pgr_kruskalDD
¶
pgr_kruskalDD
— Catchament nodes using Kruskal’s algorithm.
Availability
- Version 3.0.0
- New Official function
Description¶
Using Kruskal’s algorithm, extracts the nodes that have aggregate costs less than or equal to a distance from a root vertex (or vertices) within the calculated minimum spanning tree.
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: \(O(E * log E)\)
- Extracts all the nodes that have costs less than or equal to the value distance.
- The edges extracted will conform to the corresponding spanning tree. Edge
- Edge \((u, v)\) will not be included when:
- The distance from the root to \(u\) > limit distance.
- The distance from the root to \(v\) > limit distance.
- No new nodes are created on the graph, so when is within the limit and is not within the limit, the edge is not included.
- Returned tree nodes from a root vertex are on Depth First Search order.
- Depth First Search running time: \(O(E + V)\)
Signatures¶
pgr_kruskalDD(Edges SQL, Root vid, distance) pgr_kruskalDD(Edges SQL, Root vids, distance) RETURNS SET OF (seq, depth, start_vid, node, edge, cost, agg_cost)
Single vertex¶
pgr_kruskalDD(Edges SQL, Root vid, distance) RETURNS SET OF (seq, depth, start_vid, node, edge, cost, agg_cost)
Example: | The Minimum Spanning Tree starting on vertex \(6\) with \(distance \leq 3.5\) |
---|
SELECT * FROM pgr_kruskalDD(
'SELECT id, source, target, cost, reverse_cost FROM edges ORDER BY id',
6, 3.5);
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
(5 rows)
Multiple vertices¶
pgr_kruskalDD(Edges SQL, Root vids, distance) RETURNS SET OF (seq, depth, start_vid, node, edge, cost, agg_cost)
Example: | The Minimum Spanning Tree starting on vertices \(\{9, 6\}\) with \(distance \leq 3.5\) |
---|
SELECT * FROM pgr_kruskalDD(
'SELECT id, source, target, cost, reverse_cost FROM edges ORDER BY id',
ARRAY[9, 6], 3.5);
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.
|
distance | FLOAT |
Upper limit for the inclusion of a node in the result. |
Where:
ANY-INTEGER: | SMALLINT , INTEGER , BIGINT |
---|---|
ANY-NUMERIC: | SMALLINT , INTEGER , BIGINT , REAL , FLOAT |
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 |