# pgRouting Manual (3.6)

## pgr_lengauerTarjanDominatorTree -Experimental

`pgr_lengauerTarjanDominatorTree` — Returns the immediate dominator of all vertices.

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 3.2.0

  - New experimental function

## Description

The algorithm calculates the immidiate dominator of each vertex called idom, once idom of each vertex is calculated then by making every idom of each vertex as its parent, the dominator tree can be built.

The main Characteristics are:

- The algorithm works in directed graph only.

- The returned values are not ordered.

- The algorithm returns idom of each vertex.

- If the root vertex not present in the graph then it returns empty set.

- Running time: \(O((V+E)log(V+E))\)

## Signatures

Summary

pgr_lengauerTarjanDominatorTree(Edges SQL, root vertex)
Returns set of `(seq, vertex_id, idom)`
OR EMPTY SET

Example:

  The dominator tree with root vertex \(5\)

    SELECT * FROM pgr_lengauertarjandominatortree(
      $$SELECT id,source,target,cost,reverse_cost FROM edges$$,
      5) ORDER BY vertex_id;
     seq | vertex_id | idom
    -----+-----------+------
       1 |         1 |    2
       9 |         2 |    0
       2 |         3 |    3
      10 |         4 |    0
      17 |         5 |    0
       4 |         6 |   17
       3 |         7 |    4
       7 |         8 |    3
      11 |         9 |    7
       5 |        10 |   16
       6 |        11 |    3
       8 |        12 |    3
      12 |        13 |    0
      13 |        14 |    0
      16 |        15 |   15
      15 |        16 |    3
      14 |        17 |    3
    (17 rows)

## Parameters

Column | Type | Description
--- | --- | ---
Edges SQL | `TEXT` | SQL query as described above.
root vertex | `BIGINT` | Identifier of the starting vertex.

## 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`

## Result columns

Returns set of `(seq, vertex_id, idom)`

Column | Type | Description
--- | --- | ---
`seq` | `INTEGER` | Sequential value starting from 1.
`vertex_id` | `BIGINT` | Identifier of vertex .
`idom` | `BIGINT` | Immediate dominator of vertex.

## Additional Examples

Example:

  Dominator tree of another component.

    SELECT * FROM pgr_lengauertarjandominatortree(
      $$SELECT id,source,target,cost,reverse_cost FROM edges$$,
      13) ORDER BY vertex_id;
     seq | vertex_id | idom
    -----+-----------+------
       1 |         1 |    0
       9 |         2 |    0
       2 |         3 |    0
      10 |         4 |    0
      17 |         5 |    0
       4 |         6 |    0
       3 |         7 |    0
       7 |         8 |    0
      11 |         9 |    0
       5 |        10 |    0
       6 |        11 |    0
       8 |        12 |    0
      12 |        13 |    0
      13 |        14 |   12
      16 |        15 |    0
      15 |        16 |    0
      14 |        17 |    0
    (17 rows)

## See Also

- Sample Data

- Boost: Lengauer-Tarjan dominator tree algorithm

- Wikipedia: dominator tree

Indices and tables

- Index

- Search Page