/// <summary>
/// Verifies if the given graph is a t-spanner for the given ratio a_t.
/// </summary>
/// <param name="a_graph"></param>
/// <param name="a_t"></param>
/// <returns>A vertification struct which holds the ratio and possibly a falsification pair. </returns>
public static SpannerVerification VerifySpanner(IGraph a_graph, float a_t)
{
//first determine the possible edges
var completeGraph = new AdjacencyListGraph(new List <Vertex>(a_graph.Vertices));
completeGraph.MakeComplete();
var edges = completeGraph.Edges.ToList();
edges.Sort();
Vertex Start = null;
Vertex End = null;
var ratio = 1f; // best possible ratio
foreach (var edge in edges)
{
// find distance in given graph
// TODO all-pair shortest path
var dist = ShortestPath.ShorthestDistance(a_graph, edge.Start, edge.End);
// compare ratios
float edgeratio = dist / edge.Weight;
if (edgeratio > a_t)
{
Start = edge.Start;
End = edge.End;
}
if (ratio <= edgeratio)
{
ratio = edgeratio;
}
}
return(new SpannerVerification(Start, End, ratio));
}
/// <summary>
/// Creates a t-spanner using a greedy algorithm trying the shortest edges first.
/// </summary>
/// <param name="a_graph"> the graph on which we want to construct a t-spanner</param>
/// <param name="a_t"> parameter t in the definition of t-spanner. Each pair of vertices should have a path
/// of at most length t*eucledian distance</param>
/// <returns></returns>
public static IGraph GreedySpanner(IGraph a_graph, float a_t)
{
var result = new AdjacencyListGraph(a_graph.Vertices);
var edges = a_graph.Edges.ToList();
edges.Sort(); // by default sorts on weight
foreach (var edge in edges)
{
// add edge if t-spanner criteria not satisfied
if (ShortestPath.ShorthestDistance(result, edge.Start, edge.End) > a_t * edge.Weight)
{
result.AddEdge(edge);
}
}
return(result);
}