private static void Visit(UndirectedGraph graph, IReporter reporter,
ISet <Vertex> candidates, ISet <Vertex> excluded, ImmutableArray <Vertex> cliqueInProgress)
{
Debug.Assert(candidates.All(v => graph.Degree(v) > 0));
Debug.Assert(excluded.All(v => graph.Degree(v) > 0));
Debug.Assert(!candidates.Overlaps(excluded));
Debug.Assert(candidates.Any());
while (candidates.Any())
{
var v = CollectionsUtil.PopArbitrary(candidates);
var neighbours = graph.Neighbours(v);
var neighbouringCandidates = CollectionsUtil.Intersection(candidates, neighbours);
if (neighbouringCandidates.Any())
{
var neighbouringExcluded = CollectionsUtil.Intersection(excluded, neighbours);
Visit(graph, reporter,
neighbouringCandidates, neighbouringExcluded,
CollectionsUtil.Append(cliqueInProgress, v));
}
else if (CollectionsUtil.AreDisjoint(excluded, neighbours))
{
reporter.Record(CollectionsUtil.Append(cliqueInProgress, v));
}
var added = excluded.Add(v);
Debug.Assert(added);
}
}
public void AreDisjoint()
{
var empty = new HashSet <int> {
};
var one = new HashSet <int> {
1
};
var two = new HashSet <int> {
1, 2
};
var six = new HashSet <int> {
0, 1, 2, 3, 4, 5
};
Assert.That(CollectionsUtil.AreDisjoint(empty, one));
Assert.That(CollectionsUtil.AreDisjoint(one, empty));
Assert.That(CollectionsUtil.AreDisjoint(empty, two));
Assert.That(CollectionsUtil.AreDisjoint(two, empty));
Assert.That(CollectionsUtil.AreDisjoint(empty, six));
Assert.That(CollectionsUtil.AreDisjoint(six, empty));
Assert.That(!CollectionsUtil.AreDisjoint(one, two));
Assert.That(!CollectionsUtil.AreDisjoint(two, one));
Assert.That(!CollectionsUtil.AreDisjoint(one, six));
Assert.That(!CollectionsUtil.AreDisjoint(six, one));
Assert.That(!CollectionsUtil.AreDisjoint(two, six));
Assert.That(!CollectionsUtil.AreDisjoint(six, two));
Assert.That(!CollectionsUtil.AreDisjoint(one, one));
Assert.That(!CollectionsUtil.AreDisjoint(two, two));
Assert.That(!CollectionsUtil.AreDisjoint(six, six));
}
public static void Explore(UndirectedGraph graph, IReporter finalReporter)
{
var scheduler = TaskScheduler.Default;
int sent = 0;
int received = 0;
// Step 3: collect results.
var collect = new ActionBlock <ImmutableArray <Vertex> >(clique => finalReporter.Record(clique));
// Step 2: visit vertices.
var reporter = new NestedReporter(collect);
int waitgroup = 1;
void completion(Task _)
{
if (Interlocked.Decrement(ref waitgroup) == 0)
{
reporter.Close();
collect.Complete();
}
}
var excluded = new HashSet <Vertex>();
var visit = new ActionBlock <Vertex>(v =>
{
var neighbours = graph.Neighbours(v);
Debug.Assert(neighbours.Any());
var neighbouringCandidates = CollectionsUtil.Difference(neighbours, excluded);
if (neighbouringCandidates.Any())
{
var neighbouringExcluded = CollectionsUtil.Intersection(excluded, neighbours);
_ = Interlocked.Increment(ref waitgroup);
_ = Task.Run(delegate
{
Pivot.Visit(graph, reporter, Pivot.Choice.MaxDegreeLocal,
neighbouringCandidates, neighbouringExcluded,
ImmutableArray.Create(v));
}).ContinueWith(completion, scheduler);
}
else
{
Debug.Assert(!CollectionsUtil.AreDisjoint(neighbours, excluded));
}
var added = excluded.Add(v);
Debug.Assert(added);
++received;
});
_ = visit.Completion.ContinueWith(completion, scheduler);
// Step 1: feed vertices in order.
_ = Task.Run(delegate
{
foreach (var v in Degeneracy.Ordering(graph, drop: 1))
{
while (!visit.Post(v))
{
throw new InvalidOperationException("Post failed");
}
++sent;
}
visit.Complete();
});
collect.Completion.Wait();
if (sent != received)
{
throw new InvalidOperationException($"{sent} sent <> {received} received");
}
}