pgr_sequentialVertexColoring - Proposed

pgr_sequentialVertexColoring - Returns the vertex coloring of an undirected graph, using greedy approach.

images/boost-inside.jpeg

Boost Graph Inside

Warning

Proposed functions for next mayor release.

  • They are not officially in the current release.

  • They will likely officially be part of the next mayor release:

    • The functions make use of ANY-INTEGER and ANY-NUMERICAL

    • Name might not change. (But still can)

    • Signature might not change. (But still can)

    • Functionality might not change. (But still can)

    • pgTap tests have being done. But might need more.

    • Documentation might need refinement.

Availability

  • Version 3.3.0

    • Promoted to proposed signature

  • Version 3.2.0

    • New experimental signature

Description

Sequential vertex coloring algorithm is a graph coloring algorithm in which color identifiers are assigned to the vertices of a graph in a sequential manner, such that no edge connects two identically colored vertices.

The main Characteristics are:

  • The implementation is applicable only for undirected graphs.

  • Provides the color to be assigned to all the vertices present in the graph.

  • Color identifiers values are in the Range \([1, V]\)

  • The algorithm tries to assign the least possible color to every vertex.

  • Efficient graph coloring is an NP-Hard problem, and therefore, this algorithm does not always produce optimal coloring. It follows a greedy strategy by iterating through all the vertices sequentially, and assigning the smallest possible color that is not used by its neighbors, to each vertex.

  • The returned rows are ordered in ascending order of the vertex value.

  • Sequential Vertex Coloring Running Time: \(O(V*(d + k))\)

    • where \(V\) is the number of vertices,

    • \(d\) is the maximum degree of the vertices in the graph,

    • \(k\) is the number of colors used.

Signatures

pgr_sequentialVertexColoring( Edges SQL )
RETURNS SET OF (vertex_id, color_id)
OR EMPTY SET
Example :

Graph coloring of pgRouting Sample Data 

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

Parameters

Parameter

Type

Description

Edges SQL

TEXT

Edges SQL as described below.

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 (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.

See Also

Indices and tables