public void Tree()
{
var reader = new DotReader(new StringReader(@"
strict graph {
1 -- 2
2 -- 3
2 -- 4
1 -- 5
}
strict graph {
1 -- 2
2 -- 3
2 -- 4
1 -- 5
}"));
var g = reader.Read();
var h = reader.Read();
var coloring = ColorRefinement.FindColoring(g, h);
Assert.Equal(10, coloring.Count);
Assert.Equal(4, coloring.Values.Distinct().Count());
Assert.Equal(coloring[g.Nodes["1"]], coloring[h.Nodes["1"]]);
Assert.Equal(coloring[g.Nodes["2"]], coloring[h.Nodes["2"]]);
Assert.Equal(coloring[g.Nodes["3"]], coloring[h.Nodes["3"]]);
Assert.Equal(coloring[g.Nodes["4"]], coloring[h.Nodes["4"]]);
Assert.Equal(coloring[g.Nodes["5"]], coloring[h.Nodes["5"]]);
}
private static IEnumerable <IDictionary <int, ISet <Node> > > FindIsomorphisms(Graph g, IList <Node> d, IList <Node> i)
{
var refinement = new ColorRefinement(g);
refinement.D.AddRange(d);
refinement.I.AddRange(i);
refinement.RefinePartitioning();
// Unbalanced colorings can never result in isomorphisms.
if (!IsBalanced(refinement.ColorSets.Values))
{
yield break;
}
// Base case: If we found a bijection, then this is an isomorphism!
if (IsBijection(refinement.ColorSets.Values))
{
yield return(refinement.ColorSets);
yield break;
}
// Find any of the cells that can be refined further by choosing one element.
var bigSet = refinement.ColorSets.Values.First(x => x.Count >= 4);
var nodeA = bigSet.First(x => x.Name.StartsWith(GraphAPrefix));
var d1 = new List <Node>(d)
{
nodeA
};
// See if the selected node can be mapped to any of the other graph's nodes.
foreach (var nodeB in bigSet.Where(x => x.Name.StartsWith(GraphBPrefix)))
{
var i1 = new List <Node>(i)
{
nodeB
};
foreach (var isomorphism in FindIsomorphisms(g, d1, i1))
{
yield return(isomorphism);
}
}
}
public void Simple()
{
var reader = new DotReader(new StringReader(@"
strict graph {
1 -- 2 -- 3
}
strict graph {
3 -- 2 -- 1
}"));
var g = reader.Read();
var h = reader.Read();
var coloring = ColorRefinement.FindColoring(g, h);
Assert.Equal(6, coloring.Count);
Assert.Equal(2, coloring.Values.Distinct().Count());
Assert.Equal(coloring[g.Nodes["1"]], coloring[h.Nodes["1"]]);
Assert.Equal(coloring[g.Nodes["2"]], coloring[h.Nodes["2"]]);
Assert.Equal(coloring[g.Nodes["3"]], coloring[h.Nodes["3"]]);
}
public void Branching()
{
var reader = new DotReader(new StringReader(@"
strict graph {
1 -- 2 -- 4
1 -- 3 -- 4
}
strict graph {
4 -- 2 -- 1
4 -- 3 -- 1
}"));
var g = reader.Read();
var h = reader.Read();
var coloring = ColorRefinement.FindColoring(g, h);
Assert.Equal(8, coloring.Count);
Assert.Single(coloring.Values.Distinct());
Assert.Equal(coloring[g.Nodes["1"]], coloring[h.Nodes["1"]]);
Assert.Equal(coloring[g.Nodes["2"]], coloring[h.Nodes["2"]]);
Assert.Equal(coloring[g.Nodes["3"]], coloring[h.Nodes["3"]]);
Assert.Equal(coloring[g.Nodes["4"]], coloring[h.Nodes["4"]]);
}