pgr_kruskalBFS

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

Boost Graph Inside

Availability

• 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, node, edge, cost, agg_cost)

Single vertex

pgr_kruskalBFS(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_kruskalBFS(
  '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 |     7 |         6 |    9 |   14 |    1 |        7
  12 |     8 |         6 |    3 |    7 |    1 |        8
  13 |     9 |         6 |    1 |    6 |    1 |        9
(13 rows)

Multiple vertices

pgr_kruskalBFS(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_kruskalBFS(
  '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 |     2 |         9 |   12 |   12 |    1 |        2
  10 |     3 |         9 |    3 |    7 |    1 |        3
  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. When value is \(0\) then gets the spanning forest starting in aleatory nodes for each tree in the forest.
root vids	ARRAY [ ANY-INTEGER ]	Array of identifiers of the root vertices. \(0\) values are ignored For optimization purposes, any duplicated value is ignored.

Where:

ANY-INTEGER:

SMALLINT, INTEGER, BIGINT

ANY-NUMERIC:

SMALLINT, INTEGER, BIGINT, REAL, FLOAT, NUMERIC

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, 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