# pgRouting Manual (3.0-rc1)

## pgr_kruskalDFS

`pgr_kruskalDFS` — Kruskal algorithm for Minimum Spanning Tree with Depth First Search ordering.

Boost Graph Inside

Availability

- Version 3.0.0
  - New Official function

Support

- Supported versions: current(3.0)

## Description

Visits and extracts the nodes information in Depth First Search ordering of the Minimum Spanning Tree created using Kruskal’s algorithm.

The main Characteristics are:

- It’s implementation is only on undirected graph.
- Process is done only on edges with positive costs.
- The total weight of all the edges in the tree or forest is minimized.
- When the graph is connected
  - The resulting edges make up a tree
- When the graph is not connected,
  - Finds a minimum spanning tree for each connected component.
  - The resulting edges make up a forest.
- Kruskal’s running time: \(O(E * log E)\)

- Returned tree nodes from a root vertex are on Depth First Search order
- Depth First Search Running time: \(O(E + V)\)

## Signatures

    pgr_kruskalDFS(Edges SQL, Root vid [, max_depth])
    pgr_kruskalDFS(Edges SQL, Root vids [, max_depth])

    RETURNS SET OF (seq, depth, start_vid, node, edge, cost, agg_cost)

### Single vertex

    pgr_kruskalDFS(Edges SQL, Root vid [, max_depth])

    RETURNS SET OF (seq, depth, start_vid, node, edge, cost, agg_cost)

Example: | The Minimum Spanning Tree starting on vertex \(2\)

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

### Multiple vertices

    pgr_kruskalDFS(Edges SQL, Root vids [, max_depth])

    RETURNS SET OF (seq, depth, start_vid, node, edge, cost, agg_cost)

Example: | The Minimum Spanning Tree starting on vertices \(\{13, 2\}\) with \(depth <= 3\)

    SELECT * FROM pgr_kruskalDFS(
        'SELECT id, source, target, cost, reverse_cost FROM edge_table ORDER BY id',
        ARRAY[13,2], max_depth := 3
    );
     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 |     3 |         2 |    9 |   16 |    1 |        3
       6 |     0 |        13 |   13 |   -1 |    0 |        0
       7 |     1 |        13 |   10 |   14 |    1 |        1
       8 |     2 |        13 |    5 |   10 |    1 |        2
       9 |     3 |        13 |    8 |    7 |    1 |        3
      10 |     2 |        13 |   11 |   12 |    1 |        2
      11 |     3 |        13 |    6 |   11 |    1 |        3
      12 |     3 |        13 |   12 |   13 |    1 |        3
    (12 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
- 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.

- Used on Multiple vertices
- \(0\) values are ignored
- For optimization purposes, any duplicated value is ignored.

### Optional Parameters

Parameter | Type | Default | Description
--- | --- | --- | ---

max_depth

`BIGINT`

\(9223372036854775807\)

Upper limit for depth of node in the tree

- When value is `Negative` then throws error

## Inner query

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)

- When negative: edge (source, target) does not exist, therefore it’s not part of the graph.

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)`

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`.

## See Also

- Spanning Tree - Category
- Kruskal - Family of functions
- The queries use the Sample Data network.
- Boost: Kruskal’s algorithm documentation
- Wikipedia: Kruskal’s algorithm

Indices and tables

- Index
- Search Page