/// <summary>
/// Runs the Special Distance Test to reduce the graph.
/// </summary>
/// <param name="graph">The graph on which to run the test.</param>
/// <returns>The reduced graph.</returns>
public static ReductionResult RunTest(Graph graph)
{
List<Edge> redundant = new List<Edge>();
var result = new ReductionResult();
var distanceGraph = graph.CreateDistanceGraph();
var specialDistanceGraph = CreateInitialSpecialDistanceGraph(graph);
for (int i = 0; i < graph.NumberOfVertices; i++)
{
Console.Write("SD Test: {0}/{1} \r", i, graph.NumberOfVertices);
// Step 1. L := { i }
// for all j set delta_j = d_ij
// In each iteration, delta_j means the current special distance from the start vertex to j.
var vFrom = graph.Vertices[i];
List<Vertex> L = new List<Vertex>(new [] { vFrom }); // Initially only the start veretx is labeled.
// Initially set special distance equal to distance
foreach (var edge in specialDistanceGraph.GetEdgesForVertex(vFrom))
{
edge.Cost =
distanceGraph.GetEdgesForVertex(vFrom).Single(x => x.Other(vFrom) == edge.Other(vFrom)).Cost;
//edge.Cost = Math.Min(edge.Cost,
// distanceGraph.GetEdgesForVertex(vFrom).Single(x => x.Other(vFrom) == edge.Other(vFrom)).Cost);
}
List<Vertex> unhandledTerminals = null; // K \ L
while ((unhandledTerminals = graph.Terminals.Where(x => !L.Contains(x)).ToList()).Count > 0)
{ // While K \ L is not empty
// Find the terminal which minimizes delta(j) for all j in K \ L
int currentMinimum = int.MaxValue;
Vertex k = null;
var edgesFrom = specialDistanceGraph.GetEdgesForVertex(vFrom);
foreach (var terminal in unhandledTerminals)
{
var deltaEdge = edgesFrom.First(x => x.Other(vFrom) == terminal);
if (deltaEdge.Cost < currentMinimum)
{
currentMinimum = deltaEdge.Cost;
k = terminal;
}
}
L.Add(k);
// Re-lable all vertices that haven't gotten a definitive label yet.
var delta_k = edgesFrom.First(x => x.Other(vFrom) == k).Cost;
foreach (var unlabeled in graph.Vertices.Where(x => !L.Contains(x)))
{
var d_kj = distanceGraph.GetEdgesForVertex(k).First(x => x.Other(k) == unlabeled).Cost;
var deltaEdge = edgesFrom.First(x => x.Other(vFrom) == unlabeled);
deltaEdge.Cost = Math.Min(deltaEdge.Cost, Math.Max(delta_k, d_kj));
}
}
var specialEdges = specialDistanceGraph.GetEdgesForVertex(vFrom);
var distanceEdges = distanceGraph.GetEdgesForVertex(vFrom);
var edges = graph.GetEdgesForVertex(vFrom);
foreach (var redundantEdge in specialEdges.Where(x => x.Cost < distanceEdges.First(y => y.Other(vFrom) == x.Other(vFrom)).Cost))
{
// Special distance is smaller than distance. Edge is redundant.
var edge = edges.FirstOrDefault(x => x.Other(vFrom) == redundantEdge.Other(vFrom));
if (edge != null)
redundant.Add(edge);
}
}
foreach (var edge in redundant)
{
graph.RemoveEdge(edge);
result.RemovedEdges.Add(edge);
}
Console.Write(" \r");
return result;
}
