// Constructor for creating a new representative table. We directly fill the table depending on the given sequence.
public LinearRepresentativeTable(Graph graph, List<int> sequence)
{
// Initialize the table
_table = new Dictionary<BitSet, LinearRepresentativeList>();
int n = graph.Size;
// Save these initial representatives for the cut(empty, V(G))
LinearRepresentativeList reps = new LinearRepresentativeList();
reps.Update(new BitSet(0, n), new BitSet(0, n));
_table[new BitSet(0, n)] = reps;
_table[graph.Vertices] = reps;
FillTable(graph, sequence);
List<int> reverseSequence = new List<int>();
for (int i = sequence.Count - 1; i >= 0; i--)
reverseSequence.Add(sequence[i]);
FillTable(graph, reverseSequence);
}
private void FillTable(Graph graph, List<int> sequence)
{
int n = graph.Size;
// Processed vertices
BitSet left = new BitSet(0, n);
// Unprocessed vertices
BitSet right = graph.Vertices;
// Lists of representatives that we keep track of on each level of the algorithm
LinearRepresentativeList reps = new LinearRepresentativeList();
// Initial insertions, the empty set always has the empty neighborhood set as a representative initially
reps.Update(new BitSet(0, n), new BitSet(0, n));
for (int i = 0; i < sequence.Count; i++)
{
/// We give v the possibility to be a representative instead of being contained in neighborhoods
int v = sequence[i];
// Actually move v from one set to the other set
left += v;
right -= v;
// We don't want to disturb any pointers so we create new empty datastructures to save everything for the next iteration
LinearRepresentativeList nextReps = new LinearRepresentativeList();
// We are iterating over all representatives saved inside the list of the previous step. For each entry there are only two possibilities to create a new neighborhood
foreach (BitSet representative in reps)
{
// Case 1: The neighborhood possibly contained v (thus v has to be removed), but is still valid
BitSet neighborhood = reps.GetNeighborhood(representative) - v;
nextReps.Update(representative, neighborhood);
// Case 2: The union of the old neighborhood, together with v's neighborhood, creates a new entry. The representative is uniond together with v and saved.
BitSet representative_ = representative + v;
BitSet neighborhood_ = neighborhood + (graph.OpenNeighborhood(v) * right);
nextReps.Update(representative_, neighborhood_);
}
// Update the values for the next iteration
reps = nextReps;
// Save the maximum size that we encounter during all iterations; this will be the boolean dimension of the graph.
MaxDimension = Math.Max(MaxDimension, reps.Count);
// Save the representatives at the current cut in the table
_table[left] = reps;
}
}