/// <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 miminum spanning tree of the given list of vertices, where the vertices form a complete graph.
/// </summary>
/// <param name="a_vertices"></param>
/// <returns>A graph representing the minimum spanning tree</returns>
public static IGraph MinimumSpanningTree(IEnumerable <Vertex> a_vertices)
{
var graph = new AdjacencyListGraph(a_vertices);
graph.MakeComplete();
return(MinimumSpanningTree(graph));
}
/// <summary>
/// Tries to find a perfect matching with minimum weight of the given vertices, where the vertices form a complete graph
/// </summary>
/// <param name="a_vertices"></param>
/// <returns>Collection of matching edges.</returns>
public static IEnumerable <Edge> MinimumWeightPerfectMatching(List <Vertex> a_vertices)
{
// first, create a complete graph of the vertices
var result = new AdjacencyListGraph(a_vertices);
result.MakeComplete();
return(GreedyMinimumWeightPerfectMatching(result));
}
/// <summary>
/// Creates a t-spanner using a greedy algorithm trying the shortest edges first.
/// </summary>
/// <param name="a_vertices"> the vertices on which we want to construct a t-spanner</param>
/// <param name="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(List <Vertex> a_vertices, float a_t)
{
var completeGraph = new AdjacencyListGraph(a_vertices);
completeGraph.MakeComplete();
// return t-spanner of complete graph
return(GreedySpanner(completeGraph, a_t));
}
public void GreedySpannerCompleteTest()
{
Assert.True(m_complete4.Equals(Spanner.GreedySpanner(m_complete4pos, 1)));
//large test case
var pos = new List <Vertex> {
new Vertex(9, 3), new Vertex(5, 6), new Vertex(4, 7), new Vertex(-2, 5), new Vertex(6, -3), new Vertex(23, 3), new Vertex(22, 4),
new Vertex(9.5f, -3.4f), new Vertex(5.5f, -6.3f), new Vertex(-4.5f, 7.4f), new Vertex(-2.5f, -5.3f), new Vertex(6.5f, -3.3f), new Vertex(23.5f, -4.3f), new Vertex(22.5f, -5.3f)
};
var completegraph = new AdjacencyListGraph(pos);
completegraph.MakeComplete();
var spanner = Spanner.GreedySpanner(pos, 1);
Assert.True(completegraph.Equals(spanner));
}
public void EqualGraphTest()
{
var otherGraph = new AdjacencyListGraph();
var lv2complete = new AdjacencyListGraph(m_level2pos);
lv2complete.MakeComplete();
Assert.True(m_complete4.Equals(m_complete4));
Assert.False(otherGraph.Equals(m_complete4));
// Graph on the same vertices
Assert.False(lv2complete.Equals(otherGraph));
//Same graphs on different vertex set
Assert.True(lv2complete.Equals(lv2complete));
}
public TSPTest()
{
m_points = new List <Vertex>()
{
new Vertex(0, 0),
new Vertex(2, 0),
new Vertex(0, 1),
new Vertex(1.5f, -1)
};
m_graph = new AdjacencyListGraph(m_points);
m_graph.AddEdge(m_points[0], m_points[2]);
m_graph.AddEdge(m_points[2], m_points[1]);
m_graph.AddEdge(m_points[1], m_points[3]);
m_graph.AddEdge(m_points[3], m_points[0]);
m_complete4 = new AdjacencyListGraph(m_points);
m_complete4.MakeComplete();
expTSP = 1 + Mathf.Sqrt(5) + Mathf.Sqrt(1.25f) + Mathf.Sqrt(3.25f);
}
