# pgr_breadthFirstSearch - Experimental¶

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

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

## 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

options: [max_depth, directed]
RETURNS SET OF (seq, depth, start_vid, node, edge, cost, agg_cost)

### Single vertex¶

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¶

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

## 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

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.