pgr_kruskalDFS

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

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Availability

  • New on v3.0.0

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.