pgr_primBFS

pgr_primBFS — Prim’s algorithm for Minimum Spanning Tree with Depth First Search ordering.

_images/boost-inside.jpeg

Boost Graph Inside

Availability

  • 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 with Prims’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.

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

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

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

Signatures

pgr_primBFS(Edges SQL, Root vid [, max_depth])
pgr_primBFS(Edges SQL, Root vids [, max_depth])
RETURNS SET OF (seq, depth, start_vid, node, edge, cost, agg_cost)

Single vertex

pgr_primBFS(Edges SQL, Root vid [, max_depth])
RETURNS SET OF (seq, depth, start_vid, node, edge, cost, agg_cost)
Example:

The Minimum Spanning Tree having as root vertex \(6\)

SELECT * FROM pgr_primBFS(
  'SELECT id, source, target, cost, reverse_cost FROM edges ORDER BY id',
  6);
 seq | depth | start_vid | node | edge | cost | agg_cost
-----+-------+-----------+------+------+------+----------
   1 |     0 |         6 |    6 |   -1 |    0 |        0
   2 |     1 |         6 |    5 |    1 |    1 |        1
   3 |     1 |         6 |   10 |    2 |    1 |        1
   4 |     1 |         6 |    7 |    4 |    1 |        1
   5 |     2 |         6 |   15 |    3 |    1 |        2
   6 |     2 |         6 |   11 |    5 |    1 |        2
   7 |     2 |         6 |    3 |    7 |    1 |        2
   8 |     2 |         6 |    8 |   10 |    1 |        2
   9 |     3 |         6 |   16 |    9 |    1 |        3
  10 |     3 |         6 |   12 |   11 |    1 |        3
  11 |     3 |         6 |    1 |    6 |    1 |        3
  12 |     3 |         6 |    9 |   14 |    1 |        3
  13 |     4 |         6 |   17 |   13 |    1 |        4
(13 rows)

Multiple vertices

pgr_primBFS(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 \(\{9, 6\}\) with \(depth \leq 3\)

SELECT * FROM pgr_primBFS(
  'SELECT id, source, target, cost, reverse_cost FROM edges ORDER BY id',
  ARRAY[9, 6], max_depth => 3);
 seq | depth | start_vid | node | edge | cost | agg_cost
-----+-------+-----------+------+------+------+----------
   1 |     0 |         6 |    6 |   -1 |    0 |        0
   2 |     1 |         6 |    5 |    1 |    1 |        1
   3 |     1 |         6 |   10 |    2 |    1 |        1
   4 |     1 |         6 |    7 |    4 |    1 |        1
   5 |     2 |         6 |   15 |    3 |    1 |        2
   6 |     2 |         6 |   11 |    5 |    1 |        2
   7 |     2 |         6 |    3 |    7 |    1 |        2
   8 |     2 |         6 |    8 |   10 |    1 |        2
   9 |     3 |         6 |   16 |    9 |    1 |        3
  10 |     3 |         6 |   12 |   11 |    1 |        3
  11 |     3 |         6 |    1 |    6 |    1 |        3
  12 |     3 |         6 |    9 |   14 |    1 |        3
  13 |     0 |         9 |    9 |   -1 |    0 |        0
  14 |     1 |         9 |    8 |   14 |    1 |        1
  15 |     2 |         9 |    7 |   10 |    1 |        2
  16 |     3 |         9 |    6 |    4 |    1 |        3
  17 |     3 |         9 |    3 |    7 |    1 |        3
(17 rows)

Parameters

Parameter

Type

Description

Edges SQL

TEXT

Edges SQL as described below.

Root vid

BIGINT

Identifier of the root vertex of the tree.

  • 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.

  • \(0\) values are ignored

  • For optimization purposes, any duplicated value is ignored.

Where:

ANY-INTEGER:

SMALLINT, INTEGER, BIGINT

ANY-NUMERIC:

SMALLINT, INTEGER, BIGINT, REAL, FLOAT, NUMERIC

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, 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.

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.

Where:

ANY-INTEGER:

SMALLINT, INTEGER, BIGINT

ANY-NUMERIC:

SMALLINT, INTEGER, BIGINT, REAL, FLOAT, NUMERIC

See Also

Indices and tables