# pgr_depthFirstSearch - Proposed¶

pgr_depthFirstSearch — Returns a depth first search traversal of the graph. The graph can be directed or undirected.

Warning

Proposed functions for next mayor release.

• They are not officially in the current release.

• They will likely officially be part of the next mayor release:

• The functions make use of ANY-INTEGER and ANY-NUMERICAL

• Name might not change. (But still can)

• Signature might not change. (But still can)

• Functionality might not change. (But still can)

• pgTap tests have being done. But might need more.

• Documentation might need refinement.

Availability

• Version 3.3.0

• Promoted to proposed function

• Version 3.2.0

## Description¶

Depth First Search algorithm is a traversal algorithm which starts from a root vertex, goes as deep as possible, and backtracks once a vertex is reached with no adjacent vertices or with all visited adjacent vertices. The traversal continues until all the vertices reachable from the root vertex are visited.

The main Characteristics are:

• The implementation works for both directed and undirected graphs.

• Provides the Depth First Search traversal order from a root vertex or from a set of root vertices.

• An optional non-negative maximum depth parameter to limit the results up to a particular depth.

• For optimization purposes, any duplicated values in the Root vids are ignored.

• It does not produce the shortest path from a root vertex to a target vertex.

• The aggregate cost of traversal is not guaranteed to be minimal.

• The returned values are ordered in ascending order of start_vid.

• Depth First Search Running time: $$O(E + V)$$

## Signatures¶

Summary

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

### Single vertex¶

pgr_depthFirstSearch(Edges SQL, Root vid [, directed] [, max_depth])
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_depthFirstSearch(
'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 |     3 |         6 |    1 |    6 |    1 |        3
6 |     2 |         6 |   11 |    8 |    1 |        2
7 |     3 |         6 |   16 |    9 |    1 |        3
8 |     4 |         6 |   17 |   15 |    1 |        4
9 |     4 |         6 |   15 |   16 |    1 |        4
10 |     5 |         6 |   10 |    3 |    1 |        5
11 |     3 |         6 |   12 |   11 |    1 |        3
12 |     2 |         6 |    8 |   10 |    1 |        2
13 |     3 |         6 |    9 |   14 |    1 |        3
(13 rows)



### Multiple vertices¶

pgr_depthFirstSearch(Edges SQL, Root vids [, directed] [, max_depth])
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_depthFirstSearch(
'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 |     2 |         6 |   15 |    3 |    1 |        2
5 |     2 |         6 |   11 |    5 |    1 |        2
6 |     1 |         6 |    7 |    4 |    1 |        1
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 |     2 |        12 |   10 |    5 |    1 |        2
12 |     2 |        12 |    7 |    8 |    1 |        2
13 |     2 |        12 |   16 |    9 |    1 |        2
14 |     1 |        12 |    8 |   12 |    1 |        1
15 |     2 |        12 |    9 |   14 |    1 |        2
16 |     1 |        12 |   17 |   13 |    1 |        1
(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 but with edges in descending order of id.

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