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..
****************************************************************************
pgRouting Manual
Copyright(c) pgRouting Contributors
This documentation is licensed under a Creative Commons Attribution-Share
Alike 3.0 License: https://creativecommons.org/licenses/by-sa/3.0/
****************************************************************************
.. index::
single: Coloring Family ; pgr_sequentialVertexColoring - Proposed
single: sequentialVertexColoring - Proposed on v3.3
|
``pgr_sequentialVertexColoring`` - Proposed
===============================================================================
``pgr_sequentialVertexColoring`` — Returns the vertex coloring of an undirected
graph, using greedy approach.
.. include:: proposed.rst
:start-after: warning-begin
:end-before: end-warning
.. rubric:: Availability
.. rubric:: Version 4.0.0
* Output columns standardized to |result_node_color|
.. rubric:: Version 3.3.0
* Function promoted to proposed.
.. rubric:: Version 3.2.0
* New experimental function.
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 :math:`[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: :math:`O(|V|*(d + k))`
- where :math:`|V|` is the number of vertices,
- :math:`d` is the maximum degree of the vertices in the graph,
- :math:`k` is the number of colors used.
|Boost| Boost Graph Inside
Signatures
------------------------------------------------------------------------------
.. admonition:: \ \
:class: signatures
| pgr_sequentialVertexColoring(`Edges SQL`_)
| Returns set of |result_node_color|
| OR EMPTY SET
:Example: Graph coloring of pgRouting :doc:`sampledata`
.. literalinclude:: sequentialVertexColoring.queries
:start-after: -- q1
:end-before: -- q2
.. Parameters, Inner Queries & result columns
Parameters
-------------------------------------------------------------------------------
.. include:: pgRouting-concepts.rst
:start-after: only_edge_param_start
:end-before: only_edge_param_end
Inner Queries
-------------------------------------------------------------------------------
Edges SQL
...............................................................................
.. include:: pgRouting-concepts.rst
:start-after: basic_edges_sql_start
:end-before: basic_edges_sql_end
Result columns
-------------------------------------------------------------------------------
.. include:: coloring-family.rst
:start-after: result-node-color-start
:end-before: result-node-color-end
See Also
-------------------------------------------------------------------------------
* :doc:`sampledata`
* `Boost: Sequential Vertex Coloring
<https://www.boost.org/libs/graph/doc/sequential_vertex_coloring.html>`__
* `Wikipedia: Graph coloring <https://en.wikipedia.org/wiki/Graph_coloring>`__
.. rubric:: Indices and tables
* :ref:`genindex`
* :ref:`search`
|
