pgr_kruskalDD - pgRouting Manual (3.4)

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 \((u, v)\) 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

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)

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

Where:

ANY-INTEGER :

SMALLINT , INTEGER , BIGINT

ANY-NUMERIC :

SMALLINT , INTEGER , BIGINT , REAL , FLOAT

Inner Queries

Result Columns

Returns SET OF (seq, depth, start_vid, node, edge, cost, agg_cost)

Where:

ANY-INTEGER :

SMALLINT, INTEGER, BIGINT

ANY-NUMERIC :

SMALLINT, INTEGER, BIGINT, REAL, FLOAT, NUMERIC

See Also

• Spanning Tree - Category

• Kruskal - Family of functions

• Sample Data

• Boost: Kruskal’s algorithm

• Wikipedia: Kruskal’s algorithm

Indices and tables

• Index

• Search Page