Supported versions: Latest (3.3) 3.2

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 function
Version 3.2.0
- New experimental function

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 edge_table
    ORDER BY id'
);
 vertex_id | color_id
-----------+----------
         1 |        1
         2 |        2
         3 |        1
         4 |        2
         5 |        1
         6 |        2
         7 |        1
         8 |        2
         9 |        1
        10 |        2
        11 |        1
        12 |        2
        13 |        1
        14 |        1
        15 |        2
        16 |        1
        17 |        2
(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.

Column

Type

Description

vertex_id

BIGINT

Identifier of the vertex.

color_id