pgr_kruskalDFS

pgr_kruskalDFS - Kruskal algorithm for Minimum Spanning Tree with Depth First Search ordering.

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Availability

  • Version 3.0.0

    • New Official function

Description

Visits and extracts the nodes information in Depth 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.

  • The total weight of all the edges in the tree or forest is minimized.

  • 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.

  • Kruskal’s running time: \(O(E * log E)\)

  • Returned tree nodes from a root vertex are on Depth First Search order

  • Depth First Search Running time: \(O(E + V)\)

Signatures 

pgr_kruskalDFS(Edges SQL, Root vid [, max_depth])
pgr_kruskalDFS(Edges SQL, Root vids [, max_depth])

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

Single vertex 

pgr_kruskalDFS(Edges SQL, Root vid [, max_depth])

RETURNS SET OF (seq, depth, start_vid, node, edge, cost, agg_cost)
Example :

The Minimum Spanning Tree starting on vertex \(2\) 

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

Multiple vertices 

pgr_kruskalDFS(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 \(\{13, 2\}\) with \(depth <= 3\) 

SELECT * FROM pgr_kruskalDFS(
    'SELECT id, source, target, cost, reverse_cost FROM edge_table ORDER BY id',
    ARRAY[13,2], max_depth := 3
);
 seq  depth  start_vid  node  edge  cost  agg_cost
-----+-------+-----------+------+------+------+----------
   1      0          2     2    -1     0         0
   2      1          2     1     1     1         1
   3      1          2     3     2     1         1
   4      2          2     4     3     1         2
   5      3          2     9    16     1         3
   6      0         13    13    -1     0         0
   7      1         13    10    14     1         1
   8      2         13     5    10     1         2
   9      3         13     8     7     1         3
  10      2         13    11    12     1         2
  11      3         13     6    11     1         3
  12      3         13    12    13     1         3
(12 rows)

Parameters

Parameter

Type

Description

Edges SQL

TEXT

SQL query described in Inner query .

Root vid

BIGINT

Identifier of the root vertex of the tree.

  • Used on Single vertex

  • 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.

  • Used on Multiple vertices

  • \(0\) values are ignored

  • For optimization purposes, any duplicated value is ignored.

Optional Parameters

Parameter

Type

Default

Description

max_depth

BIGINT

\(9223372036854775807\)

Upper limit for depth of node in the tree

  • When value is Negative then throws error

Inner query

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)

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

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)

Column

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 .

See Also

Indices and tables