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 ANYINTEGER and ANYNUMERICAL
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 NPHard 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¶
(vertex_id, color_id)
 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 as described below. 
Inner Queries¶
Edges SQL¶
Column 
Type 
Default 
Description 


ANYINTEGER 
Identifier of the edge. 


ANYINTEGER 
Identifier of the first end point vertex of the edge. 


ANYINTEGER 
Identifier of the second end point vertex of the edge. 


ANYNUMERICAL 
Weight of the edge ( 


ANYNUMERICAL 
1 
Weight of the edge (

Where:
 ANYINTEGER:
SMALLINT
,INTEGER
,BIGINT
 ANYNUMERICAL:
SMALLINT
,INTEGER
,BIGINT
,REAL
,FLOAT
Result columns¶
Returns set of (vertex_id, color_id)
Column 
Type 
Description 



Identifier of the vertex. 


Identifier of the color of the vertex.

See Also¶
The queries use the Sample Data network.
Indices and tables