def fvs_via_mif(g: MultiGraph, k: int) -> set: mif_set = mif(g, g.order()-k) if mif_set: nodes = set(g.nodes()) mif_set = nodes.difference(mif_set) return mif_set
def mif_main(g: MultiGraph, f: set, t, k: int) -> set: k_set = k != None new_k1 = new_k2 = None if k_set and k > g.order(): return None if f == g.nodes() or (k_set and k <= 0): return f if (not f): g_degree = g.degree() g_max_degree_node = max(g_degree, key=lambda n: g_degree[n]) if (g_degree[g_max_degree_node] <= 1): return set(g.nodes()) else: fx = f.copy() fx.add(g_max_degree_node) gx = g.copy() gx.remove_node(g_max_degree_node) if k_set: new_k1 = k-1 new_k2 = k mif_set1 = mif_preprocess_1(g, fx, t, new_k1) mif_set2 = mif_preprocess_1(gx, f, t, new_k2) if not mif_set1: return mif_set2 elif not mif_set2: return mif_set1 else: return max(mif_set1, mif_set2, key=len) # Set t as active vertex if t == None or not t in f: t = next(iter(f)) gd_over_3 = None gd_2 = None for v in g.neighbors_iter(t): (gd_v, gn_v) = generalized_degree(g, f, t, v) if gd_v <= 1: f.add(v) if k_set: new_k1 = k-1 return mif_preprocess_1(g, f, t, new_k1) elif gd_v >= 3: gd_over_3 = v else: gd_2 = (v, gn_v) if gd_over_3 != None: # Cannot simply use "if gd_over_3" because v might be 0 fx = f.copy() fx.add(gd_over_3) gx = g.copy() gx.remove_node(gd_over_3) if k_set: new_k1 = k-1 new_k2 = k mif_set1 = mif_preprocess_1(g, fx, t, new_k1) mif_set2 = mif_preprocess_1(gx, f, t, new_k2) if not mif_set1: return mif_set2 elif not mif_set2: return mif_set1 else: return max(mif_set1, mif_set2, key=len) elif gd_2 != None: (v, gn) = gd_2 fx1 = f.copy() fx2 = f.copy() fx1.add(v) for n in gn: fx2.add(n) gx = g.copy() gx.remove_node(v) if k_set: new_k1 = k-2 new_k2 = k-1 try: cyc.find_cycle(gx.subgraph(fx2)) mif_set1 = None except: mif_set1 = mif_preprocess_1(gx, fx2, t, new_k1) mif_set2 = mif_preprocess_1(g, fx1, t, new_k2) if not mif_set1: return mif_set2 elif not mif_set2: return mif_set1 else: return max(mif_set1, mif_set2, key=len) return None
