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.

  • Running time: \(O(E + V)\)

Signatures

Summary

pgr_breadthFirstSearch(Edges SQL, root vid, [options])
pgr_breadthFirstSearch(Edges SQL, root vids, [options])
options: [max_depth, directed]
Returns set of (seq, depth, start_vid, node, edge, cost, agg_cost)

Single vertex

pgr_breadthFirstSearch(Edges SQL, root vid, [options])
options: [max_depth, directed]
Returns set of (seq, depth, start_vid, node, edge, cost, agg_cost)
Example

From root vertex \(6\) on a directed graph with edges in ascending order of id

SELECT * FROM pgr_breadthFirstSearch(
  '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 |    7 |    4 |    1 |        1
   4 |     2 |         6 |    3 |    7 |    1 |        2
   5 |     2 |         6 |   11 |    8 |    1 |        2
   6 |     2 |         6 |    8 |   10 |    1 |        2
   7 |     3 |         6 |    1 |    6 |    1 |        3
   8 |     3 |         6 |   16 |    9 |    1 |        3
   9 |     3 |         6 |   12 |   11 |    1 |        3
  10 |     3 |         6 |    9 |   14 |    1 |        3
  11 |     4 |         6 |   17 |   15 |    1 |        4
  12 |     4 |         6 |   15 |   16 |    1 |        4
  13 |     5 |         6 |   10 |    3 |    1 |        5
(13 rows)

Multiple vertices

pgr_breadthFirstSearch(Edges SQL, root vids, [options])
options: [max_depth, directed]
Returns set of (seq, depth, start_vid, node, edge, cost, agg_cost)
Example

From root vertices \(\{12, 6\}\) on an undirected graph with depth \(<= 2\) and edges in ascending order of id

SELECT * FROM pgr_breadthFirstSearch(
  'SELECT id, source, target, cost, reverse_cost
  FROM edges ORDER BY id',
  ARRAY[12, 6], directed => false, max_depth => 2);
 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 |     0 |        12 |   12 |   -1 |    0 |        0
  10 |     1 |        12 |   11 |   11 |    1 |        1
  11 |     1 |        12 |    8 |   12 |    1 |        1
  12 |     1 |        12 |   17 |   13 |    1 |        1
  13 |     2 |        12 |   10 |    5 |    1 |        2
  14 |     2 |        12 |    7 |    8 |    1 |        2
  15 |     2 |        12 |   16 |    9 |    1 |        2
  16 |     2 |        12 |    9 |   14 |    1 |        2
(16 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

Optional parameters

Column

Type

Default

Description

directed

BOOLEAN

true

  • When true the graph is considered Directed

  • When false the graph is considered as Undirected.

DFS 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

Additional Examples

Example

Same as Single vertex with edges in ascending order of id.

SELECT * FROM pgr_breadthFirstSearch(
  '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 |    7 |    4 |    1 |        1
   4 |     2 |         6 |    3 |    7 |    1 |        2
   5 |     2 |         6 |   11 |    8 |    1 |        2
   6 |     2 |         6 |    8 |   10 |    1 |        2
   7 |     3 |         6 |    1 |    6 |    1 |        3
   8 |     3 |         6 |   16 |    9 |    1 |        3
   9 |     3 |         6 |   12 |   11 |    1 |        3
  10 |     3 |         6 |    9 |   14 |    1 |        3
  11 |     4 |         6 |   17 |   15 |    1 |        4
  12 |     4 |         6 |   15 |   16 |    1 |        4
  13 |     5 |         6 |   10 |    3 |    1 |        5
(13 rows)

Example

Same as Single vertex with edges in descending order of id.

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

The resulting traversal is different.

The left image shows the result with ascending order of ids and the right image shows with descending order of the edge identifiers.

ascending descending