# pgRouting Manual (3.3)

## pgr_depthFirstSearch - Proposed

- Supported versions: Latest (3.3) 3.2

# pgr_depthFirstSearch - Proposed

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

Boost Graph Inside

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

  - New experimental function

## 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)

Using defaults

Example

  From root vertex \(2\) on a directed graph

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

### 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 \(2\) on an undirected graph, with \(depth <= 2\)

    SELECT * FROM pgr_depthFirstSearch(
        'SELECT id, source, target, cost, reverse_cost FROM edge_table
        ORDER BY id',
        2, directed => false, max_depth => 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 |    3 |    2 |    1 |        1
       4 |     2 |         2 |    4 |    3 |    1 |        2
       5 |     2 |         2 |    6 |    5 |    1 |        2
       6 |     1 |         2 |    5 |    4 |    1 |        1
       7 |     2 |         2 |    8 |    7 |    1 |        2
       8 |     2 |         2 |   10 |   10 |    1 |        2
    (8 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 \(\{11, 2\}\) on an undirected graph with \(depth <= 2\)

    SELECT * FROM pgr_depthFirstSearch(
        'SELECT id, source, target, cost, reverse_cost FROM edge_table
        ORDER BY id',
        ARRAY[11, 2], directed => false, max_depth => 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 |    3 |    2 |    1 |        1
       4 |     2 |         2 |    4 |    3 |    1 |        2
       5 |     2 |         2 |    6 |    5 |    1 |        2
       6 |     1 |         2 |    5 |    4 |    1 |        1
       7 |     2 |         2 |    8 |    7 |    1 |        2
       8 |     2 |         2 |   10 |   10 |    1 |        2
       9 |     0 |        11 |   11 |   -1 |    0 |        0
      10 |     1 |        11 |    6 |   11 |    1 |        1
      11 |     2 |        11 |    3 |    5 |    1 |        2
      12 |     2 |        11 |    5 |    8 |    1 |        2
      13 |     2 |        11 |    9 |    9 |    1 |        2
      14 |     1 |        11 |   10 |   12 |    1 |        1
      15 |     2 |        11 |   13 |   14 |    1 |        2
      16 |     1 |        11 |   12 |   13 |    1 |        1
    (16 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.

- Used on Single Vertex.

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
--- | --- | --- | ---

directed

`BOOLEAN`

`true`

- When `true` Graph is Directed

- When `false` the graph is Undirected.

max_depth

`BIGINT`

\(9223372036854775807\)

Upper limit for the depth of traversal

- When value is `Negative` then throws error

## Inner query

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`

- When positive: edge (source, target) exist on the graph.

- When negative: edge (source, target) does not exist on the graph.

reverse_cost

`ANY-NUMERICAL`

-1

- When positive: edge (target, source) exist on the graph.

- When negative: edge (target, source) does not exist on 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

The examples of this section are based on the Sample Data network.

Example: No internal ordering on traversal

In the following query, the inner query of the example: “Using defaults” is modified so that the data is entered into the algorithm is given in the reverse ordering of the id.

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

## See Also

- The queries use the Sample Data network.

- Boost: Depth First Search algorithm documentation

- Boost: Undirected DFS algorithm documentation

- Wikipedia: Depth First Search algorithm

Indices and tables

- Index

- Search Page