public Dictionary <int, int> ColourGraph(Graph graph)
{
stopwatch.Restart();
var dummySolution = new Solution()
{
colourCount = int.MaxValue,
};
var initialSolution = new Solution()
{
colourCount = 0,
colourLayer = new Stack <List <int> >()
};
graph = graph.CloneNeighboursSorted(v => graph.VerticesKVPs[v].Length);
// var solution = Recurse(graph, initialSolution, dummySolution, ref leftSteps, alphaRatio).vertexToColour;
var dictionary = new Dictionary <int, int>();
//var misCount = 0;
//var largestMIS = 0;
//foreach (var mis in EnumerateMIS(graph))
//{
// misCount += 1;
// if (mis.vertices.Count > largestMIS)
// largestMIS = mis.vertices.Count;
//}
//System.Console.WriteLine($"MIS count: {misCount}, largest: {largestMIS}");
var ignoredVertices = new bool[graph.VerticesKVPs.Length];
var primaryGraph = new GraphFast(graph);
var complementaryGraph = new GraphFast(graph);
var bestSolution = Recurse(graph.VerticesKVPs.Length, primaryGraph, complementaryGraph, initialSolution, dummySolution);
var layerColour = 0;
foreach (var layer in bestSolution.colourLayer)
{
foreach (var vertex in layer)
{
dictionary.Add(vertex, layerColour);
}
layerColour += 1;
}
stopwatch.Stop();
return(dictionary);
}
//public IEnumerable<List<int>> EnumerateMIS(Graph graph)
//{
// var primaryGraph = new GraphFast(graph);
// var complementaryGraph = new GraphFast(graph);
// var ignoredVertex = new bool[graph.VerticesKVPs.Length];
// var verticesAlreadyInMIS = new List<int>();
// foreach (var mis in FindMIS(primaryGraph, complementaryGraph, verticesAlreadyInMIS, ignoredVertex, 0))
// {
// yield return mis.vertices;
// }
//}
private Solution Recurse(int n, GraphFast primaryGraph, GraphFast complementaryGraph, Solution currentSolution, Solution bestSolution, int latestMisSize = int.MaxValue, int lastMisId = int.MaxValue)
{
if (complementaryGraph.vertexCount == 0)
{
if (currentSolution.colourCount < bestSolution.colourCount)
{
bestSolution = currentSolution.DeepClone();
NewBestSolutionFound?.Invoke(null, new PerformanceReport()
{
minimalNumberOfColoursUsed = bestSolution.colourCount,
elapsedProcessorTime = stopwatch.Elapsed
});
}
}
else if (currentSolution.colourCount + 1 < bestSolution.colourCount) // could improve this bound by finding a clique
{
// get MIS get and complimentary graph
// compute subsolution
var verticesAlreadyInMIS = new List <int>();
currentSolution.colourCount += 1;
var ignoredVertex = new bool[n];
FindMIS(primaryGraph, complementaryGraph, verticesAlreadyInMIS, ignoredVertex, 0, mis =>
{
// optionally check for cliques to delete
if (mis.vertices.Count < latestMisSize || (mis.vertices.Count == latestMisSize && mis.vertices[0] > lastMisId))// pre-optimization
{
currentSolution.colourLayer.Push(mis.vertices);
bestSolution = Recurse(n, complementaryGraph, complementaryGraph.DeepIrreversibleClone(), currentSolution, bestSolution, mis.vertices.Count, mis.vertices[0]);
currentSolution.colourLayer.Pop();
}
// need to fix the enumerator to ensure breakability
return(currentSolution.colourCount < bestSolution.colourCount);
});
currentSolution.colourCount -= 1;
}
return(bestSolution);
}
// ignoredVertexCount might turn out to be useless
private bool FindMIS(
GraphFast graph,
GraphFast complementaryGraph,
List <int> verticesAlreadyInMIS,
bool[] ignoredVertex,
int ignoredVertexCount,
Func <MisResult, bool> consumeAndDecideToContinue)
{
var continueExecution = true;
// add detailed parameters
if (graph.vertexCount == 0)
{
// ignored vertices can only be removed by nonignored so the following if is unnecessary
// if (ignoredVertexCount == 0)
continueExecution = consumeAndDecideToContinue(new MisResult()
{
graphWithoutMIS = complementaryGraph,
vertices = verticesAlreadyInMIS
});
}
else
{
// choose a vertex v
var chosenVertex = -1;
var vertexScore = int.MinValue;
for (int i = 0; i < graph.vertexCount; i++)
{
var tmpVertex = graph.vertices[i];
if (!ignoredVertex[tmpVertex])
{
var tmpVertexScore = graph.neighbourCount[tmpVertex];
if (tmpVertexScore > vertexScore)
{
chosenVertex = tmpVertex;
vertexScore = tmpVertexScore;
}
}
}
if (chosenVertex != -1)
{
// ADD VERTEX V TO MIS
// remove the vertex and all its neighbours
var neighbours = graph.neighbours[chosenVertex];
var neighbourCount = graph.neighbourCount[chosenVertex];
graph.RemoveVertex(chosenVertex);
var newIgnoredVertexCount = ignoredVertexCount;
for (int i = 0; i < neighbourCount; i++)
{
var neighbour = neighbours[i];
if (ignoredVertex[neighbour])
{
newIgnoredVertexCount -= 1;
}
graph.RemoveVertex(neighbour);
}
// construct complementary graph
complementaryGraph.RemoveVertex(chosenVertex);
verticesAlreadyInMIS.Add(chosenVertex);
continueExecution = FindMIS(graph, complementaryGraph, verticesAlreadyInMIS, ignoredVertex, newIgnoredVertexCount, consumeAndDecideToContinue);
verticesAlreadyInMIS.RemoveAt(verticesAlreadyInMIS.Count - 1);
complementaryGraph.RestoreDeletedVertex();
// restore
for (int i = 0; i < neighbourCount; i++)
{
graph.RestoreDeletedVertex();
}
graph.RestoreDeletedVertex();
// DO NOT ADD VERTEX V TO MIS
// TODO: add warnings to his neighbours, add notion that the chosen vertex needs to be "covered" by someone!
// each vertex has a satifiability list
// there is a variable representing vertices left to satisfy
// each vertex has a counter that (when >0) triggers satisfiability stuff
// TODO make extra checks here and there is it possible to satisfy an ignored vertex, if not STOP
if (continueExecution && graph.neighbourCount[chosenVertex] > 0)
{
ignoredVertex[chosenVertex] = true;
continueExecution = FindMIS(graph, complementaryGraph, verticesAlreadyInMIS, ignoredVertex, ignoredVertexCount + 1, consumeAndDecideToContinue);
ignoredVertex[chosenVertex] = false;
}
}
}
return(continueExecution);
}