# 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 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.