pgr_contraction

pgr_contraction — Performs graph contraction and returns the contracted vertices and edges.

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Boost Graph Inside

Availability

  • Version 3.0.0
    • Return columns change: seq is removed
    • Name change from pgr_contractGraph
    • Bug fixes
    • Official function
  • Version 2.3.0
    • New experimental function

Support

Description

Contraction reduces the size of the graph by removing some of the vertices and edges and, for example, might add edges that represent a sequence of original edges decreasing the total time and space used in graph algorithms.

The main Characteristics are:
  • Process is done only on edges with positive costs.
  • Does not return the full contracted graph
    • Only changes on the graph are returned
  • Currnetly there are two types of contraction methods
    • Dead End Contraction
    • Linear Contraction
  • The returned values include
    • the added edges by linear contraction.
    • the modified vertices by dead end contraction.
  • The returned values are ordered as follows:
    • column id ascending when type = v
    • column id descending when type = e

Signatures

Summary

The pgr_contraction function has the following signature:

pgr_contraction(Edges SQL, Contraction order [, max_cycles] [, forbidden_vertices] [, directed])
RETURNS SETOF (type, id, contracted_vertices, source, target, cost)
Example:Making a dead end contraction and a linear contraction with vertex 2 forbidden from being contracted 
SELECT * FROM pgr_contraction(
    'SELECT id, source, target, cost, reverse_cost FROM edge_table',
ARRAY[1, 2], forbidden_vertices:=ARRAY[2]);
 type | id | contracted_vertices | source | target | cost
------+----+---------------------+--------+--------+------
 v    |  2 | {1}                 |     -1 |     -1 |   -1
 v    |  5 | {7,8}               |     -1 |     -1 |   -1
 v    | 10 | {13}                |     -1 |     -1 |   -1
 v    | 15 | {14}                |     -1 |     -1 |   -1
 v    | 17 | {16}                |     -1 |     -1 |   -1
(5 rows)

Parameters

Column Type Description
Edges SQL TEXT SQL query as described in Inner query
Ccontraction Order ARRAY[ANY-INTEGER]
Ordered contraction operations.
  • 1 = Dead end contraction
  • 2 = Linear contraction

Optional Parameters

Column Type Default Description
forbidden_vertices ARRAY[ANY-INTEGER] Empty Identifiers of vertices forbidden from contraction.
max_cycles INTEGER \(1\) Number of times the contraction operations on contraction_order will be performed.
directed BOOLEAN true
  • When true the graph is considered as Directed.
  • When false the graph is considered as Undirected.

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 SETOF (type, id, contracted_vertices, source, target, cost)

The function returns a single row. The columns of the row are:

Column Type Description
type TEXT
Type of the id.
  • ‘v’ when the row is a vertex.
  • ‘e’ when the row is an edge.
id BIGINT
All numbers on this column are DISTINCT
  • When type = ‘v’.
    • Identifier of the modified vertex.
  • When type = ‘e’.
    • Decreasing sequence starting from -1.
    • Representing a pseudo id as is not incorporated in the set of original edges.
contracted_vertices ARRAY[BIGINT] Array of contracted vertex identifiers.
source BIGINT
  • When type = ‘v’: \(-1\)
  • When type = ‘e’: Identifier of the source vertex of the current edge (source, target).
target BIGINT
  • When type = ‘v’: \(-1\)
  • When type = ‘e’: Identifier of the target vertex of the current edge (source, target).
cost FLOAT
  • When type = ‘v’: \(-1\)
  • When type = ‘e’: Weight of the current edge (source, target).

Additional Examples

Example:Only dead end contraction 
SELECT * FROM pgr_contraction(
    'SELECT id, source, target, cost, reverse_cost FROM edge_table',
ARRAY[1]);
 type | id | contracted_vertices | source | target | cost
------+----+---------------------+--------+--------+------
 v    |  2 | {1}                 |     -1 |     -1 |   -1
 v    |  5 | {7,8}               |     -1 |     -1 |   -1
 v    | 10 | {13}                |     -1 |     -1 |   -1
 v    | 15 | {14}                |     -1 |     -1 |   -1
 v    | 17 | {16}                |     -1 |     -1 |   -1
(5 rows)
Example:Only linear contraction 
SELECT * FROM pgr_contraction(
    'SELECT id, source, target, cost, reverse_cost FROM edge_table',
ARRAY[2]);
 type | id | contracted_vertices | source | target | cost
------+----+---------------------+--------+--------+------
 e    | -1 | {8}                 |      5 |      7 |    2
 e    | -2 | {8}                 |      7 |      5 |    2
(2 rows)