pgr_sequentialVertexColoring - Proposed

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

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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

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.