## pgr_sequentialVertexColoring - Proposed

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

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.