pgr_edgeColoring - Experimental - pgRouting Manual (3.3)

Description

Edge Coloring is an algorithm used for coloring of the edges for the vertices in the graph. It is an assignment of colors to the edges of the graph so that no two adjacent edges have the same color.

The main Characteristics are:

• The implementation is applicable only for undirected and loop-free (i.e no self-loops and no parallel edges ) graphs.

• Provides the color to be assigned to all the edges present in the graph.

• At most Δ + 1 colors are used, where Δ is the degree of the graph. This is optimal for some graphs, and by Vizing’s theorem it uses at most one color more than the optimal for all others.

• It can tell us whether a graph is Bipartite . If in a graph, the chromatic number χ′(G) i.e. minimum number of colors needed for proper edge coloring of graph is equal to degree Δ of the graph, (i.e. χ′(G) = Δ ) then graph is said to be Bipartite. But, the vice-versa is not always true.

• The algorithm tries to assign the least possible color to every edge.

• Efficient graph coloring is an NP-Hard problem, and therefore, this algorithm does not always produce optimal coloring.

• The returned rows are ordered in ascending order of the edge value.

• This algorithm is the fastest known almost-optimal algorithm for edge coloring.

• Edge Coloring Running Time: \(O(EV)\)

  • where \(E\) is the number of edges in the graph,

  • \(V\) is the number of vertices in the graph.

Signatures

pgr_edgeColoring(Edges SQL)

RETURNS SET OF (edge_id, color_id)
OR EMPTY SET

Example :

Graph coloring of pgRouting Sample Data

SELECT * FROM pgr_edgeColoring(
    'SELECT id, source, target, cost, reverse_cost FROM edge_table
    ORDER BY id'
);
 edge_id  color_id
---------+----------
       1         3
       2         2
       3         3
       4         4
       5         4
       6         1
       7         2
       8         1
       9         2
      10         5
      11         5
      12         3
      13         2
      14         1
      15         3
      16         1
      17         1
      18         1
(18 rows)

Parameters

Inner query

Edges SQL :

an SQL query of an undirected graph, which should return a set of rows with the following columns:

Where:

ANY-INTEGER :

SMALLINT, INTEGER, BIGINT

ANY-NUMERICAL :

SMALLINT, INTEGER, BIGINT, REAL, FLOAT

Result Columns

Returns SET OF (edge_id, color_id)

See Also

• The queries use the Sample Data network.

• Boost: Edge Coloring Algorithm documentation

• Wikipedia: Graph Coloring

Indices and tables

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