NearestNeighborsGNAT.h

Go to the documentation of this file.

/*********************************************************************
 * Software License Agreement (BSD License)
 *
 *  Copyright (c) 2011, Rice University
 *  All rights reserved.
 *
 *  Redistribution and use in source and binary forms, with or without
 *  modification, are permitted provided that the following conditions
 *  are met:
 *
 *   * Redistributions of source code must retain the above copyright
 *     notice, this list of conditions and the following disclaimer.
 *   * Redistributions in binary form must reproduce the above
 *     copyright notice, this list of conditions and the following
 *     disclaimer in the documentation and/or other materials provided
 *     with the distribution.
 *   * Neither the name of the Rice University nor the names of its
 *     contributors may be used to endorse or promote products derived
 *     from this software without specific prior written permission.
 *
 *  THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
 *  "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
 *  LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
 *  FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
 *  COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
 *  INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
 *  BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
 *  LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
 *  CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
 *  LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
 *  ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
 *  POSSIBILITY OF SUCH DAMAGE.
 *********************************************************************/

/* Author: Mark Moll, Bryant Gipson */

// This file is a slightly modified version of <ompl/datastructures/NearestNeighborsGNAT.h>

#ifndef MOVEIT_ROS_PLANNING_CACHED_IK_KINEMATICS_NEAREST_NEIGHBORS_GNAT_
#define MOVEIT_ROS_PLANNING_CACHED_IK_KINEMATICS_NEAREST_NEIGHBORS_GNAT_

#include "NearestNeighbors.h"
#include "GreedyKCenters.h"
#include <moveit/exceptions/exceptions.h>
#include <unordered_set>
#include <queue>
#include <algorithm>
#include <utility>

namespace cached_ik_kinematics_plugin
{
template <typename _T>
class NearestNeighborsGNAT : public NearestNeighbors<_T>
{
protected:
  // \cond IGNORE
  // internally, we use a priority queue for nearest neighbors, paired
  // with their distance to the query point
  using DataDist = std::pair<const _T*, double>;
  struct DataDistCompare
  {
    bool operator()(const DataDist& d0, const DataDist& d1)
    {
      return d0.second < d1.second;
    }
  };
  using NearQueue = std::priority_queue<DataDist, std::vector<DataDist>, DataDistCompare>;

  // another internal data structure is a priority queue of nodes to
  // check next for possible nearest neighbors
  class Node;
  using NodeDist = std::pair<Node*, double>;
  struct NodeDistCompare
  {
    bool operator()(const NodeDist& n0, const NodeDist& n1) const
    {
      return (n0.second - n0.first->maxRadius_) > (n1.second - n1.first->maxRadius_);
    }
  };
  using NodeQueue = std::priority_queue<NodeDist, std::vector<NodeDist>, NodeDistCompare>;
  // \endcond

public:
  NearestNeighborsGNAT(unsigned int degree = 8, unsigned int minDegree = 4, unsigned int maxDegree = 12,
                       unsigned int maxNumPtsPerLeaf = 50, unsigned int removedCacheSize = 500,
                       bool rebalancing = false)
    : NearestNeighbors<_T>()
    , degree_(degree)
    , minDegree_(std::min(degree, minDegree))
    , maxDegree_(std::max(maxDegree, degree))
    , maxNumPtsPerLeaf_(maxNumPtsPerLeaf)
    , rebuildSize_(rebalancing ? maxNumPtsPerLeaf * degree : std::numeric_limits<std::size_t>::max())
    , removedCacheSize_(removedCacheSize)
  {
  }

  ~NearestNeighborsGNAT() override
  {
    if (tree_)
      delete tree_;
  }
  // \brief Set the distance function to use
  void setDistanceFunction(const typename NearestNeighbors<_T>::DistanceFunction& distFun) override
  {
    NearestNeighbors<_T>::setDistanceFunction(distFun);
    pivotSelector_.setDistanceFunction(distFun);
    if (tree_)
      rebuildDataStructure();
  }

  void clear() override
  {
    if (tree_)
    {
      delete tree_;
      tree_ = nullptr;
    }
    size_ = 0;
    removed_.clear();
    if (rebuildSize_ != std::numeric_limits<std::size_t>::max())
      rebuildSize_ = maxNumPtsPerLeaf_ * degree_;
  }

  bool reportsSortedResults() const override
  {
    return true;
  }

  void add(const _T& data) override
  {
    if (tree_)
    {
      if (isRemoved(data))
        rebuildDataStructure();
      tree_->add(*this, data);
    }
    else
    {
      tree_ = new Node(degree_, maxNumPtsPerLeaf_, data);
      size_ = 1;
    }
  }
  void add(const std::vector<_T>& data) override
  {
    if (tree_)
      NearestNeighbors<_T>::add(data);
    else if (!data.empty())
    {
      tree_ = new Node(degree_, maxNumPtsPerLeaf_, data[0]);
      for (unsigned int i = 1; i < data.size(); ++i)
        tree_->data_.push_back(data[i]);
      size_ += data.size();
      if (tree_->needToSplit(*this))
        tree_->split(*this);
    }
  }
  // \brief Rebuild the internal data structure.
  void rebuildDataStructure()
  {
    std::vector<_T> lst;
    list(lst);
    clear();
    add(lst);
  }
  // \brief Remove data from the tree.
  // The element won't actually be removed immediately, but just marked
  // for removal in the removed_ cache. When the cache is full, the tree
  // will be rebuilt and the elements marked for removal will actually
  // be removed.
  bool remove(const _T& data) override
  {
    if (size_ == 0u)
      return false;
    NearQueue nbhQueue;
    // find data in tree
    bool isPivot = nearestKInternal(data, 1, nbhQueue);
    const _T* d = nbhQueue.top().first;
    if (*d != data)
      return false;
    removed_.insert(d);
    size_--;
    // if we removed a pivot or if the capacity of removed elements
    // has been reached, we rebuild the entire GNAT
    if (isPivot || removed_.size() >= removedCacheSize_)
      rebuildDataStructure();
    return true;
  }

  _T nearest(const _T& data) const override
  {
    if (size_)
    {
      NearQueue nbhQueue;
      nearestKInternal(data, 1, nbhQueue);
      if (!nbhQueue.empty())
        return *nbhQueue.top().first;
    }
    throw moveit::Exception("No elements found in nearest neighbors data structure");
  }

  // Return the k nearest neighbors in sorted order
  void nearestK(const _T& data, std::size_t k, std::vector<_T>& nbh) const override
  {
    nbh.clear();
    if (k == 0)
      return;
    if (size_)
    {
      NearQueue nbhQueue;
      nearestKInternal(data, k, nbhQueue);
      postprocessNearest(nbhQueue, nbh);
    }
  }

  // Return the nearest neighbors within distance \c radius in sorted order
  void nearestR(const _T& data, double radius, std::vector<_T>& nbh) const override
  {
    nbh.clear();
    if (size_)
    {
      NearQueue nbhQueue;
      nearestRInternal(data, radius, nbhQueue);
      postprocessNearest(nbhQueue, nbh);
    }
  }

  std::size_t size() const override
  {
    return size_;
  }

  void list(std::vector<_T>& data) const override
  {
    data.clear();
    data.reserve(size());
    if (tree_)
      tree_->list(*this, data);
  }

  // \brief Print a GNAT structure (mostly useful for debugging purposes).
  friend std::ostream& operator<<(std::ostream& out, const NearestNeighborsGNAT<_T>& gnat)
  {
    if (gnat.tree_)
    {
      out << *gnat.tree_;
      if (!gnat.removed_.empty())
      {
        out << "Elements marked for removal:\n";
        for (typename std::unordered_set<const _T*>::const_iterator it = gnat.removed_.begin();
             it != gnat.removed_.end(); it++)
          out << **it << '\t';
        out << std::endl;
      }
    }
    return out;
  }

  // for debugging purposes
  void integrityCheck()
  {
    std::vector<_T> lst;
    std::unordered_set<const _T*> tmp;
    // get all elements, including those marked for removal
    removed_.swap(tmp);
    list(lst);
    // check if every element marked for removal is also in the tree
    for (typename std::unordered_set<const _T*>::iterator it = tmp.begin(); it != tmp.end(); it++)
    {
      unsigned int i;
      for (i = 0; i < lst.size(); ++i)
        if (lst[i] == **it)
          break;
      if (i == lst.size())
      {
        // an element marked for removal is not actually in the tree
        std::cout << "***** FAIL!! ******\n" << *this << '\n';
        for (unsigned int j = 0; j < lst.size(); ++j)
          std::cout << lst[j] << '\t';
        std::cout << std::endl;
      }
      assert(i != lst.size());
    }
    // restore
    removed_.swap(tmp);
    // get elements in the tree with elements marked for removal purged from the list
    list(lst);
    if (lst.size() != size_)
      std::cout << "#########################################\n" << *this << std::endl;
    assert(lst.size() == size_);
  }

protected:
  using GNAT = NearestNeighborsGNAT<_T>;

  // Return true iff data has been marked for removal.
  bool isRemoved(const _T& data) const
  {
    return !removed_.empty() && removed_.find(&data) != removed_.end();
  }

  // \brief Return in nbhQueue the k nearest neighbors of data.
  // For k=1, return true if the nearest neighbor is a pivot.
  // (which is important during removal; removing pivots is a
  // special case).
  bool nearestKInternal(const _T& data, std::size_t k, NearQueue& nbhQueue) const
  {
    bool isPivot;
    double dist;
    NodeDist nodeDist;
    NodeQueue nodeQueue;

    dist = NearestNeighbors<_T>::distFun_(data, tree_->pivot_);
    isPivot = tree_->insertNeighborK(nbhQueue, k, tree_->pivot_, data, dist);
    tree_->nearestK(*this, data, k, nbhQueue, nodeQueue, isPivot);
    while (!nodeQueue.empty())
    {
      dist = nbhQueue.top().second;  // note the difference with nearestRInternal
      nodeDist = nodeQueue.top();
      nodeQueue.pop();
      if (nbhQueue.size() == k &&
          (nodeDist.second > nodeDist.first->maxRadius_ + dist || nodeDist.second < nodeDist.first->minRadius_ - dist))
        continue;
      nodeDist.first->nearestK(*this, data, k, nbhQueue, nodeQueue, isPivot);
    }
    return isPivot;
  }
  // \brief Return in nbhQueue the elements that are within distance radius of data.
  void nearestRInternal(const _T& data, double radius, NearQueue& nbhQueue) const
  {
    double dist = radius;  // note the difference with nearestKInternal
    NodeQueue nodeQueue;
    NodeDist nodeDist;

    tree_->insertNeighborR(nbhQueue, radius, tree_->pivot_, NearestNeighbors<_T>::distFun_(data, tree_->pivot_));
    tree_->nearestR(*this, data, radius, nbhQueue, nodeQueue);
    while (!nodeQueue.empty())
    {
      nodeDist = nodeQueue.top();
      nodeQueue.pop();
      if (nodeDist.second > nodeDist.first->maxRadius_ + dist || nodeDist.second < nodeDist.first->minRadius_ - dist)
        continue;
      nodeDist.first->nearestR(*this, data, radius, nbhQueue, nodeQueue);
    }
  }
  // \brief Convert the internal data structure used for storing neighbors
  // to the vector that NearestNeighbor API requires.
  void postprocessNearest(NearQueue& nbhQueue, std::vector<_T>& nbh) const
  {
    typename std::vector<_T>::reverse_iterator it;
    nbh.resize(nbhQueue.size());
    for (it = nbh.rbegin(); it != nbh.rend(); it++, nbhQueue.pop())
      *it = *nbhQueue.top().first;
  }

  // The class used internally to define the GNAT.
  class Node
  {
  public:
    // \brief Construct a node of given degree with at most
    // \e capacity data elements and with given pivot.
    Node(int degree, int capacity, _T pivot)
      : degree_(degree)
      , pivot_(std::move(pivot))
      , minRadius_(std::numeric_limits<double>::infinity())
      , maxRadius_(-minRadius_)
      , minRange_(degree, minRadius_)
      , maxRange_(degree, maxRadius_)
    {
      // The "+1" is needed because we add an element before we check whether to split
      data_.reserve(capacity + 1);
    }

    ~Node()
    {
      for (unsigned int i = 0; i < children_.size(); ++i)
        delete children_[i];
    }

    // \brief Update minRadius_ and maxRadius_, given that an element
    // was added with distance dist to the pivot.
    void updateRadius(double dist)
    {
      if (minRadius_ > dist)
        minRadius_ = dist;
#ifndef GNAT_SAMPLER
      if (maxRadius_ < dist)
        maxRadius_ = dist;
#else
      if (maxRadius_ < dist)
      {
        maxRadius_ = dist;
        activity_ = 0;
      }
      else
        activity_ = std::max(-32, activity_ - 1);
#endif
    }
    // \brief Update minRange_[i] and maxRange_[i], given that an
    // element was added to the i-th child of the parent that has
    // distance dist to this Node's pivot.
    void updateRange(unsigned int i, double dist)
    {
      if (minRange_[i] > dist)
        minRange_[i] = dist;
      if (maxRange_[i] < dist)
        maxRange_[i] = dist;
    }
    // Add an element to the tree rooted at this node.
    void add(GNAT& gnat, const _T& data)
    {
      if (children_.empty())
      {
        data_.push_back(data);
        gnat.size_++;
        if (needToSplit(gnat))
        {
          if (!gnat.removed_.empty())
            gnat.rebuildDataStructure();
          else if (gnat.size_ >= gnat.rebuildSize_)
          {
            gnat.rebuildSize_ <<= 1;
            gnat.rebuildDataStructure();
          }
          else
            split(gnat);
        }
      }
      else
      {
        std::vector<double> dist(children_.size());
        double minDist = dist[0] = gnat.distFun_(data, children_[0]->pivot_);
        int minInd = 0;

        for (unsigned int i = 1; i < children_.size(); ++i)
          if ((dist[i] = gnat.distFun_(data, children_[i]->pivot_)) < minDist)
          {
            minDist = dist[i];
            minInd = i;
          }
        for (unsigned int i = 0; i < children_.size(); ++i)
          children_[i]->updateRange(minInd, dist[i]);
        children_[minInd]->updateRadius(minDist);
        children_[minInd]->add(gnat, data);
      }
    }
    // Return true iff the node needs to be split into child nodes.
    bool needToSplit(const GNAT& gnat) const
    {
      unsigned int sz = data_.size();
      return sz > gnat.maxNumPtsPerLeaf_ && sz > degree_;
    }
    // \brief The split operation finds pivot elements for the child
    // nodes and moves each data element of this node to the appropriate
    // child node.
    void split(GNAT& gnat)
    {
      typename GreedyKCenters<_T>::Matrix dists(data_.size(), degree_);
      std::vector<unsigned int> pivots;

      children_.reserve(degree_);
      gnat.pivotSelector_.kcenters(data_, degree_, pivots, dists);
      for (unsigned int& pivot : pivots)
        children_.push_back(new Node(degree_, gnat.maxNumPtsPerLeaf_, data_[pivot]));
      degree_ = pivots.size();  // in case fewer than degree_ pivots were found
      for (unsigned int j = 0; j < data_.size(); ++j)
      {
        unsigned int k = 0;
        for (unsigned int i = 1; i < degree_; ++i)
          if (dists(j, i) < dists(j, k))
            k = i;
        Node* child = children_[k];
        if (j != pivots[k])
        {
          child->data_.push_back(data_[j]);
          child->updateRadius(dists(j, k));
        }
        for (unsigned int i = 0; i < degree_; ++i)
          children_[i]->updateRange(k, dists(j, i));
      }

      for (unsigned int i = 0; i < degree_; ++i)
      {
        // make sure degree lies between minDegree_ and maxDegree_
        children_[i]->degree_ =
            std::min(std::max((unsigned int)((degree_ * children_[i]->data_.size()) / data_.size()), gnat.minDegree_),
                     gnat.maxDegree_);
        // singleton
        if (children_[i]->minRadius_ >= std::numeric_limits<double>::infinity())
          children_[i]->minRadius_ = children_[i]->maxRadius_ = 0.;
      }
      // this does more than clear(); it also sets capacity to 0 and frees the memory
      std::vector<_T> tmp;
      data_.swap(tmp);
      // check if new leaves need to be split
      for (unsigned int i = 0; i < degree_; ++i)
        if (children_[i]->needToSplit(gnat))
          children_[i]->split(gnat);
    }

    // Insert data in nbh if it is a near neighbor. Return true iff data was added to nbh.
    bool insertNeighborK(NearQueue& nbh, std::size_t k, const _T& data, const _T& key, double dist) const
    {
      if (nbh.size() < k)
      {
        nbh.push(std::make_pair(&data, dist));
        return true;
      }
      if (dist < nbh.top().second || (dist < std::numeric_limits<double>::epsilon() && data == key))
      {
        nbh.pop();
        nbh.push(std::make_pair(&data, dist));
        return true;
      }
      return false;
    }

    // \brief Compute the k nearest neighbors of data in the tree.
    // For k=1, isPivot is true if the nearest neighbor is a pivot
    // (which is important during removal; removing pivots is a
    // special case). The nodeQueue, which contains other Nodes
    // that need to be checked for nearest neighbors, is updated.
    void nearestK(const GNAT& gnat, const _T& data, std::size_t k, NearQueue& nbh, NodeQueue& nodeQueue,
                  bool& isPivot) const
    {
      for (unsigned int i = 0; i < data_.size(); ++i)
        if (!gnat.isRemoved(data_[i]))
        {
          if (insertNeighborK(nbh, k, data_[i], data, gnat.distFun_(data, data_[i])))
            isPivot = false;
        }
      if (!children_.empty())
      {
        double dist;
        Node* child;
        std::vector<double> distToPivot(children_.size());
        std::vector<int> permutation(children_.size());
        for (unsigned int i = 0; i < permutation.size(); ++i)
          permutation[i] = i;
        std::random_shuffle(permutation.begin(), permutation.end());

        for (unsigned int i = 0; i < children_.size(); ++i)
          if (permutation[i] >= 0)
          {
            child = children_[permutation[i]];
            distToPivot[permutation[i]] = gnat.distFun_(data, child->pivot_);
            if (insertNeighborK(nbh, k, child->pivot_, data, distToPivot[permutation[i]]))
              isPivot = true;
            if (nbh.size() == k)
            {
              dist = nbh.top().second;  // note difference with nearestR
              for (unsigned int j = 0; j < children_.size(); ++j)
                if (permutation[j] >= 0 && i != j &&
                    (distToPivot[permutation[i]] - dist > child->maxRange_[permutation[j]] ||
                     distToPivot[permutation[i]] + dist < child->minRange_[permutation[j]]))
                  permutation[j] = -1;
            }
          }

        dist = nbh.top().second;
        for (unsigned int i = 0; i < children_.size(); ++i)
          if (permutation[i] >= 0)
          {
            child = children_[permutation[i]];
            if (nbh.size() < k || (distToPivot[permutation[i]] - dist <= child->maxRadius_ &&
                                   distToPivot[permutation[i]] + dist >= child->minRadius_))
              nodeQueue.push(std::make_pair(child, distToPivot[permutation[i]]));
          }
      }
    }
    // Insert data in nbh if it is a near neighbor.
    void insertNeighborR(NearQueue& nbh, double r, const _T& data, double dist) const
    {
      if (dist <= r)
        nbh.push(std::make_pair(&data, dist));
    }
    // \brief Return all elements that are within distance r in nbh.
    // The nodeQueue, which contains other Nodes that need to
    // be checked for nearest neighbors, is updated.
    void nearestR(const GNAT& gnat, const _T& data, double r, NearQueue& nbh, NodeQueue& nodeQueue) const
    {
      double dist = r;  // note difference with nearestK

      for (unsigned int i = 0; i < data_.size(); ++i)
        if (!gnat.isRemoved(data_[i]))
          insertNeighborR(nbh, r, data_[i], gnat.distFun_(data, data_[i]));
      if (!children_.empty())
      {
        Node* child;
        std::vector<double> distToPivot(children_.size());
        std::vector<int> permutation(children_.size());
        for (unsigned int i = 0; i < permutation.size(); ++i)
          permutation[i] = i;
        std::random_shuffle(permutation.begin(), permutation.end());

        for (unsigned int i = 0; i < children_.size(); ++i)
          if (permutation[i] >= 0)
          {
            child = children_[permutation[i]];
            distToPivot[i] = gnat.distFun_(data, child->pivot_);
            insertNeighborR(nbh, r, child->pivot_, distToPivot[i]);
            for (unsigned int j = 0; j < children_.size(); ++j)
              if (permutation[j] >= 0 && i != j && (distToPivot[i] - dist > child->maxRange_[permutation[j]] ||
                                                    distToPivot[i] + dist < child->minRange_[permutation[j]]))
                permutation[j] = -1;
          }

        for (unsigned int i = 0; i < children_.size(); ++i)
          if (permutation[i] >= 0)
          {
            child = children_[permutation[i]];
            if (distToPivot[i] - dist <= child->maxRadius_ && distToPivot[i] + dist >= child->minRadius_)
              nodeQueue.push(std::make_pair(child, distToPivot[i]));
          }
      }
    }

    void list(const GNAT& gnat, std::vector<_T>& data) const
    {
      if (!gnat.isRemoved(pivot_))
        data.push_back(pivot_);
      for (unsigned int i = 0; i < data_.size(); ++i)
        if (!gnat.isRemoved(data_[i]))
          data.push_back(data_[i]);
      for (unsigned int i = 0; i < children_.size(); ++i)
        children_[i]->list(gnat, data);
    }

    friend std::ostream& operator<<(std::ostream& out, const Node& node)
    {
      out << "\ndegree:\t" << node.degree_;
      out << "\nminRadius:\t" << node.minRadius_;
      out << "\nmaxRadius:\t" << node.maxRadius_;
      out << "\nminRange:\t";
      for (unsigned int i = 0; i < node.minRange_.size(); ++i)
        out << node.minRange_[i] << '\t';
      out << "\nmaxRange: ";
      for (unsigned int i = 0; i < node.maxRange_.size(); ++i)
        out << node.maxRange_[i] << '\t';
      out << "\npivot:\t" << node.pivot_;
      out << "\ndata: ";
      for (unsigned int i = 0; i < node.data_.size(); ++i)
        out << node.data_[i] << '\t';
      out << "\nthis:\t" << &node;
      out << "\nchildren:\n";
      for (unsigned int i = 0; i < node.children_.size(); ++i)
        out << node.children_[i] << '\t';
      out << '\n';
      for (unsigned int i = 0; i < node.children_.size(); ++i)
        out << *node.children_[i] << '\n';
      return out;
    }

    // Number of child nodes
    unsigned int degree_;
    // Data element stored in this Node
    const _T pivot_;
    // Minimum distance between the pivot element and the elements stored in data_
    double minRadius_;
    // Maximum distance between the pivot element and the elements stored in data_
    double maxRadius_;
    // \brief The i-th element in minRange_ is the minimum distance between the
    // pivot and any data_ element in the i-th child node of this node's parent.
    std::vector<double> minRange_;
    // \brief The i-th element in maxRange_ is the maximum distance between the
    // pivot and any data_ element in the i-th child node of this node's parent.
    std::vector<double> maxRange_;
    // \brief The data elements stored in this node (in addition to the pivot
    // element). An internal node has no elements stored in data_.
    std::vector<_T> data_;
    // \brief The child nodes of this node. By definition, only internal nodes
    // have child nodes.
    std::vector<Node*> children_;
  };

  // \brief The data structure containing the elements stored in this structure.
  Node* tree_{ nullptr };
  // The desired degree of each node.
  unsigned int degree_;
  // \brief After splitting a Node, each child Node has degree equal to
  // the default degree times the fraction of data elements from the
  // original node that got assigned to that child Node. However, its
  // degree can be no less than minDegree_.
  unsigned int minDegree_;
  // \brief After splitting a Node, each child Node has degree equal to
  // the default degree times the fraction of data elements from the
  // original node that got assigned to that child Node. However, its
  // degree can be no larger than maxDegree_.
  unsigned int maxDegree_;
  // \brief Maximum number of elements allowed to be stored in a Node before
  // it needs to be split into several nodes.
  unsigned int maxNumPtsPerLeaf_;
  // \brief Number of elements stored in the tree.
  std::size_t size_{ 0 };
  // \brief If size_ exceeds rebuildSize_, the tree will be rebuilt (and
  // automatically rebalanced), and rebuildSize_ will be doubled.
  std::size_t rebuildSize_;
  // \brief Maximum number of removed elements that can be stored in the
  // removed_ cache. If the cache is full, the tree will be rebuilt with
  // the elements in removed_ actually removed from the tree.
  std::size_t removedCacheSize_;
  // \brief The data structure used to split data into subtrees.
  GreedyKCenters<_T> pivotSelector_;
  // \brief Cache of removed elements.
  std::unordered_set<const _T*> removed_;
};
}

#endif