/// <summary>
/// Saves a graph to a file in the GraphML format.
/// </summary>
/// <typeparam name="TNode"></typeparam>
/// <typeparam name="TLabel"></typeparam>
/// <param name="graph"></param>
/// <param name="labels"></param>
public static void SaveToGraphML <TNode, TLabel>(MultiDirectedGraph <TNode, TLabel> graph, string path)
{
List <string> lines = new List <string>();
lines.Add("<?xml version=\"1.0\" encoding=\"utf-8\" ?>");
lines.Add("<graphml xmlns=\"http://graphml.graphdrawing.org/xmlns\" xmlns:xsi=\"http://www.w3.org/2001/XMLSchema-instance\" xsi:schemaLocation=\"http://graphml.graphdrawing.org/xmlns http://graphml.graphdrawing.org/xmlns/1.0/graphml.xsd\">");
lines.Add("\t<key id=\"label\" for=\"all\" attr.name=\"label\" attr.type=\"string\">");
lines.Add("\t\t<default>0</default>");
lines.Add("\t</key>");
lines.Add("\t<graph id=\"" + graph.Name + "\" edgedefault=\"" + (graph.IsDirected ? "directed" : "undirected") + "\">");
foreach (var node in graph.Nodes)
{
lines.Add("\t\t<node id=\"" + node + "\">");
lines.Add("\t\t\t<data key=\"label\">" + graph.NodeLabel(node) + "</data>");
lines.Add("\t\t</node>");
}
foreach (var edge in graph.Edges)
{
var s = graph.Source(edge);
var t = graph.Target(edge);
lines.Add("\t\t<edge source=\"" + s + "\" target=\"" + t + "\">");
lines.Add("\t\t\t<data key=\"label\">" + graph.EdgeLabel(edge) + "</data>");
lines.Add("\t\t</edge>");
}
lines.Add("\t</graph>");
lines.Add("</graphml>");
File.WriteAllLines(path, lines);
}
/// <summary>
///
/// </summary>
/// <param name="owner"></param>
private void setOwner(IDictionary <TNode, ExactBisimulationWorker <TNode, TLabel> > owner)
{
this.owner = owner;
this.ownerInverted = Utils.Invert(owner);
this.interestedIn = new Dictionary <ExactBisimulationWorker <TNode, TLabel>, HashSet <TNode> >();
// Initialize interested-in function
foreach (var worker in ownerInverted.Keys)
{
interestedIn.Add(worker, new HashSet <TNode>());
}
foreach (var target in ownerInverted[this])
{
foreach (var ei in graph.In(target))
{
var source = graph.Source(ei);
if (!interestedIn[owner[source]].Contains(target))
{
interestedIn[owner[source]].Add(target);
}
}
}
interestedIn.Remove(this);
}
/// <summary>
/// Measures the cut of a partition of a graph.
/// </summary>
/// <typeparam name="TNode"></typeparam>
/// <typeparam name="TLabel"></typeparam>
/// <param name="graph"></param>
/// <param name="partition"></param>
/// <returns></returns>
public static int Cut <TNode, TLabel>(MultiDirectedGraph <TNode, TLabel> graph, IDictionary <TNode, int> partition)
{
int cut = 0;
foreach (var edge in graph.Edges)
{
var s = graph.Source(edge);
var t = graph.Target(edge);
if (partition[s] != partition[t])
{
cut += 1;
}
}
return(cut);
}
/// <summary>
/// Sample edges randomly uniformly.
/// </summary>
/// <typeparam name="TNode"></typeparam>
/// <param name="graph"></param>
/// <param name="m">Upper bound on the number of edges to sample.</param>
/// <returns></returns>
public static IEnumerable <TNode> RE <TNode, TLabel>(this MultiDirectedGraph <TNode, TLabel> graph, int m)
{
var edges = Utils.Shuffled(graph.Edges.ToArray()).Take(Math.Min(m, graph.NumEdges)).ToArray();
var nodes = new HashSet <TNode>();
foreach (var edge in edges)
{
var s = graph.Source(edge);
var t = graph.Target(edge);
if (!nodes.Contains(s))
{
nodes.Add(s);
}
if (!nodes.Contains(t))
{
nodes.Add(t);
}
}
return(nodes);
}
/// <summary>
/// KerninghanLin algorithm which refines a partition.
/// Equalizes block sizes and swaps nodes between partition blocks to minimize the edge cut.
/// </summary>
/// <typeparam name="TNode">Type of node.</typeparam>
/// <typeparam name="TLabel">Type of label.</typeparam>
/// <param name="graph">The graph of the partition.</param>
/// <param name="partition">The partition to refine.</param>
/// <param name="K">Maximum number of iterations.</param>
public static void KernighanLin <TNode, TLabel>(MultiDirectedGraph <TNode, TLabel> graph, Dictionary <TNode, int> partition, int K)
{
// Compute ED and ID of each node
var ED = new Dictionary <TNode, int>();
var ID = new Dictionary <TNode, int>();
Func <TNode, int> D = node => ED[node] - ID[node];
foreach (var node in graph.Nodes)
{
ED.Add(node, 0);
ID.Add(node, 0);
}
foreach (var edge in graph.Edges)
{
var s = graph.Source(edge);
var t = graph.Target(edge);
if (partition[s] == partition[t])
{
ID[s] += 1;
ID[t] += 1;
}
else
{
ED[s] += 1;
ED[t] += 1;
}
}
// Stick nodes into sets of their partition block
var inverted = Utils.Invert(partition);
var AI = inverted.Keys.First();
var BI = inverted.Keys.Last();
// Swaps a node from its original partition block to the other
Action <TNode> swap = node =>
{
foreach (var edge in graph.Out(node).Concat(graph.In(node)))
{
var neighbor = graph.Target(edge);
if (node.Equals(neighbor))
{
continue;
}
if (partition[node] == partition[neighbor])
{
// Will be in other block now
ID[neighbor] -= 1;
ID[node] -= 1;
ED[neighbor] += 1;
ED[node] += 1;
}
else
{
// Will be in same block now
ID[neighbor] += 1;
ID[node] += 1;
ED[neighbor] -= 1;
ED[node] -= 1;
}
}
if (partition[node] == AI)
{
partition[node] = BI;
inverted[AI].Remove(node);
inverted[BI].Add(node);
}
else
{
partition[node] = AI;
inverted[AI].Add(node);
inverted[BI].Remove(node);
}
};
// Equalize block sizes
while (Math.Abs(inverted[AI].Count - inverted[BI].Count) > 1)
{
if (inverted[AI].Count > inverted[BI].Count)
{
// Move from A to B
var a = inverted[AI].MaxBy(node => D(node));
swap(a);
}
else
{
// Move from B to A
var b = inverted[BI].MaxBy(node => D(node));
swap(b);
}
}
// Keep performing positive swaps
int n = Math.Min(inverted[AI].Count, inverted[BI].Count);
for (int i = 0; i < K; i++)
{
bool hasGained = false;
var AA = new HashSet <TNode>(inverted[AI]);
var BB = new HashSet <TNode>(inverted[BI]);
for (int j = 0; j < n; j++)
{
var a = AA.MaxBy(node => D(node));
var b = BB.MaxBy(node => D(node));
int gain = D(a) + D(b);
if (graph.HasEdge(a, b))
{
gain -= 2;
}
if (graph.HasEdge(b, a))
{
gain -= 2;
}
if (gain > 0)
{
hasGained = true;
swap(a);
swap(b);
}
AA.Remove(a);
BB.Remove(b);
}
if (!hasGained)
{
break;
}
}
}
/// <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);
}