/// <summary>
/// Measures the weighted k-bisimulation partition equivalence between two graphs.
/// </summary>
/// <typeparam name="TNode"></typeparam>
/// <typeparam name="TLabel"></typeparam>
/// <param name="G1"></param>
/// <param name="G2"></param>
/// <param name="L1"></param>
/// <param name="L2"></param>
/// <param name="k">A tuple indicating how many nodes of G1 and G2 are in partition blocks that are shared between G1 and G2.</param>
/// <returns></returns>
public static Tuple <int, int> WeightedBisimulationEquivalence <TNode, TLabel>(MultiDirectedGraph <TNode, TLabel> G1, MultiDirectedGraph <TNode, TLabel> G2, int k)
{
// Create new empty graph and label provider
var G = new MultiDirectedGraph <Tuple <int, TNode>, TLabel>();
// Add nodes of G1
foreach (var node in G1.Nodes.Select(node => Tuple.Create(1, node)))
{
G.AddNode(node, G1.NodeLabel(node.Item2));
}
// Add nodes of G2
foreach (var node in G2.Nodes.Select(node => Tuple.Create(2, node)))
{
G.AddNode(node, G2.NodeLabel(node.Item2));
}
// Add edges of G1
foreach (var edge in G1.Edges)
{
var s = Tuple.Create(1, G1.Source(edge));
var t = Tuple.Create(1, G1.Target(edge));
G.AddEdge(s, t, G1.EdgeLabel(edge));
}
// Add edges of G2
foreach (var edge in G2.Edges)
{
var s = Tuple.Create(2, G2.Source(edge));
var t = Tuple.Create(2, G2.Target(edge));
G.AddEdge(s, t, G2.EdgeLabel(edge));
}
// Perform bisimulation reduction
var partitioner = new GraphPartitioner <Tuple <int, TNode>, TLabel>(G);
var partition = partitioner.BoundedExactBisimulationReduction(k);
// Partition blocks of G1 and G2
HashSet <int> P1 = new HashSet <int>();
HashSet <int> P2 = new HashSet <int>();
foreach (var node in G.Nodes)
{
int block = partition[node];
switch (node.Item1)
{
case 1:
if (!P1.Contains(block))
{
P1.Add(block);
}
break;
case 2:
if (!P2.Contains(block))
{
P2.Add(block);
}
break;
}
}
int s1 = 0;
int s2 = 0;
foreach (var node in G.Nodes)
{
if (P1.Contains(partition[node]) && P2.Contains(partition[node]))
{
switch (node.Item1)
{
case 1:
s1 += 1;
break;
case 2:
s2 += 1;
break;
}
}
}
return(Tuple.Create(s1, s2));
}
/// <summary>
///
/// </summary>
/// <param name="D"></param>
/// <param name="b"></param>
/// <returns></returns>
public static MultiDirectedGraph <int, int> GenerateNiceDAG(int D, int b)
{
// Create empty graph and label provider
var graph = new MultiDirectedGraph <int, int>();
graph.Name = "Synthetic_DAG_" + D + "_" + b;
// Define parent function
Func <int, int> parent = node =>
{
// Assume node > 0 (not the root node)
return(graph.In(node).First());
};
// Define level function
Func <int, int> level = Utils.Y <int, int>(fix => node =>
{
if (node == 0)
{
// Root node
return(0);
}
else
{
return(1 + fix(parent(node)));
}
});
// Create initial tree
int counter = 0;
graph.AddNode(counter, 0);
counter += 1;
while (graph.Nodes.Select(node => level(node)).Max() < D)
{
int max = graph.Nodes.Select(node => level(node)).Max();
var lowest = graph.Nodes.Where(node => level(node) == max).ToArray();
foreach (var node in lowest)
{
int k = StaticRandom.Next(b + 1);
for (int i = 0; i < k; i++)
{
graph.AddNode(counter, 0);
graph.AddEdge(node, counter, i);
// graph.AddEdge(node, counter, 0);
counter += 1;
}
}
}
// Transform tree to DAG with nicer partition block distribution
var copy = graph.Clone();
var partitioner = new GraphPartitioner <int, int>(graph);
var partition = partitioner.BoundedExactBisimulationReduction(D);
var partitionInverted = Utils.Invert(partition);
var blocks = partition.Values.Distinct();
var blockSizes = Utils.Distribution(partition.Values);
int blockMax = blockSizes.Values.Max();
foreach (var block in blocks)
{
int size = blockSizes[block];
var nodes = new List <int>(partitionInverted[block]);
for (int i = size; i < blockMax; i++)
{
// Replicate a random node in this partition block
int k = StaticRandom.Next(size);
var v = nodes[k];
// Replicate the node
graph.AddNode(counter, graph.NodeLabel(v));
// Replicate its incoming edges
foreach (var ei in copy.In(v))
{
var u = graph.Source(ei);
graph.AddEdge(u, counter, graph.EdgeLabel(ei));
}
// Replicate its outgoing edges
foreach (var eo in copy.Out(v))
{
var w = graph.Target(eo);
graph.AddEdge(counter, w, graph.EdgeLabel(eo));
}
counter += 1;
}
}
return(graph);
}