Ejemplo n.º 1
0
  /**
   * 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);
  }
Ejemplo n.º 2
0
  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;
  }
Ejemplo n.º 4
0
  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);
  }