/** * Compute a distance-2 coloring of a bipartite graph G_b * * <p>Input: - G_b bipartite graph - V contained vertices are colored in the given ordering v_1, * ..., v_n * * <p>Output: - G_b bipartite graph with colors as weights vertex_color */ public static int PartialD2Coloring(GraphModel g, Vector<Integer> V) { Vector<Integer> N2 = new Vector<>(); Vector<Integer> forbidden = new Vector<>(g.numOfVertices()); for (int i = 0; i < g.numOfVertices(); i++) forbidden.add(-1); for (int v : V) g.getVertex(v).setColor(0); for (int v : V) { if (g.getDegree(g.getVertex(v)) > 0) { forbidden.set(0, v); N2 = Neighbors.N_2(g, v); for (int n2 : N2) { if (g.getVertex(n2).getColor() > 0) { forbidden.set(g.getVertex(n2).getColor(), v); } } for (int i = 0; i < forbidden.size(); i++) { if (forbidden.get(i) != v) { g.getVertex(v).setColor(i); break; } } } else { g.getVertex(v).setColor(0); } } return getNumOfCols(g); }
public Object calculate(GraphModel g) { ZagrebIndexFunctions zif = new ZagrebIndexFunctions(g); ZagrebIndexFunctions zifL = new ZagrebIndexFunctions(LineGraph.createLineGraph(g)); RendTable ret = new RendTable(); ret.add(new Vector<Object>()); ret.get(0).add(" M^3_1(G) "); ret.get(0).add("Z1"); ret.get(0).add("Z2"); ret.get(0).add("Z3"); ret.get(0).add("Z4"); ret.get(0).add("Ep3"); ret.get(0).add("Ep4"); ret.get(0).add("Psi1"); ret.get(0).add("Psi2"); ret.get(0).add("illc"); ret.get(0).add("N2"); ret.get(0).add("N1"); double maxDeg = 0; double maxDeg2 = 0; double minDeg = Integer.MAX_VALUE; ArrayList<Integer> al = AlgorithmUtils.getDegreesList(g); Collections.sort(al); maxDeg = al.get(al.size() - 1); if (al.size() - 2 >= 0) maxDeg2 = al.get(al.size() - 2); else maxDeg2 = maxDeg; minDeg = al.get(0); if (maxDeg2 == 0) maxDeg2 = maxDeg; double a = 0; double b = 0; for (Vertex v : g) { if (g.getDegree(v) == maxDeg) a++; if (g.getDegree(v) == minDeg) b++; } if (maxDeg == minDeg) b = 0; double m = g.getEdgesCount(); double n = g.getVerticesCount(); double M12 = zif.getSecondZagreb(1); double M21 = zif.getFirstZagreb(1); double M31 = zif.getFirstZagreb(2); double M41 = zif.getFirstZagreb(3); double M22 = zif.getSecondZagreb(2); double Mm31 = zif.getFirstZagreb(-4); double Mm11 = zif.getFirstZagreb(-2); double EM1 = zifL.getFirstZagreb(1); double Psi1 = (Math.pow( (2 * (m + 1) - (n + maxDeg + maxDeg2) + Math.sqrt( (2 * m - maxDeg - maxDeg2) * (Mm11 - ((1 / maxDeg) + (1 / maxDeg2))))), 2) / (n - 2)); double Psi2 = (Math.pow( (2 * (m + 1) - (n + maxDeg + minDeg) + Math.sqrt( (2 * m - maxDeg - minDeg) * (Mm11 - ((1 / maxDeg) + (1 / minDeg))))), 2) / (n - 2)); double Zeta1 = 2 * m - maxDeg - maxDeg2 + (M21 - maxDeg * maxDeg - maxDeg2 * maxDeg2 - n + 2) * (M21 - maxDeg * maxDeg - maxDeg2 * maxDeg2 - n + 2) / (2 * m - maxDeg - maxDeg2 - Mm11 + (1 / maxDeg) + (1 / maxDeg2)); double Zeta2 = 2 * m - (maxDeg) - (minDeg) + Math.pow((M21 - (maxDeg * maxDeg) - (minDeg * minDeg) - (n - 2)), 2) / (2 * m - maxDeg - minDeg - Mm11 + (1 / maxDeg) + (1 / minDeg)); double Zeta3 = M21 - maxDeg * maxDeg - maxDeg2 * maxDeg2 + (Math.pow((M21 - maxDeg * maxDeg - maxDeg2 * maxDeg2 - 2 * m + maxDeg + maxDeg2), 2) / (2 * m - maxDeg - maxDeg2 - n + 2)); double Zeta4 = M21 - maxDeg * maxDeg - minDeg * minDeg + (Math.pow((M21 - maxDeg * maxDeg - minDeg * minDeg - 2 * m + maxDeg + minDeg), 2) / (2 * m - maxDeg - minDeg - n + 2)); double Eps3 = (Math.pow( (M21 - (maxDeg * maxDeg) - (maxDeg2 * maxDeg2)) + Math.sqrt((n - 2) * (M21 - (maxDeg * maxDeg) - (maxDeg2 * maxDeg2))) - (2 * m - maxDeg - maxDeg2), 2) / (2 * m - maxDeg - maxDeg2)); double Eps4 = (Math.pow( (M21 - (maxDeg * maxDeg) - (minDeg * minDeg)) + Math.sqrt((n - 2) * (M21 - (maxDeg * maxDeg) - (minDeg * minDeg))) - (2 * m - maxDeg - minDeg), 2) / (2 * m - maxDeg - minDeg)); ret.add(new Vector<Object>()); ret.get(1).add(zifL.getFirstZagreb(1)); // new3 ret.get(1) .add( (maxDeg * maxDeg * maxDeg) + (maxDeg2 * maxDeg2 * maxDeg2) + (Zeta3) - (4 * M21) + (2 * M12) + (4 * m)); // new4 ret.get(1) .add( (maxDeg * maxDeg * maxDeg) + (minDeg * minDeg * minDeg) + (Zeta4) - (4 * M21) + (2 * M12) + (4 * m)); // new1 ret.get(1) .add( (maxDeg * maxDeg * maxDeg) + (maxDeg2 * maxDeg2 * maxDeg2) + (Zeta1) - (4 * M21) + (2 * M12) + (4 * m)); // new2 ret.get(1) .add( (maxDeg * maxDeg * maxDeg) + (minDeg * minDeg * minDeg) + (Zeta2) - (4 * M21) + (2 * M12) + (4 * m)); // Eps3 ret.get(1) .add( (maxDeg * maxDeg * maxDeg) + (maxDeg2 * maxDeg2 * maxDeg2) + (Eps3) - (4 * M21) + (2 * M12) + (4 * m)); // Eps4 ret.get(1) .add( (maxDeg * maxDeg * maxDeg) + (minDeg * minDeg * minDeg) + (Eps4) - (4 * M21) + (2 * M12) + (4 * m)); // Psi1 ret.get(1) .add( M31 - (4 * M21) + (2 * maxDeg * maxDeg) + (2 * maxDeg2 * maxDeg2) + (2 * Psi1) + 2 * (M12 - M21 + m) + 2 * m); // Psi2 ret.get(1) .add( M31 - (4 * M21) + (2 * maxDeg * maxDeg) + (2 * minDeg * minDeg) + (2 * Psi2) + 2 * (M12 - M21 + m) + 2 * m); // illc ret.get(1).add(((2 * m / n) * M21) + (4 * m) + (2 * M12) - (4 * M21)); // nilanjan de 2 ret.get(1).add(Math.pow(M21 - (2 * m), 2) / m); // nilanjan de 1 ret.get(1).add(4 * m * (minDeg - 1) * (minDeg - 1)); return ret; }
public Object calculate(GraphModel g) { ZagrebIndexFunctions zif = new ZagrebIndexFunctions(g); RenderTable ret = new RenderTable(); Vector<String> titles = new Vector<>(); titles.add(" E(G) "); titles.add(" 1.1 "); titles.add(" 1.2 "); titles.add(" 1.3 "); titles.add(" 1.4 "); titles.add(" 1.5 "); titles.add(" 1.6 "); titles.add(" 1.7 "); titles.add(" Eigenvalues "); titles.add(" 2-degree sum "); titles.add("new query"); ret.setTitles(titles); Matrix A = g.getWeightedAdjacencyMatrix(); EigenvalueDecomposition ed = A.eig(); double rv[] = ed.getRealEigenvalues(); double sum = 0; double detA = Math.abs(A.det()); // positiv RV Double[] prv = new Double[rv.length]; for (int i = 0; i < rv.length; i++) { prv[i] = Math.abs(rv[i]); prv[i] = (double) Math.round(prv[i] * 100000d) / 100000d; sum += prv[i]; } Arrays.sort(prv, Collections.reverseOrder()); double maxDeg = 0; double maxDeg2 = 0; double minDeg = Integer.MAX_VALUE; ArrayList<Integer> al = AlgorithmUtils.getDegreesList(g); Collections.sort(al); maxDeg = al.get(al.size() - 1); if (al.size() - 2 >= 0) maxDeg2 = al.get(al.size() - 2); else maxDeg2 = maxDeg; minDeg = al.get(0); if (maxDeg2 == 0) maxDeg2 = maxDeg; double a = 0; double b = 0; for (Vertex v : g) { if (g.getDegree(v) == maxDeg) a++; if (g.getDegree(v) == minDeg) b++; } if (maxDeg == minDeg) b = 0; double m = g.getEdgesCount(); double n = g.getVerticesCount(); double M12 = zif.getSecondZagreb(1); double M21 = zif.getFirstZagreb(1); double M22 = zif.getSecondZagreb(2); double Mm11 = zif.getFirstZagreb(-2); Vector<Object> v = new Vector<>(); v.add(sum); // 1 v.add(Math.sqrt(2 * m)); // 2 v.add( (2 * Math.sqrt(2 * m * n) * Math.sqrt(prv[0] * prv[prv.length - 1])) / (prv[0] + prv[prv.length - 1])); // 3 v.add((prv[0] * prv[prv.length - 1] * n + 2 * m) / (prv[0] + prv[prv.length - 1])); // 4 v.add(Math.sqrt(2 * m * n - (Math.pow(n * (prv[0] - prv[prv.length - 1]), 2) / 4))); // 5 double alpha = n * Math.floor(n / 2) * (1 - (1 / n) * Math.floor(n / 2)); v.add(Math.sqrt(2 * m * n - (Math.pow((prv[0] - prv[prv.length - 1]), 2) * alpha))); // 6 if (detA == 0) v.add(0); else v.add(Math.sqrt(2 * m + n * (n - 1) * Math.pow(detA, 2 / n))); // 7 double up = n * Math.pow(prv[0] - prv[prv.length - 1], 2); double down = 4 * (prv[0] + prv[prv.length - 1]); v.add(Math.sqrt(2 * m * n) - (up / down)); // eigenvalues v.add(getEigenValues(g)); // 2-degree sum v.add(Utils.getDegreeSum(g, 1)); // new query double eigenVal_k = prv[prv.length - 1]; int cnt = prv.length - 1; if (eigenVal_k == 0) { while (eigenVal_k == 0) { eigenVal_k = prv[--cnt]; } } int numOfNZEigenValue = 0; for (int i = 0; i < prv.length; i++) { if (prv[i] != 0) numOfNZEigenValue++; } double alpha_k = numOfNZEigenValue * Math.floor(numOfNZEigenValue / 2) * (1 - (1 / numOfNZEigenValue) * Math.floor(numOfNZEigenValue / 2)); System.out.println(alpha_k + " " + numOfNZEigenValue); System.out.println(prv[0] + " " + eigenVal_k); v.add(Math.sqrt(2 * m * numOfNZEigenValue - (Math.pow((prv[0] - eigenVal_k), 2) * alpha_k))); ret.add(v); return ret; }
public static int StarBicoloringSchemeCombinedVertexCoverColoringRestricted( GraphModel g, final Vector<Integer> V_rr, final Vector<Integer> V_cc, final int Mode) { Vector<Integer> IS = new Vector<>(); Vector<Integer> V_r = new Vector<>(); Vector<Integer> V_c = new Vector<>(); V_r.addAll(V_rr); V_c.addAll(V_cc); Vector<Integer> num_colors; Vector<Integer> V_r_aux = new Vector<>(); Vector<Integer> V_c_aux = new Vector<>(); V_r_aux.addAll(V_r); V_c_aux.addAll(V_c); GraphModel gaux = g.getCopy(); float ratio = 1; if (Mode != 1) ratio = Mode / 2; Vector<Pair<Integer, Integer>> Degree_V_r_aux = new Vector<>(); Vector<Pair<Integer, Integer>> Degree_V_c_aux = new Vector<>(); Vector<Pair<Integer, Integer>> copy_real_r = new Vector<>(); Vector<Pair<Integer, Integer>> copy_real_c = new Vector<>(); Vector<Integer> forbiddenColors = new Vector<>(V_r.size()); for (int i = 0; i < V_r.size(); i++) { forbiddenColors.add(-1); } Iterator<Integer> v_r_aux_it = V_r_aux.iterator(); for (int v_r : V_r) { if (v_r_aux_it.hasNext()) { int v_r_aux = v_r_aux_it.next(); copy_real_r.add(new Pair<>(v_r, v_r_aux)); } } Iterator<Integer> v_c_aux_it = V_c_aux.iterator(); for (int v_c : V_c) { if (v_c_aux_it.hasNext()) { int v_c_aux = v_c_aux_it.next(); copy_real_c.add(new Pair<>(v_c, v_c_aux)); } } for (int v_r : V_r_aux) { Degree_V_r_aux.add(new Pair<>(v_r, gaux.getDegree(gaux.getVertex(v_r)))); } for (int v_c : V_c_aux) { Degree_V_c_aux.add(new Pair<>(v_c, gaux.getDegree(gaux.getVertex(v_c)))); } while (gaux.getEdgesCount() > 0) { int max_degree_V_r_aux = 0; for (Pair<Integer, Integer> di : Degree_V_r_aux) { di.second = gaux.getDegree(gaux.getVertex(di.first)); int degree_v_r = di.second; if (degree_v_r > max_degree_V_r_aux) { max_degree_V_r_aux = degree_v_r; } } System.out.println("1"); int max_degree_V_c_aux = 0; for (Pair<Integer, Integer> di : Degree_V_c_aux) { di.second = gaux.getDegree(gaux.getVertex(di.first)); int degree_v_c = di.second; if (degree_v_c > max_degree_V_c_aux) { max_degree_V_c_aux = degree_v_c; } } System.out.println("2"); if (max_degree_V_r_aux > ratio * max_degree_V_c_aux) { Vector<Pair<Integer, Integer>> removedEdges = new Vector<>(); for (Pair<Integer, Integer> di : Degree_V_r_aux) { if (max_degree_V_r_aux == di.second) { Pair<Integer, Integer> cr = new Pair<>(0, 0); for (Pair<Integer, Integer> crtmp : copy_real_r) { if (crtmp.second.equals(di.first)) { cr = crtmp; break; } } int v = 0; for (int tmp : V_r) { if (cr.first == v) { v = tmp; break; } } System.out.println("33"); IndSet.clearVertex(gaux.getVertex(di.first), gaux); removedEdges.add(di); System.out.println("44"); forbiddenColors.set(0, v); for (Vertex w : g.getNeighbors(g.getVertex(v))) { if (w.getColor() <= 0) { for (Vertex x : g.getNeighbors(w)) { if (x.getColor() > 0) { if (g.getEdge(w, g.getVertex(v)).getWeight() == 1 || g.getEdge(w, x).getWeight() == 1) { forbiddenColors.set(x.getId(), v); } } } } else { // Color[w]>0 for (Vertex x : g.getNeighbors(w)) { if (x.getColor() > 0) { if (g.getEdge(w, x).getWeight() == 1) { for (Vertex y : g.getNeighbors(x)) { if (y.getColor() > 0) { if (w.getColor() == y.getColor() && w.getId() != y.getId()) { forbiddenColors.set(x.getId(), v); } } } } } } } System.out.println("45s"); } System.out.printf("456"); // Find first color which can be assigned to v_c for (int i = 0; i < forbiddenColors.size(); i++) { if (forbiddenColors.get(i) != v) { g.getVertex(v).setColor(forbiddenColors.get(i)); break; } } System.out.println("500"); } } Degree_V_r_aux.removeAll(removedEdges); } else { Vector<Pair<Integer, Integer>> removedEdges = new Vector<>(); for (Pair<Integer, Integer> di : Degree_V_c_aux) { if (max_degree_V_c_aux == di.second) { Pair<Integer, Integer> cr = new Pair<>(0, 0); for (Pair<Integer, Integer> crtmp : copy_real_c) { if (crtmp.second == di.first) { cr = crtmp; break; } } int v = 0; for (int tmp : V_c) { if (cr.first == v) { v = tmp; break; } } IndSet.clearVertex(gaux.getVertex(di.first), gaux); removedEdges.add(di); System.out.println("3"); forbiddenColors.set(0, v); System.out.println("3.0q" + v); for (Vertex w : g.getNeighbors(g.getVertex(v))) { System.out.println("3.1"); if (w.getColor() <= 0) { for (Vertex x : g.getNeighbors(w)) { if (x.getColor() > 0) { if (g.getEdge(w, g.getVertex(v)).getWeight() == 1 || g.getEdge(w, x).getWeight() == 1) { forbiddenColors.set(x.getId(), v); } } } System.out.println("3.2"); } else { // Color[w]>0 for (Vertex x : g.getNeighbors(w)) { System.out.println("3.3"); if (x.getColor() > 0) { if (g.getEdge(w, x).getWeight() == 1) { for (Vertex y : g.getNeighbors(x)) { if (y.getColor() > 0) { if (w.getColor() == y.getColor() && w.getId() != y.getId()) { forbiddenColors.set(x.getId(), v); } } } } } } } } System.out.println("3.5"); // Find first color which can be assigned to v_c for (int i = 0; i < forbiddenColors.size(); i++) { if (forbiddenColors.get(i) != v) { g.getVertex(v).setColor(forbiddenColors.get(i)); break; } } } } System.out.println("4"); Degree_V_c_aux.removeAll(removedEdges); } } for (Pair<Integer, Integer> di : Degree_V_r_aux) { IS.add(di.first); } for (Pair<Integer, Integer> di : Degree_V_c_aux) { IS.add(di.first); } for (int i = 0; i < IS.size(); i++) { g.getVertex(IS.get(i)).setColor(0); } return getNumOfCols(g); }