`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

Version 3.0.0
- New experimental signature:
  - pgr_breadthFirstSearch (Single Vertex)
  - pgr_breadthFirstSearch (Multiple Vertices)

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.

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.

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

Return 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.

pgr_breadthFirstSearch - Experimental¶

Description¶

Signatures¶

Single vertex¶

Multiple vertices¶

Parameters¶

Optional parameters¶

DFS optional parameters¶

Inner Queries¶

Edges SQL¶

Return columns¶

Additional Examples¶

See Also¶

`pgr_breadthFirstSearch` - Experimental¶