# pgr_lengauerTarjanDominatorTree -Experimental¶

pgr_lengauerTarjanDominatorTree — Returns the immediate dominator of all vertices.

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.

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)