pgr_bipartite -Experimental

pgr_bipartite — If graph is bipartite then function returns the vertex id along with color (0 and 1) else it will return an empty set. In particular, the is_bipartite() algorithm implemented by Boost.Graph.

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

A bipartite graph is a graph with two sets of vertices which are connected to each other, but not within themselves. A bipartite graph is possible if the graph coloring is possible using two colors such that vertices in a set are colored with the same color.

The main Characteristics are:

• The algorithm works in undirected graph only.

• The returned values are not ordered.

• The algorithm checks graph is bipartite or not. If it is bipartite then it returns the node along with two colors 0 and 1 which represents two different sets.

• If graph is not bipartite then algorithm returns empty set.

• Running time: \(O(V + E)\)

Signatures

pgr_bipartite(Edges SQL) -- Experimental on v3.2

RETURNS SET OF (vertex_id, color_id)
OR EMPTY SET

Example

The pgr_bipartite algorithm with and edge_sql as a parameter when graph is bipartite:

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

Parameters

Parameter	Type	Description
Edges SQL	TEXT	Inner query as described below.

Inner query

Edges SQL

an SQL query of an undirected graph, which should return a set of rows with the following columns:

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 (vertex_id, color_id)

Column	Type	Description
vertex_id	BIGINT	Identifier of the vertex.
color_id	BIGINT	Identifier of the color of the vertex. The minimum value of color is 1.

Additional Example

Example

The odd length cyclic graph can not be bipartite.

The following edge will make subgraph with vertices {1, 2, 5, 7, 8} an odd length cyclic graph.

INSERT INTO edge_table (source, target, cost, reverse_cost) VALUES
(1, 7, 1, 1);
INSERT 0 1

The new graph is not bipartite because it has a odd length cycle of 5 vertices. Edges in blue represent odd length cycle.

SELECT * FROM pgr_bipartite(
    $$SELECT id,source,target,cost,reverse_cost FROM edge_table$$
);
 vertex_id | color_id
-----------+----------
(0 rows)

See Also

• Boost: is_bipartite algorithm documentation

• Wikipedia: bipartite graph

• Sample Data network.

Indices and tables

• Index

• Search Page