public static int Compute(LinearDecomposition decomposition)
{
Graph graph = decomposition.Graph;
List<int> sequence = decomposition.Sequence;
// Left is the set of vertices that have been processed so far.
BitSet left = new BitSet(0, graph.Size);
// Right is the set of vertices that we have yet to process, initially set to all vertices in the graph.
BitSet right = graph.Vertices;
// The leftneighborset contains ISN elements, that save the size of each independent set in Left, and the corresponding neighborhood in Right that belongs to this IS.
LookupTable table = new LookupTable();
// Insert the initial neighborhood and IS of size 0 and an empty neighborhood.
table.Update(new ISN(new BitSet(0, graph.Size), 0));
// maxIS saves the largest independent set that we have encountered so far.
int maxIS = 0;
// Loop over all vertices in the sequence; we have to process all of them.
for (int i = 0; i < sequence.Count; i++)
{
// Take the next vertex in the sequence.
int v = sequence[i];
//Save all updated element in a new neighborset, so that we do not disturb any looping over elements.
LookupTable newTable = new LookupTable();
foreach (ISN iset in table)
{
// If a neighborhood Right contains the currently selected element, then we have to remove it from the neighborhood.
// The corresponding IS in Left is still valid, but it simply belongs to a smaller neighborhood in Right (hence the removal of v).
if (iset.Elements.Contains(v))
{
iset.Elements.Remove(v);
newTable.Update(iset);
}
// If the neighborhood does not contain v, then there are two cases that have to be handled.
else
{
// Case a: If v is not an element of the largest IS, then the previous IS is still valid.
// We have no risk of v being contained in the neighborhood of Right, because if that would be the case we would not be in the else-part of the if-statement.
// Thus, we simply add an unmodified copy of j to the new list of neighborhoodsets.
newTable.Update(iset);
// Case b: If v is an element of the largest IS, then we should include a new entry for this newly created IS.
// The size of this IS will increase by one (adding v will cause this).
// The neighborhood of this IS is the old neighborhood, plus any vertices in Right that are in the neighborhood of v. Vertex v causes the addition of these vertices.
// The largest saved IS might change because of this addition of a new erlement.
ISN newIset = new ISN(iset.Elements.Copy(), iset.Size);
newIset.Size++;
newIset.Elements = newIset.Elements + (graph.OpenNeighborhood(v) * right);
maxIS = Math.Max(maxIS, newIset.Size);
newTable.Update(newIset);
}
}
// Safely update all sets that we are working with
left.Add(v);
right.Remove(v);
table = newTable;
}
// The largest IS that we have encountered is the one we will return
return maxIS;
}
// Update will insert or update values of the hashset, depending on if an element is already contained in the set or not.
public void Update(ISN iset)
{
// Firstly check if we already have an entry for this ISN. If we don't; simply add the ISN to the set using its hash representation.
if (Data.ContainsKey(iset.Elements))
{
// If we do, then update the size if the new size is larger than the currently saved size.
// This corresponds to each neighborhood only saving the size of the largest IS in Left, since that is the only IS we are interested in.
if (iset.Size > Data[iset.Elements].Size)
Data[iset.Elements] = iset;
}
else
{
Data[iset.Elements] = iset;
}
}
