pgr_kruskalDD

pgr_kruskalDD — Catchament nodes using Kruskal’s algorithm.

Boost Graph Inside

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 \((u, v)\) 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. \(0\) values are ignored For optimization purposes, any duplicated value is ignored.
distance	FLOAT	Upper limit for the inclusion of a node in the result.

Where:

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 (target, source) When negative: edge (target, source) does not exist, therefore it’s not part of the graph.

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 node. \(0\) when node = start_vid.
start_vid	BIGINT	Identifier of the root vertex.
node	BIGINT	Identifier of node reached using edge.
edge	BIGINT	Identifier of the edge used to arrive to node. \(-1\) when node = start_vid.
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

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