pgr_kruskalBFS

pgr_kruskalBFS — Kruskal’s algorithm for Minimum Spanning Tree with breadth First Search ordering.

Boost Graph Inside

Availability

Version 3.7.0:

• Standarizing output columns to (seq, depth, start_vid, pred, node, edge, cost, agg_cost)

  • Added pred result columns.

Version 3.0.0:

• New Official function

Description

Visits and extracts the nodes information in Breath 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 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, pred, node, edge, cost, agg_cost)

Single vertex

pgr_kruskalBFS(Edges SQL, root vid, [max_depth])

Returns set of (seq, depth, start_vid, pred, node, edge, cost, agg_cost)

Example:

The Minimum Spanning Tree having as root vertex \(6\)

SELECT * FROM pgr_kruskalBFS(
  'SELECT id, source, target, cost, reverse_cost FROM edges ORDER BY id',
  6);
 seq | depth | start_vid | pred | node | edge | cost | agg_cost
-----+-------+-----------+------+------+------+------+----------
   1 |     0 |         6 |    6 |    6 |   -1 |    0 |        0
   2 |     1 |         6 |    6 |    5 |    1 |    1 |        1
   3 |     1 |         6 |    6 |   10 |    2 |    1 |        1
   4 |     2 |         6 |   10 |   15 |    3 |    1 |        2
   5 |     3 |         6 |   15 |   16 |   16 |    1 |        3
   6 |     4 |         6 |   16 |   17 |   15 |    1 |        4
   7 |     5 |         6 |   17 |   12 |   13 |    1 |        5
   8 |     6 |         6 |   12 |   11 |   11 |    1 |        6
   9 |     6 |         6 |   12 |    8 |   12 |    1 |        6
  10 |     7 |         6 |    8 |    7 |   10 |    1 |        7
  11 |     7 |         6 |    8 |    9 |   14 |    1 |        7
  12 |     8 |         6 |    7 |    3 |    7 |    1 |        8
  13 |     9 |         6 |    3 |    1 |    6 |    1 |        9
(13 rows)

Multiple vertices

pgr_kruskalBFS(Edges SQL, root vids, [max_depth])

Returns set of (seq, depth, start_vid, pred, node, edge, cost, agg_cost)

Example:

The Minimum Spanning Tree starting on vertices \(\{9, 6\}\) with \(depth \leq 3\)

SELECT * FROM pgr_kruskalBFS(
  'SELECT id, source, target, cost, reverse_cost FROM edges ORDER BY id',
  ARRAY[9, 6], max_depth => 3);
 seq | depth | start_vid | pred | node | edge | cost | agg_cost
-----+-------+-----------+------+------+------+------+----------
   1 |     0 |         6 |    6 |    6 |   -1 |    0 |        0
   2 |     1 |         6 |    6 |    5 |    1 |    1 |        1
   3 |     1 |         6 |    6 |   10 |    2 |    1 |        1
   4 |     2 |         6 |   10 |   15 |    3 |    1 |        2
   5 |     3 |         6 |   15 |   16 |   16 |    1 |        3
   6 |     0 |         9 |    9 |    9 |   -1 |    0 |        0
   7 |     1 |         9 |    9 |    8 |   14 |    1 |        1
   8 |     2 |         9 |    8 |    7 |   10 |    1 |        2
   9 |     2 |         9 |    8 |   12 |   12 |    1 |        2
  10 |     3 |         9 |    7 |    3 |    7 |    1 |        3
  11 |     3 |         9 |   12 |   11 |   11 |    1 |        3
  12 |     3 |         9 |   12 |   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

BFS optional parameters

Parameter	Type	Default	Description
max_depth	BIGINT	\(9223372036854775807\)	Upper limit of the depth of the tree. When negative throws an error.

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, pred, 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. \(depth-1\) is the depth of pred
start_vid	BIGINT	Identifier of the root vertex.
pred	BIGINT	Predecessor of node. When node = start_vid then has the value node.
node	BIGINT	Identifier of node reached using edge.
edge	BIGINT	Identifier of the edge used to arrive from pred to node. \(-1\) when node = start_vid.
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

• Sample Data

• Boost: Kruskal’s algorithm

• Wikipedia: Kruskal’s algorithm

Indices and tables

• Index

• Search Page