public static boolean meekR1Locally2(
      Graph graph, Knowledge knowledge, IndependenceTest test, int depth) {
    List<Node> nodes = graph.getNodes();
    boolean changed = true;

    while (changed) {
      changed = false;

      for (Node a : nodes) {
        List<Node> adjacentNodes = graph.getAdjacentNodes(a);

        if (adjacentNodes.size() < 2) {
          continue;
        }

        ChoiceGenerator cg = new ChoiceGenerator(adjacentNodes.size(), 2);
        int[] combination;

        while ((combination = cg.next()) != null) {
          Node b = adjacentNodes.get(combination[0]);
          Node c = adjacentNodes.get(combination[1]);

          // Skip triples that are shielded.
          if (graph.isAdjacentTo(b, c)) {
            continue;
          }

          if (graph.getEndpoint(b, a) == Endpoint.ARROW && graph.isUndirectedFromTo(a, c)) {
            if (existsLocalSepsetWithoutDet(b, a, c, test, graph, depth)) {
              continue;
            }

            if (isArrowpointAllowed(a, c, knowledge)) {
              graph.setEndpoint(a, c, Endpoint.ARROW);
              TetradLogger.getInstance()
                  .edgeOriented(SearchLogUtils.edgeOrientedMsg("Meek R1", graph.getEdge(a, c)));
              changed = true;
            }
          } else if (graph.getEndpoint(c, a) == Endpoint.ARROW && graph.isUndirectedFromTo(a, b)) {
            if (existsLocalSepsetWithoutDet(b, a, c, test, graph, depth)) {
              continue;
            }

            if (isArrowpointAllowed(a, b, knowledge)) {
              graph.setEndpoint(a, b, Endpoint.ARROW);
              TetradLogger.getInstance()
                  .edgeOriented(SearchLogUtils.edgeOrientedMsg("Meek R1", graph.getEdge(a, b)));
              changed = true;
            }
          }
        }
      }
    }

    return changed;
  }
Beispiel #2
0
  /** Orients according to background knowledge */
  private void fciOrientbk(IKnowledge bk, Graph graph, List<Node> variables) {
    logger.log("info", "Starting BK Orientation.");

    for (Iterator<KnowledgeEdge> it = bk.forbiddenEdgesIterator(); it.hasNext(); ) {
      KnowledgeEdge edge = it.next();

      // match strings to variables in the graph.
      Node from = SearchGraphUtils.translate(edge.getFrom(), variables);
      Node to = SearchGraphUtils.translate(edge.getTo(), variables);

      if (from == null || to == null) {
        continue;
      }

      if (graph.getEdge(from, to) == null) {
        continue;
      }

      // Orient to*->from
      graph.setEndpoint(to, from, Endpoint.ARROW);
      graph.setEndpoint(from, to, Endpoint.CIRCLE);
      changeFlag = true;
      logger.log(
          "knowledgeOrientation",
          SearchLogUtils.edgeOrientedMsg("Knowledge", graph.getEdge(from, to)));
    }

    for (Iterator<KnowledgeEdge> it = bk.requiredEdgesIterator(); it.hasNext(); ) {
      KnowledgeEdge edge = it.next();

      // match strings to variables in this graph
      Node from = SearchGraphUtils.translate(edge.getFrom(), variables);
      Node to = SearchGraphUtils.translate(edge.getTo(), variables);

      if (from == null || to == null) {
        continue;
      }

      if (graph.getEdge(from, to) == null) {
        continue;
      }

      graph.setEndpoint(to, from, Endpoint.TAIL);
      graph.setEndpoint(from, to, Endpoint.ARROW);
      changeFlag = true;
      logger.log(
          "knowledgeOrientation",
          SearchLogUtils.edgeOrientedMsg("Knowledge", graph.getEdge(from, to)));
    }

    logger.log("info", "Finishing BK Orientation.");
  }
  /** Orients according to background knowledge. */
  public static void pcOrientbk(Knowledge bk, Graph graph, List<Node> nodes) {
    TetradLogger.getInstance().log("info", "Staring BK Orientation.");
    for (Iterator<KnowledgeEdge> it = bk.forbiddenEdgesIterator(); it.hasNext(); ) {
      KnowledgeEdge edge = it.next();

      // match strings to variables in the graph.
      Node from = translate(edge.getFrom(), nodes);
      Node to = translate(edge.getTo(), nodes);

      if (from == null || to == null) {
        continue;
      }

      if (graph.getEdge(from, to) == null) {
        continue;
      }

      // Orient to-->from
      graph.removeEdge(from, to);
      graph.addDirectedEdge(from, to);
      graph.setEndpoint(from, to, Endpoint.TAIL);
      graph.setEndpoint(to, from, Endpoint.ARROW);

      TetradLogger.getInstance()
          .edgeOriented(SearchLogUtils.edgeOrientedMsg("Knowledge", graph.getEdge(to, from)));
    }

    for (Iterator<KnowledgeEdge> it = bk.requiredEdgesIterator(); it.hasNext(); ) {
      KnowledgeEdge edge = it.next();

      // match strings to variables in this graph
      Node from = translate(edge.getFrom(), nodes);
      Node to = translate(edge.getTo(), nodes);

      if (from == null || to == null) {
        continue;
      }

      if (graph.getEdge(from, to) == null) {
        continue;
      }

      // Orient from-->to
      graph.setEndpoint(to, from, Endpoint.TAIL);
      graph.setEndpoint(from, to, Endpoint.ARROW);
      TetradLogger.getInstance()
          .edgeOriented(SearchLogUtils.edgeOrientedMsg("Knowledge", graph.getEdge(from, to)));
    }
    TetradLogger.getInstance().log("info", "Finishing BK Orientation.");
  }
  /**
   * Performs step C of the algorithm, as indicated on page xxx of CPS, with the modification that
   * X--W--Y is oriented as X-->W<--Y if W is *determined by* the sepset of (X, Y), rather than W
   * just being *in* the sepset of (X, Y).
   */
  public static void pcdOrientC(
      SepsetMap set, IndependenceTest test, Knowledge knowledge, Graph graph) {
    TetradLogger.getInstance().log("info", "Staring Collider Orientation:");

    List<Node> nodes = graph.getNodes();

    for (Node y : nodes) {
      List<Node> adjacentNodes = graph.getAdjacentNodes(y);

      if (adjacentNodes.size() < 2) {
        continue;
      }

      ChoiceGenerator cg = new ChoiceGenerator(adjacentNodes.size(), 2);
      int[] combination;

      while ((combination = cg.next()) != null) {
        Node x = adjacentNodes.get(combination[0]);
        Node z = adjacentNodes.get(combination[1]);

        // Skip triples that are shielded.
        if (graph.isAdjacentTo(x, z)) {
          continue;
        }

        List<Node> sepset = set.get(x, z);

        if (sepset == null) {
          continue;
        }

        List<Node> augmentedSet = new LinkedList<Node>(sepset);
        augmentedSet.add(y);

        if (test.determines(sepset, y)) {
          continue;
        }
        //
        if (!test.splitDetermines(sepset, x, z) && test.splitDetermines(augmentedSet, x, z)) {
          continue;
        }

        if (!isArrowpointAllowed(x, y, knowledge) || !isArrowpointAllowed(z, y, knowledge)) {
          continue;
        }

        graph.setEndpoint(x, y, Endpoint.ARROW);
        graph.setEndpoint(z, y, Endpoint.ARROW);

        TetradLogger.getInstance()
            .log("colliderOriented", SearchLogUtils.colliderOrientedMsg(x, y, z));
      }
    }

    TetradLogger.getInstance().log("info", "Finishing Collider Orientation.");
  }
Beispiel #5
0
  private void calcStats() {
    //        Graph resultGraph = getAlgorithmRunner().getResultGraph();
    IGesRunner runner = (IGesRunner) getAlgorithmRunner();

    if (runner.getTopGraphs().isEmpty()) {
      throw new IllegalArgumentException(
          "No patterns were recorded. Please adjust the number of " + "patterns to store.");
    }

    Graph resultGraph = runner.getTopGraphs().get(runner.getIndex()).getGraph();

    if (getAlgorithmRunner().getDataModel() instanceof DataSet) {

      // resultGraph may be the output of a PC search.
      // Such graphs sometimes contain doubly directed edges.

      // /We converte such edges to directed edges here.
      // For the time being an orientation is arbitrarily selected.
      Set<Edge> allEdges = resultGraph.getEdges();

      for (Edge edge : allEdges) {
        if (edge.getEndpoint1() == Endpoint.ARROW && edge.getEndpoint2() == Endpoint.ARROW) {
          // Option 1 orient it from node1 to node2
          resultGraph.setEndpoint(edge.getNode1(), edge.getNode2(), Endpoint.ARROW);

          // Option 2 remove such edges:
          resultGraph.removeEdge(edge);
        }
      }

      Pattern pattern = new Pattern(resultGraph);
      PatternToDag ptd = new PatternToDag(pattern);
      Graph dag = ptd.patternToDagMeekRules();

      DataSet dataSet = (DataSet) getAlgorithmRunner().getDataModel();
      String report;

      if (dataSet.isContinuous()) {
        report = reportIfContinuous(dag, dataSet);
      } else if (dataSet.isDiscrete()) {
        report = reportIfDiscrete(dag, dataSet);
      } else {
        throw new IllegalArgumentException("");
      }

      JScrollPane dagWorkbenchScroll = dagWorkbenchScroll(dag);
      modelStatsText.setLineWrap(true);
      modelStatsText.setWrapStyleWord(true);
      modelStatsText.setText(report);

      removeStatsTabs();
      tabbedPane.addTab("DAG in pattern", dagWorkbenchScroll);
      tabbedPane.addTab("DAG Model Statistics", modelStatsText);
    }
  }
  /** Meek's rule R3. If a--b, a--c, a--d, c-->b, c-->b, then orient a-->b. */
  public static boolean meekR3(Graph graph, Knowledge knowledge) {

    List<Node> nodes = graph.getNodes();
    boolean changed = false;

    for (Node a : nodes) {
      List<Node> adjacentNodes = graph.getAdjacentNodes(a);

      if (adjacentNodes.size() < 3) {
        continue;
      }

      for (Node b : adjacentNodes) {
        List<Node> otherAdjacents = new LinkedList<Node>(adjacentNodes);
        otherAdjacents.remove(b);

        if (!graph.isUndirectedFromTo(a, b)) {
          continue;
        }

        ChoiceGenerator cg = new ChoiceGenerator(otherAdjacents.size(), 2);
        int[] combination;

        while ((combination = cg.next()) != null) {
          Node c = otherAdjacents.get(combination[0]);
          Node d = otherAdjacents.get(combination[1]);

          if (graph.isAdjacentTo(c, d)) {
            continue;
          }

          if (!graph.isUndirectedFromTo(a, c)) {
            continue;
          }

          if (!graph.isUndirectedFromTo(a, d)) {
            continue;
          }

          if (graph.isDirectedFromTo(c, b) && graph.isDirectedFromTo(d, b)) {
            if (isArrowpointAllowed(a, b, knowledge)) {
              graph.setEndpoint(a, b, Endpoint.ARROW);
              TetradLogger.getInstance()
                  .edgeOriented(SearchLogUtils.edgeOrientedMsg("Meek R3", graph.getEdge(a, b)));
              changed = true;
              break;
            }
          }
        }
      }
    }

    return changed;
  }
  /** If */
  public static boolean meekR2(Graph graph, Knowledge knowledge) {
    List<Node> nodes = graph.getNodes();
    boolean changed = false;

    for (Node a : nodes) {
      List<Node> adjacentNodes = graph.getAdjacentNodes(a);

      if (adjacentNodes.size() < 2) {
        continue;
      }

      ChoiceGenerator cg = new ChoiceGenerator(adjacentNodes.size(), 2);
      int[] combination;

      while ((combination = cg.next()) != null) {
        Node b = adjacentNodes.get(combination[0]);
        Node c = adjacentNodes.get(combination[1]);

        if (graph.isDirectedFromTo(b, a)
            && graph.isDirectedFromTo(a, c)
            && graph.isUndirectedFromTo(b, c)) {
          if (isArrowpointAllowed(b, c, knowledge)) {
            graph.setEndpoint(b, c, Endpoint.ARROW);
            TetradLogger.getInstance()
                .edgeOriented(SearchLogUtils.edgeOrientedMsg("Meek R2", graph.getEdge(b, c)));
          }
        } else if (graph.isDirectedFromTo(c, a)
            && graph.isDirectedFromTo(a, b)
            && graph.isUndirectedFromTo(c, b)) {
          if (isArrowpointAllowed(c, b, knowledge)) {
            graph.setEndpoint(c, b, Endpoint.ARROW);
            TetradLogger.getInstance()
                .edgeOriented(SearchLogUtils.edgeOrientedMsg("Meek R2", graph.getEdge(c, b)));
          }
        }
      }
    }

    return changed;
  }
Beispiel #8
0
  private void addColliders(
      Graph graph, final SepsetProducer sepsetProducer, IKnowledge knowledge) {
    final Map<Triple, Double> collidersPs =
        findCollidersUsingSepsets(sepsetProducer, graph, verbose, knowledge);

    List<Triple> colliders = new ArrayList<>(collidersPs.keySet());

    Collections.shuffle(colliders);

    Collections.sort(
        colliders,
        new Comparator<Triple>() {
          public int compare(Triple o1, Triple o2) {
            return -Double.compare(collidersPs.get(o1), collidersPs.get(o2));
          }
        });

    if (trueDag != null) {
      for (Triple collider : colliders) {
        Node a = collider.getX();
        Node b = collider.getY();
        Node c = collider.getZ();

        List<Node> sep = trueDag.getSepset(a, c);

        System.out.println(
            "JJJ "
                + collider
                + " collider = "
                + (sep != null && !sep.contains(b))
                + " p = "
                + collidersPs.get(collider));
      }
    }

    for (Triple collider : colliders) {
      Node a = collider.getX();
      Node b = collider.getY();
      Node c = collider.getZ();

      if (!(isArrowpointAllowed(a, b, knowledge) && isArrowpointAllowed(c, b, knowledge))) {
        continue;
      }

      if (!graph.getEdge(a, b).pointsTowards(a) && !graph.getEdge(b, c).pointsTowards(c)) {
        graph.setEndpoint(a, b, Endpoint.ARROW);
        graph.setEndpoint(c, b, Endpoint.ARROW);
      }
    }
  }
  /**
   * Step C of PC; orients colliders using specified sepset. That is, orients x *-* y *-* z as x *->
   * y <-* z just in case y is in Sepset({x, z}).
   */
  public static void orientCollidersUsingSepsets(SepsetMap set, Knowledge knowledge, Graph graph) {
    TetradLogger.getInstance().log("info", "Starting Collider Orientation:");

    //        verifySepsetIntegrity(set, graph);

    List<Node> nodes = graph.getNodes();

    for (Node a : nodes) {
      List<Node> adjacentNodes = graph.getAdjacentNodes(a);

      if (adjacentNodes.size() < 2) {
        continue;
      }

      ChoiceGenerator cg = new ChoiceGenerator(adjacentNodes.size(), 2);
      int[] combination;

      while ((combination = cg.next()) != null) {
        Node b = adjacentNodes.get(combination[0]);
        Node c = adjacentNodes.get(combination[1]);

        // Skip triples that are shielded.
        if (graph.isAdjacentTo(b, c)) {
          continue;
        }

        List<Node> sepset = set.get(b, c);
        if (sepset != null
            && !sepset.contains(a)
            && isArrowpointAllowed(b, a, knowledge)
            && isArrowpointAllowed(c, a, knowledge)) {
          graph.setEndpoint(b, a, Endpoint.ARROW);
          graph.setEndpoint(c, a, Endpoint.ARROW);
          TetradLogger.getInstance()
              .log("colliderOriented", SearchLogUtils.colliderOrientedMsg(b, a, c, sepset));
        }
      }
    }

    TetradLogger.getInstance().log("info", "Finishing Collider Orientation.");
  }
  public static void orientCollidersLocally(
      Knowledge knowledge, Graph graph, IndependenceTest test, int depth, Set<Node> nodesToVisit) {
    TetradLogger.getInstance().log("info", "Starting Collider Orientation:");

    if (nodesToVisit == null) {
      nodesToVisit = new HashSet<Node>(graph.getNodes());
    }

    for (Node a : nodesToVisit) {
      List<Node> adjacentNodes = graph.getAdjacentNodes(a);

      if (adjacentNodes.size() < 2) {
        continue;
      }

      ChoiceGenerator cg = new ChoiceGenerator(adjacentNodes.size(), 2);
      int[] combination;

      while ((combination = cg.next()) != null) {
        Node b = adjacentNodes.get(combination[0]);
        Node c = adjacentNodes.get(combination[1]);

        // Skip triples that are shielded.
        if (graph.isAdjacentTo(b, c)) {
          continue;
        }

        if (isArrowpointAllowed1(b, a, knowledge) && isArrowpointAllowed1(c, a, knowledge)) {
          if (!existsLocalSepsetWith(b, a, c, test, graph, depth)) {
            graph.setEndpoint(b, a, Endpoint.ARROW);
            graph.setEndpoint(c, a, Endpoint.ARROW);
            TetradLogger.getInstance()
                .log("colliderOriented", SearchLogUtils.colliderOrientedMsg(b, a, c));
          }
        }
      }
    }

    TetradLogger.getInstance().log("info", "Finishing Collider Orientation.");
  }
  /**
   * Transforms a DAG represented in graph <code>graph</code> into a maximally directed pattern
   * (PDAG) by modifying <code>g</code> itself. Based on the algorithm described in Chickering
   * (2002) "Optimal structure identification with greedy search" Journal of Machine Learning
   * Research. It works for both BayesNets and SEMs. R. Silva, June 2004
   */
  public static void dagToPdag(Graph graph) {
    // do topological sort on the nodes
    Graph graphCopy = new EdgeListGraph(graph);
    Node orderedNodes[] = new Node[graphCopy.getNodes().size()];
    int count = 0;
    while (graphCopy.getNodes().size() > 0) {
      Set<Node> exogenousNodes = new HashSet<Node>();

      for (Node next : graphCopy.getNodes()) {
        if (graphCopy.isExogenous(next)) {
          exogenousNodes.add(next);
          orderedNodes[count++] = graph.getNode(next.getName());
        }
      }

      graphCopy.removeNodes(new ArrayList<Node>(exogenousNodes));
    }
    // ordered edges - improvised, inefficient implementation
    count = 0;
    Edge edges[] = new Edge[graph.getNumEdges()];
    boolean edgeOrdered[] = new boolean[graph.getNumEdges()];
    Edge orderedEdges[] = new Edge[graph.getNumEdges()];

    for (Edge edge : graph.getEdges()) {
      edges[count++] = edge;
    }

    for (int i = 0; i < edges.length; i++) {
      edgeOrdered[i] = false;
    }

    while (count > 0) {
      for (Node orderedNode : orderedNodes) {
        for (int k = orderedNodes.length - 1; k >= 0; k--) {
          for (int q = 0; q < edges.length; q++) {
            if (!edgeOrdered[q]
                && edges[q].getNode1() == orderedNodes[k]
                && edges[q].getNode2() == orderedNode) {
              edgeOrdered[q] = true;
              orderedEdges[orderedEdges.length - count] = edges[q];
              count--;
            }
          }
        }
      }
    }

    // label edges
    boolean compelledEdges[] = new boolean[graph.getNumEdges()];
    boolean reversibleEdges[] = new boolean[graph.getNumEdges()];
    for (int i = 0; i < graph.getNumEdges(); i++) {
      compelledEdges[i] = false;
      reversibleEdges[i] = false;
    }
    for (int i = 0; i < graph.getNumEdges(); i++) {
      if (compelledEdges[i] || reversibleEdges[i]) {
        continue;
      }
      Node x = orderedEdges[i].getNode1();
      Node y = orderedEdges[i].getNode2();
      for (int j = 0; j < orderedEdges.length; j++) {
        if (orderedEdges[j].getNode2() == x && compelledEdges[j]) {
          Node w = orderedEdges[j].getNode1();
          if (!graph.isParentOf(w, y)) {
            for (int k = 0; k < orderedEdges.length; k++) {
              if (orderedEdges[k].getNode2() == y) {
                compelledEdges[k] = true;
                break;
              }
            }
          } else {
            for (int k = 0; k < orderedEdges.length; k++) {
              if (orderedEdges[k].getNode1() == w && orderedEdges[k].getNode2() == y) {
                compelledEdges[k] = true;
                break;
              }
            }
          }
        }
        if (compelledEdges[i]) {
          break;
        }
      }
      if (compelledEdges[i]) {
        continue;
      }
      boolean foundZ = false;

      for (Edge orderedEdge : orderedEdges) {
        Node z = orderedEdge.getNode1();
        if (z != x && orderedEdge.getNode2() == y && !graph.isParentOf(z, x)) {
          compelledEdges[i] = true;
          for (int k = i + 1; k < graph.getNumEdges(); k++) {
            if (orderedEdges[k].getNode2() == y && !reversibleEdges[k]) {
              compelledEdges[k] = true;
            }
          }
          foundZ = true;
          break;
        }
      }

      if (!foundZ) {
        reversibleEdges[i] = true;

        for (int j = i + 1; j < orderedEdges.length; j++) {
          if (!compelledEdges[j] && orderedEdges[j].getNode2() == y) {
            reversibleEdges[j] = true;
          }
        }
      }
    }

    // undirect edges that are reversible
    for (int i = 0; i < reversibleEdges.length; i++) {
      if (reversibleEdges[i]) {
        graph.setEndpoint(orderedEdges[i].getNode1(), orderedEdges[i].getNode2(), Endpoint.TAIL);
        graph.setEndpoint(orderedEdges[i].getNode2(), orderedEdges[i].getNode1(), Endpoint.TAIL);
      }
    }
  }
Beispiel #12
0
  ////////////////////////////////////////////
  // RFCI Algorithm 4.4 (Colombo et al, 2012)
  // Orient colliders
  ////////////////////////////////////////////
  private void ruleR0_RFCI(List<Node[]> rTuples) {
    List<Node[]> lTuples = new ArrayList<Node[]>();

    List<Node> nodes = graph.getNodes();

    ///////////////////////////////
    // process tuples in rTuples
    while (!rTuples.isEmpty()) {
      Node[] thisTuple = rTuples.remove(0);

      Node i = thisTuple[0];
      Node j = thisTuple[1];
      Node k = thisTuple[2];

      final List<Node> nodes1 = getSepset(i, k);

      if (nodes1 == null) continue;

      List<Node> sepSet = new ArrayList<Node>(nodes1);
      sepSet.remove(j);

      boolean independent1 = false;
      if (knowledge.noEdgeRequired(i.getName(), j.getName())) // if BK allows
      {
        try {
          independent1 = independenceTest.isIndependent(i, j, sepSet);
        } catch (Exception e) {
          independent1 = true;
        }
      }

      boolean independent2 = false;
      if (knowledge.noEdgeRequired(j.getName(), k.getName())) // if BK allows
      {
        try {
          independent2 = independenceTest.isIndependent(j, k, sepSet);
        } catch (Exception e) {
          independent2 = true;
        }
      }

      if (!independent1 && !independent2) {
        lTuples.add(thisTuple);
      } else {
        // set sepSets to minimal separating sets
        if (independent1) {
          setMinSepSet(sepSet, i, j);
          graph.removeEdge(i, j);
        }
        if (independent2) {
          setMinSepSet(sepSet, j, k);
          graph.removeEdge(j, k);
        }

        // add new unshielded tuples to rTuples
        for (Node thisNode : nodes) {
          List<Node> adjacentNodes = graph.getAdjacentNodes(thisNode);
          if (independent1) // <i, ., j>
          {
            if (adjacentNodes.contains(i) && adjacentNodes.contains(j)) {
              Node[] newTuple = {i, thisNode, j};
              rTuples.add(newTuple);
            }
          }
          if (independent2) // <j, ., k>
          {
            if (adjacentNodes.contains(j) && adjacentNodes.contains(k)) {
              Node[] newTuple = {j, thisNode, k};
              rTuples.add(newTuple);
            }
          }
        }

        // remove tuples involving either (if independent1) <i, j>
        // or (if independent2) <j, k> from rTuples
        Iterator<Node[]> iter = rTuples.iterator();
        while (iter.hasNext()) {
          Node[] curTuple = iter.next();
          if ((independent1 && (curTuple[1] == i) && ((curTuple[0] == j) || (curTuple[2] == j)))
              || (independent2 && (curTuple[1] == k) && ((curTuple[0] == j) || (curTuple[2] == j)))
              || (independent1 && (curTuple[1] == j) && ((curTuple[0] == i) || (curTuple[2] == i)))
              || (independent2
                  && (curTuple[1] == j)
                  && ((curTuple[0] == k) || (curTuple[2] == k)))) {
            iter.remove();
          }
        }

        // remove tuples involving either (if independent1) <i, j>
        // or (if independent2) <j, k> from lTuples
        iter = lTuples.iterator();
        while (iter.hasNext()) {
          Node[] curTuple = iter.next();
          if ((independent1 && (curTuple[1] == i) && ((curTuple[0] == j) || (curTuple[2] == j)))
              || (independent2 && (curTuple[1] == k) && ((curTuple[0] == j) || (curTuple[2] == j)))
              || (independent1 && (curTuple[1] == j) && ((curTuple[0] == i) || (curTuple[2] == i)))
              || (independent2
                  && (curTuple[1] == j)
                  && ((curTuple[0] == k) || (curTuple[2] == k)))) {
            iter.remove();
          }
        }
      }
    }

    ///////////////////////////////////////////////////////
    // orient colliders (similar to original FCI ruleR0)
    for (Node[] thisTuple : lTuples) {
      Node i = thisTuple[0];
      Node j = thisTuple[1];
      Node k = thisTuple[2];

      List<Node> sepset = getSepset(i, k);

      if (sepset == null) {
        continue;
      }

      if (!sepset.contains(j) && graph.isAdjacentTo(i, j) && graph.isAdjacentTo(j, k)) {

        if (!isArrowpointAllowed(i, j)) {
          continue;
        }

        if (!isArrowpointAllowed(k, j)) {
          continue;
        }

        graph.setEndpoint(i, j, Endpoint.ARROW);
        graph.setEndpoint(k, j, Endpoint.ARROW);

        printWrongColliderMessage(i, j, k, "R0_RFCI");
      }
    }
  }