pgr_kruskalDD

pgr_kruskalDD — Catchament nodes using Kruskal’s algorithm.

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Availability

  • Version 3.0.0

    • New Official function

Support

  • Supported versions: current(3.1) 3.0

Description

Using Kruskal’s algorithm, extracts the nodes that have aggregate costs less than or equal to the value Distance from a root vertex (or vertices) within the calculated minimum spanning tree.

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_kruskalDD(edges_sql, root_vid, distance)
pgr_kruskalDD(edges_sql, root_vids, distance)

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

Single vertex

pgr_kruskalDD(edges_sql, root_vid, distance)

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

The Minimum Spanning Tree starting on vertex \(2\) with \(agg\_cost <= 3.5\)

SELECT * FROM pgr_kruskalDD(
    'SELECT id, source, target, cost, reverse_cost FROM edge_table ORDER BY id',
    2, 3.5
);
 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
(5 rows)

Multiple vertices

pgr_kruskalDD(edges_sql, root_vids, distance)

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

The Minimum Spanning Tree starting on vertices \(\{13, 2\}\) with \(agg\_cost <= 3.5\);

SELECT * FROM pgr_kruskalDD(
    'SELECT id, source, target, cost, reverse_cost FROM edge_table ORDER BY id',
    ARRAY[13,2],
    3.5
);
 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 \(0\) gets the spanning forest starting in aleatory nodes for each tree.

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.

Distance

ANY-NUMERIC

Upper limit for the inclusion of the node in the result.

  • When the value is Negative throws error

Where:

ANY-INTEGER

SMALLINT, INTEGER, BIGINT

ANY-NUMERIC

SMALLINT, INTEGER, BIGINT, REAL, FLOAT, NUMERIC

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.