions
- The queries use the Sample Data network.
- Boost: Kruskal’s algorithm documentation
- Wikipedia: Kruskal’s algorithm
Indices and tables