pgr_sequentialVertexColoring - Proposed - pgRouting Manual (3.4)

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

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

Inner Queries

Result Columns

Returns SET OF (vertex_id, color_id)

See Also

• The queries use the Sample Data network.

• Boost: Sequential Vertex Coloring algorithm documentation

• Wikipedia: Graph coloring

Indices and tables

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