pgr_kruskalBFS

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

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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

Indices and tables