Hypergraph ParBMAlgorithm::transversal (const Hypergraph& H) const {
BOOST_LOG_TRIVIAL(debug) << "Starting BM with " << num_threads
<< " threads. Hypergraph has "
<< H.num_verts() << " vertices and "
<< H.num_edges() << " edges.";
// Set up inputs
Hypergraph Hmin = H.minimization();
Hypergraph G (H.num_verts());
Hypergraph::Edge V = Hmin.verts_covered();
// Initialize using any HS we can find
Hypergraph::Edge first_hs = FKAlgorithm::minimize_new_hs(Hmin, G, V);
G.add_edge(first_hs);
// Grow G until it covers all vertices
bool G_has_full_coverage = false;
while (not G_has_full_coverage) {
Hypergraph::Edge new_hs = V - coverage_condition_check(H, G);
if (new_hs.is_proper_subset_of(V)) {
Hypergraph::Edge new_mhs = FKAlgorithm::minimize_new_hs(Hmin, G, new_hs);
G.add_edge(new_mhs);
} else {
G_has_full_coverage = true;
}
}
// Apply the BM algorithm repeatedly, generating new transversals
// until duality is confirmed
bool still_searching_for_transversals = true;
Hypergraph::EdgeQueue new_hses, new_mhses;
#pragma omp parallel shared(Hmin, G, new_hses, new_mhses) num_threads(num_threads)
#pragma omp master
while (still_searching_for_transversals) {
find_new_hses(Hmin, G, Hmin.verts_covered(), new_hses);
if (new_hses.size_approx() == 0) {
still_searching_for_transversals = false;
} else {
minimize_new_hses(Hmin, G, new_hses, new_mhses);
Hypergraph::Edge new_mhs;
while (new_mhses.try_dequeue(new_mhs)) {
// The results will all be inclusion-minimal, but
// there may be some overlap. Thus, we try to add
// them...
try {
G.add_edge(new_mhs, true);
}
// But ignore any minimality_violated_exception
// that is thrown.
catch (minimality_violated_exception& e) {}
}
BOOST_LOG_TRIVIAL(debug) << "New |G|: " << G.num_edges();
}
}
return G;
}
Hypergraph FKAlgorithmA::transversal (const Hypergraph& H) const {
BOOST_LOG_TRIVIAL(debug) << "Starting FKA. Hypergraph has "
<< H.num_verts() << " vertices and "
<< H.num_edges() << " edges.";
Hypergraph G (H.num_verts());
Hypergraph Hmin = H.minimization();
Hypergraph::Edge V = Hmin.verts_covered();
bool still_searching_for_transversals = true;
while (still_searching_for_transversals) {
Hypergraph::Edge omit_set = find_omit_set(Hmin, G);
if (omit_set.none() and G.num_edges() > 0) {
BOOST_LOG_TRIVIAL(debug) << "Received empty omit_set, so we're done.";
still_searching_for_transversals = false;
} else {
Hypergraph::Edge new_hs = V - omit_set;
Hypergraph::Edge new_mhs = minimize_new_hs(H, G, new_hs);
BOOST_LOG_TRIVIAL(trace) << "Received witness."
<< "\nomit_set:\t" << omit_set
<< "\nMHS:\t\t" << new_mhs;
G.add_edge(new_mhs, true);
BOOST_LOG_TRIVIAL(debug) << "New G size: " << G.num_edges();
}
}
return G;
}
Hypergraph ParBMAlgorithm::l5_full_cover (const Hypergraph& H,
const Hypergraph::Edge& base_transversal) {
/**
Find a full cover of the dual of H from the given base_transversal
in accordance with lemma 5 of BM.
**/
Hypergraph C (H.num_verts());
Hypergraph::Edge V = H.verts_covered();
C.add_edge(base_transversal, false);
Hypergraph::EdgeIndex i = base_transversal.find_first();
while (i != Hypergraph::Edge::npos) {
V.reset(i);
C.add_edge(V, false);
V.set(i);
i = base_transversal.find_next(i);
}
return C;
}
Hypergraph ParBMAlgorithm::l4_full_cover (const Hypergraph& H,
const Hypergraph::Edge& base_edge) {
/**
Find a full cover of the dual of H from the given base_edge
in accordance with lemma 4 of BM.
**/
Hypergraph C (H.num_verts());
Hypergraph::Edge V = H.verts_covered();
for (auto& edge: H) {
Hypergraph::Edge intersection = edge & base_edge;
Hypergraph::EdgeIndex i = intersection.find_first();
while (i != Hypergraph::Edge::npos) {
Hypergraph::Edge new_edge = V - edge;
new_edge.set(i);
C.add_edge(new_edge, false);
i = intersection.find_next(i);
}
}
return C;
}
