// Alternative way of calculating the boolean width of a decomposition by counting the number of maximal independent sets in bipartite graphs,
// constructed for each cut of the decomposition
private long CalculateBooleanWidthBiPartite()
{
BitSet left = new BitSet(0, Graph.Size);
BitSet right = Graph.Vertices;
long max = int.MinValue;
foreach (int v in Sequence)
{
left.Add(v);
right.Remove(v);
// Construct the bipartite graph
BipartiteGraph bg = new BipartiteGraph(Graph, left, right);
// Count the number of maximal independent sets in this bipartite graph
max = Math.Max(max, CC_MIS.Compute(bg));
}
return max;
}
// Implementation of Algorithm 13 of the PhD thesis by Sadia Sharmin
// The LeastCutValue selection method picks the next vertex based on a greedy choice, namely what is the vertex that will have the least
// influence on the boolean dimension at this point.
// While this generally gives great results, the runtime is very high because we construct multiple bipartite graphs during every iteration.
private static int LeastCutValue(Graph graph, BitSet left, BitSet right)
{
// Minimum boolean dimension that we can have for our next cut
long minBoolDim = long.MaxValue;
// Vertex that we will choose
int chosen = -1;
// Foreach candidate vertex we construct a bipartite graph and count the number of minimal independent sets in this bipartite graph
//This number is equal to the boolean-dimension at this cut
foreach (int v in right)
{
// Construct the bipartite graph
BipartiteGraph bg = new BipartiteGraph(graph, left + v, right - v);
// Count the number of MIS in the bipartite graph
long boolDim = CC_MIS.Compute(bg);
// Possibly update the minimum value found so far
if (boolDim < minBoolDim)
{
chosen = v;
minBoolDim = boolDim;
}
}
return chosen;
}
