/// <summary>
/// Colors graph vertices greedily processing them in order of <paramref name="verticesOrdered"/>.
/// </summary>
/// <param name="graph">Graph to be colored.</param>
/// <param name="verticesOrdered">Ordering of graph vertices to use in algorithm.</param>
/// <param name="adjacency"><paramref name="graph"/> adjacency to save calculations
/// when doing multiple colorings.</param>
/// <returns>Vertex coloring of provided graph.</returns>
public static GraphColoring ColorGreedilyWithVertexOrder(this Graph graph, IEnumerable <Vertex> verticesOrdered,
VertexAdjacency adjacency)
{
var maxDegree = adjacency.AdjacentVertices.Max(p => p.Value.Count);
var colors = Enumerable.Range(1, maxDegree + 2);
var coloring = new MutableGraphColoring(graph);
foreach (var vertex in verticesOrdered)
{
var adjacentVertices = adjacency.AdjacentVertices[vertex];
var usedColors = adjacentVertices.Select(v => coloring[v]).Where(c => c != null).Select(c => c.Value);
var color = colors.Except(usedColors).First();
coloring[vertex] = color;
}
return(coloring.ToImmutable());
}
/// <summary>
/// Colors graph using G.I.S (Greedy Independent Sets) algorithm. See remarks in <see cref="ColorGreedyIndependentSets(Graph)"/>.
/// </summary>
/// <param name="graph">Graph to be colored.</param>
/// <param name="adjacency"><paramref name="graph"/> adjacency to save calculations
/// when doing multiple colorings.</param>
/// <returns>Vertex coloring of provided graph.</returns>
public static GraphColoring ColorGreedyIndependentSets(this Graph graph, VertexAdjacency adjacency)
{
var maxDegree = adjacency.AdjacentVertices.Max(p => p.Value.Count);
var color = 1;
var coloring = new MutableGraphColoring(graph);
while (coloring.VertexColors.Count < graph.Vertices.Count)
{
var induced = adjacency.InducedSubgraphByRemovingVertices(coloring.VertexColors.Keys);
var inducedAdjacency = induced.Adjacency();
while (induced.Subgraph.Vertices.Count > 0)
{
var vertex = induced.Subgraph.MinDegreeVertex(inducedAdjacency.VertexDegrees());
coloring[vertex] = color;
induced = inducedAdjacency.InducedSubgraphByRemovingVertices(inducedAdjacency.AdjacentVertices[vertex].Add(vertex));
inducedAdjacency = induced.Adjacency();
}
color++;
}
return(coloring.ToImmutable());
}