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.

Column

Type

Description

vertex_id

BIGINT

Identifier of the vertex.

color_id