pgr_kruskalDFS
¶
pgr_kruskalDFS
— Kruskal’s algorithm for Minimum Spanning Tree with Depth
First Search ordering.
Availability
- Version 3.0.0
- New Official function
Description¶
Visits and extracts the nodes information in Depth First Search ordering of the Minimum Spanning Tree created 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: \(O(E * log E)\)
- Returned tree nodes from a root vertex are on Depth First Search order
- Depth First Search Running time: \(O(E + V)\)
Signatures¶
pgr_kruskalDFS(Edges SQL, Root vid [, max_depth]) pgr_kruskalDFS(Edges SQL, Root vids [, max_depth]) RETURNS SET OF (seq, depth, start_vid, node, edge, cost, agg_cost)
Single vertex¶
pgr_kruskalDFS(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 \(6\) |
---|
SELECT * FROM pgr_kruskalDFS(
'SELECT id, source, target, cost, reverse_cost FROM edges ORDER BY id',
6);
seq | depth | start_vid | node | edge | cost | agg_cost
-----+-------+-----------+------+------+------+----------
1 | 0 | 6 | 6 | -1 | 0 | 0
2 | 1 | 6 | 5 | 1 | 1 | 1
3 | 1 | 6 | 10 | 2 | 1 | 1
4 | 2 | 6 | 15 | 3 | 1 | 2
5 | 3 | 6 | 16 | 16 | 1 | 3
6 | 4 | 6 | 17 | 15 | 1 | 4
7 | 5 | 6 | 12 | 13 | 1 | 5
8 | 6 | 6 | 11 | 11 | 1 | 6
9 | 6 | 6 | 8 | 12 | 1 | 6
10 | 7 | 6 | 7 | 10 | 1 | 7
11 | 8 | 6 | 3 | 7 | 1 | 8
12 | 9 | 6 | 1 | 6 | 1 | 9
13 | 7 | 6 | 9 | 14 | 1 | 7
(13 rows)
Multiple vertices¶
pgr_kruskalDFS(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 \(\{9, 6\}\) with \(depth \leq 3\) |
---|
SELECT * FROM pgr_kruskalDFS(
'SELECT id, source, target, cost, reverse_cost FROM edges ORDER BY id',
ARRAY[9, 6], max_depth => 3);
seq | depth | start_vid | node | edge | cost | agg_cost
-----+-------+-----------+------+------+------+----------
1 | 0 | 6 | 6 | -1 | 0 | 0
2 | 1 | 6 | 5 | 1 | 1 | 1
3 | 1 | 6 | 10 | 2 | 1 | 1
4 | 2 | 6 | 15 | 3 | 1 | 2
5 | 3 | 6 | 16 | 16 | 1 | 3
6 | 0 | 9 | 9 | -1 | 0 | 0
7 | 1 | 9 | 8 | 14 | 1 | 1
8 | 2 | 9 | 7 | 10 | 1 | 2
9 | 3 | 9 | 3 | 7 | 1 | 3
10 | 2 | 9 | 12 | 12 | 1 | 2
11 | 3 | 9 | 11 | 11 | 1 | 3
12 | 3 | 9 | 17 | 13 | 1 | 3
(12 rows)
Parameters¶
Parameter | Type | Description |
---|---|---|
Edges SQL | TEXT |
Edges SQL as described below. |
Root vid | BIGINT |
Identifier of the root vertex of the tree.
|
Root vids | ARRAY[ANY-INTEGER] |
Array of identifiers of the root vertices.
|
Where:
ANY-INTEGER: | SMALLINT, INTEGER, BIGINT |
---|---|
ANY-NUMERIC: | SMALLINT, INTEGER, BIGINT, REAL, FLOAT, NUMERIC |
DFS optional parameters¶
Parameter | Type | Default | Description |
---|---|---|---|
max_depth |
BIGINT |
\(9223372036854775807\) | Upper limit of the depth of the tree.
|
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 (seq, depth, start_vid, node, edge, cost, agg_cost)
Parameter | 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 . |
Where:
ANY-INTEGER: | SMALLINT, INTEGER, BIGINT |
---|---|
ANY-NUMERIC: | SMALLINT, INTEGER, BIGINT, REAL, FLOAT, NUMERIC |