pgr_breadthFirstSearch - Experimental

pgr_breadthFirstSearch — Returns the traversal order(s) using Breadth First Search algorithm.

_images/boost-inside.jpeg

Boost Graph Inside

Warning

Possible server crash

  • These functions might create a server crash

Warning

Experimental functions

  • They are not officially of the current release.
  • They likely will not be officially be part of the next release:
    • The functions might not make use of ANY-INTEGER and ANY-NUMERICAL
    • Name might change.
    • Signature might change.
    • Functionality might change.
    • pgTap tests might be missing.
    • Might need c/c++ coding.
    • May lack documentation.
    • Documentation if any might need to be rewritten.
    • Documentation examples might need to be automatically generated.
    • Might need a lot of feedback from the comunity.
    • Might depend on a proposed function of pgRouting
    • Might depend on a deprecated function of pgRouting

Availability

Description

Provides the Breadth First Search traversal order from a root vertex to a particular depth.

The main Characteristics are:

  • The implementation will work on any type of graph.
  • Provides the Breadth First Search traversal order from a source node to a target depth level
  • Breath First Search Running time: \(O(E + V)\)

Signatures

pgr_breadthFirstSearch(Edges SQL, Root vid [, max_depth] [, directed])
pgr_breadthFirstSearch(Edges SQL, Root vids [, max_depth] [, directed])

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

Single Vertex

pgr_breadthFirstSearch(Edges SQL, Root vid [, max_depth] [, directed])

RETURNS SET OF (seq, depth, start_vid, node, edge, cost, agg_cost)
Example:The Breadth First Search traversal with root vertex \(2\) 
SELECT * FROM pgr_breadthFirstSearch(
    '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 |    5 |    4 |    1 |        1
   4 |     2 |         2 |    8 |    7 |    1 |        2
   5 |     2 |         2 |    6 |    8 |    1 |        2
   6 |     2 |         2 |   10 |   10 |    1 |        2
   7 |     3 |         2 |    7 |    6 |    1 |        3
   8 |     3 |         2 |    9 |    9 |    1 |        3
   9 |     3 |         2 |   11 |   11 |    1 |        3
  10 |     3 |         2 |   13 |   14 |    1 |        3
  11 |     4 |         2 |   12 |   15 |    1 |        4
  12 |     4 |         2 |    4 |   16 |    1 |        4
  13 |     5 |         2 |    3 |    3 |    1 |        5
(13 rows)

Multiple Vertices

pgr_breadthFirstSearch(Edges SQL, Root vids [, max_depth] [, directed])

RETURNS SET OF (seq, depth, start_vid, node, edge, cost, agg_cost)
Example:The Breadth First Search traverls starting on vertices \(\{11, 12\}\) with \(depth <= 2\) 
SELECT * FROM pgr_breadthFirstSearch(
    'SELECT id, source, target, cost, reverse_cost FROM edge_table ORDER BY id',
    ARRAY[11,12], max_depth := 2
);
 seq | depth | start_vid | node | edge | cost | agg_cost
-----+-------+-----------+------+------+------+----------
   1 |     0 |        11 |   11 |   -1 |    0 |        0
   2 |     1 |        11 |   12 |   13 |    1 |        1
   3 |     2 |        11 |    9 |   15 |    1 |        2
   4 |     0 |        12 |   12 |   -1 |    0 |        0
   5 |     1 |        12 |    9 |   15 |    1 |        1
   6 |     2 |        12 |    6 |    9 |    1 |        2
   7 |     2 |        12 |    4 |   16 |    1 |        2
(7 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.
Root vids ARRAY[ANY-INTEGER]

Array of identifiers of the root vertices.

  • Used on Multiple Vertices.
  • 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
directed BOOLEAN true
  • When true Graph is considered Directed
  • When false the graph is considered as Undirected.

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.

  • In Multiple Vertices results are in ascending order.
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.

Additional Examples

Undirected Graph

Example:The Breadth First Search traverls starting on vertices \(\{11, 12\}\) with \(depth <= 2\) as well as considering the graph to be undirected. 
SELECT * FROM pgr_breadthFirstSearch(
    'SELECT id, source, target, cost, reverse_cost FROM edge_table ORDER BY id',
    ARRAY[11,12], max_depth := 2, directed := false
);
 seq | depth | start_vid | node | edge | cost | agg_cost
-----+-------+-----------+------+------+------+----------
   1 |     0 |        11 |   11 |   -1 |    0 |        0
   2 |     1 |        11 |    6 |   11 |    1 |        1
   3 |     1 |        11 |   10 |   12 |    1 |        1
   4 |     1 |        11 |   12 |   13 |    1 |        1
   5 |     2 |        11 |    3 |    5 |    1 |        2
   6 |     2 |        11 |    5 |    8 |    1 |        2
   7 |     2 |        11 |    9 |    9 |    1 |        2
   8 |     2 |        11 |   13 |   14 |    1 |        2
   9 |     0 |        12 |   12 |   -1 |    0 |        0
  10 |     1 |        12 |   11 |   13 |    1 |        1
  11 |     1 |        12 |    9 |   15 |    1 |        1
  12 |     2 |        12 |    6 |   11 |    1 |        2
  13 |     2 |        12 |   10 |   12 |    1 |        2
  14 |     2 |        12 |    4 |   16 |    1 |        2
(14 rows)

Vertex Out Of Graph

Example:The output of the function when a vertex not present in the graph is passed as a parameter. 
SELECT * FROM pgr_breadthFirstSearch(
    'SELECT id, source, target, cost, reverse_cost FROM edge_table ORDER BY id',
    -10
);
 seq | depth | start_vid | node | edge | cost | agg_cost
-----+-------+-----------+------+------+------+----------
(0 rows)