pgr_kruskalDD

pgr_kruskalDD — Catchament nodes using Kruskal’s algorithm.

_images/boost-inside.jpeg

Boost Graph Inside

Availability

  • New on v3.0.0

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.