diff --git a/amalgamation/xgboost-all0.cc b/amalgamation/xgboost-all0.cc
index 389be8ab7767..8220135d9e32 100644
--- a/amalgamation/xgboost-all0.cc
+++ b/amalgamation/xgboost-all0.cc
@@ -70,6 +70,7 @@
 #include "../src/common/common.cc"
 #include "../src/common/charconv.cc"
 #include "../src/common/timer.cc"
+#include "../src/common/quantile.cc"
 #include "../src/common/host_device_vector.cc"
 #include "../src/common/hist_util.cc"
 #include "../src/common/json.cc"
diff --git a/include/xgboost/data.h b/include/xgboost/data.h
index e7350fffeeba..05b75323f7f4 100644
--- a/include/xgboost/data.h
+++ b/include/xgboost/data.h
@@ -239,6 +239,21 @@ struct BatchParam {
   }
 };
 
+struct HostSparsePageView {
+  using Inst = common::Span<Entry const>;
+
+  common::Span<bst_row_t const> offset;
+  common::Span<Entry const> data;
+
+  Inst operator[](size_t i) const {
+    auto size = *(offset.data() + i + 1) - *(offset.data() + i);
+    return {data.data() + *(offset.data() + i),
+            static_cast<Inst::index_type>(size)};
+  }
+
+  size_t Size() const { return offset.size() == 0 ? 0 : offset.size() - 1; }
+};
+
 /*!
  * \brief In-memory storage unit of sparse batch, stored in CSR format.
  */
@@ -270,6 +285,11 @@ class SparsePage {
             static_cast<Inst::index_type>(size)};
   }
 
+  HostSparsePageView GetView() const {
+    return {offset.ConstHostSpan(), data.ConstHostSpan()};
+  }
+
+
   /*! \brief constructor */
   SparsePage() {
     this->Clear();
diff --git a/src/common/hist_util.cc b/src/common/hist_util.cc
index f8e42f2f454a..efd62d701ccd 100644
--- a/src/common/hist_util.cc
+++ b/src/common/hist_util.cc
@@ -113,346 +113,12 @@ void GHistIndexMatrix::ResizeIndex(const size_t rbegin, const SparsePage& batch,
 }
 
 HistogramCuts::HistogramCuts() {
-  monitor_.Init(__FUNCTION__);
   cut_ptrs_.HostVector().emplace_back(0);
 }
 
-// Dispatch to specific builder.
-void HistogramCuts::Build(DMatrix* dmat, uint32_t const max_num_bins) {
-  auto const& info = dmat->Info();
-  size_t const total = info.num_row_ * info.num_col_;
-  size_t const nnz = info.num_nonzero_;
-  float const sparsity = static_cast<float>(nnz) / static_cast<float>(total);
-  // Use a small number to avoid calling `dmat->GetColumnBatches'.
-  float constexpr kSparsityThreshold = 0.0005;
-  // FIXME(trivialfis): Distributed environment is not supported.
-  if (sparsity < kSparsityThreshold && (!rabit::IsDistributed())) {
-    LOG(INFO) << "Building quantile cut on a sparse dataset.";
-    SparseCuts cuts(this);
-    cuts.Build(dmat, max_num_bins);
-  } else {
-    LOG(INFO) << "Building quantile cut on a dense dataset or distributed environment.";
-    DenseCuts cuts(this);
-    cuts.Build(dmat, max_num_bins);
-  }
-  LOG(INFO) << "Total number of hist bins: " << cut_ptrs_.HostVector().back();
-}
-
-bool CutsBuilder::UseGroup(DMatrix* dmat) {
-  auto& info = dmat->Info();
-  return CutsBuilder::UseGroup(info);
-}
-
-bool CutsBuilder::UseGroup(MetaInfo const& info) {
-  size_t const num_groups = info.group_ptr_.size() == 0 ?
-                            0 : info.group_ptr_.size() - 1;
-  // Use group index for weights?
-  bool const use_group_ind = num_groups != 0 &&
-                             (info.weights_.Size() != info.num_row_);
-  return use_group_ind;
-}
-
-void SparseCuts::SingleThreadBuild(SparsePage const& page, MetaInfo const& info,
-                                   uint32_t max_num_bins,
-                                   bool const use_group_ind,
-                                   uint32_t beg_col, uint32_t end_col,
-                                   uint32_t thread_id) {
-  CHECK_GE(end_col, beg_col);
-
-  // Data groups, used in ranking.
-  std::vector<bst_uint> const& group_ptr = info.group_ptr_;
-  auto &local_min_vals = p_cuts_->min_vals_.HostVector();
-  auto &local_cuts = p_cuts_->cut_values_.HostVector();
-  auto &local_ptrs = p_cuts_->cut_ptrs_.HostVector();
-  local_min_vals.resize(end_col - beg_col, 0);
-
-  for (uint32_t col_id = beg_col; col_id < page.Size() && col_id < end_col; ++col_id) {
-    // Using a local variable makes things easier, but at the cost of memory trashing.
-    WQSketch sketch;
-    common::Span<xgboost::Entry const> const column = page[col_id];
-    uint32_t const n_bins = std::min(static_cast<uint32_t>(column.size()),
-                                     max_num_bins);
-    if (n_bins == 0) {
-      // cut_ptrs_ is initialized with a zero, so there's always an element at the back
-      CHECK_GE(local_ptrs.size(), 1);
-      local_ptrs.emplace_back(local_ptrs.back());
-      continue;
-    }
-
-    sketch.Init(info.num_row_, 1.0 / (n_bins * WQSketch::kFactor));
-    for (auto const& entry : column) {
-      uint32_t weight_ind = 0;
-      if (use_group_ind) {
-        auto row_idx = entry.index;
-        uint32_t group_ind =
-            this->SearchGroupIndFromRow(group_ptr, page.base_rowid + row_idx);
-        weight_ind = group_ind;
-      } else {
-        weight_ind = entry.index;
-      }
-      sketch.Push(entry.fvalue, info.GetWeight(weight_ind));
-    }
-
-    WQSketch::SummaryContainer out_summary;
-    sketch.GetSummary(&out_summary);
-    WQSketch::SummaryContainer summary;
-    summary.Reserve(n_bins + 1);
-    summary.SetPrune(out_summary, n_bins + 1);
-
-    // Can be use data[1] as the min values so that we don't need to
-    // store another array?
-    float mval = summary.data[0].value;
-    local_min_vals[col_id - beg_col]  = mval - (fabs(mval) + 1e-5);
-
-    this->AddCutPoint(summary, max_num_bins);
-
-    bst_float cpt = (summary.size > 0) ?
-                    summary.data[summary.size - 1].value :
-                    local_min_vals[col_id - beg_col];
-    cpt += fabs(cpt) + 1e-5;
-    local_cuts.emplace_back(cpt);
-
-    local_ptrs.emplace_back(local_cuts.size());
-  }
-}
-
-std::vector<size_t> SparseCuts::LoadBalance(SparsePage const& page,
-                                            size_t const nthreads) {
-  /* Some sparse datasets have their mass concentrating on small
-   * number of features.  To avoid wating for a few threads running
-   * forever, we here distirbute different number of columns to
-   * different threads according to number of entries. */
-  size_t const total_entries = page.data.Size();
-  size_t const entries_per_thread = common::DivRoundUp(total_entries, nthreads);
-
-  std::vector<size_t> cols_ptr(nthreads+1, 0);
-  size_t count {0};
-  size_t current_thread {1};
-
-  for (size_t col_id = 0; col_id < page.Size(); ++col_id) {
-    auto const column = page[col_id];
-    cols_ptr[current_thread]++;  // add one column to thread
-    count += column.size();
-    if (count > entries_per_thread + 1) {
-      current_thread++;
-      count = 0;
-      cols_ptr[current_thread] = cols_ptr[current_thread-1];
-    }
-  }
-  // Idle threads.
-  for (; current_thread < cols_ptr.size() - 1; ++current_thread) {
-    cols_ptr[current_thread+1] = cols_ptr[current_thread];
-  }
-
-  return cols_ptr;
-}
-
-void SparseCuts::Build(DMatrix* dmat, uint32_t const max_num_bins) {
-  monitor_.Start(__FUNCTION__);
-  // Use group index for weights?
-  auto use_group = UseGroup(dmat);
-  uint32_t nthreads = omp_get_max_threads();
-  CHECK_GT(nthreads, 0);
-  std::vector<HistogramCuts> cuts_containers(nthreads);
-  std::vector<std::unique_ptr<SparseCuts>> sparse_cuts(nthreads);
-  for (size_t i = 0; i < nthreads; ++i) {
-    sparse_cuts[i].reset(new SparseCuts(&cuts_containers[i]));
-  }
-
-  for (auto const& page : dmat->GetBatches<CSCPage>()) {
-    CHECK_LE(page.Size(), dmat->Info().num_col_);
-    monitor_.Start("Load balance");
-    std::vector<size_t> col_ptr = LoadBalance(page, nthreads);
-    monitor_.Stop("Load balance");
-    // We here decouples the logic between build and parallelization
-    // to simplify things a bit.
-#pragma omp parallel for num_threads(nthreads) schedule(static)
-    for (omp_ulong i = 0; i < nthreads; ++i) {
-      common::Monitor t_monitor;
-      t_monitor.Init("SingleThreadBuild: " + std::to_string(i));
-      t_monitor.Start(std::to_string(i));
-      sparse_cuts[i]->SingleThreadBuild(page, dmat->Info(), max_num_bins, use_group,
-                                        col_ptr[i], col_ptr[i+1], i);
-      t_monitor.Stop(std::to_string(i));
-    }
-
-    this->Concat(sparse_cuts, dmat->Info().num_col_);
-  }
-
-  monitor_.Stop(__FUNCTION__);
-}
-
-void SparseCuts::Concat(
-    std::vector<std::unique_ptr<SparseCuts>> const& cuts, uint32_t n_cols) {
-  monitor_.Start(__FUNCTION__);
-  uint32_t nthreads = omp_get_max_threads();
-  auto &local_min_vals = p_cuts_->min_vals_.HostVector();
-  auto &local_cuts = p_cuts_->cut_values_.HostVector();
-  auto &local_ptrs = p_cuts_->cut_ptrs_.HostVector();
-  local_min_vals.resize(n_cols, std::numeric_limits<float>::max());
-  size_t min_vals_tail = 0;
-
-  for (uint32_t t = 0; t < nthreads; ++t) {
-    auto& thread_min_vals = cuts[t]->p_cuts_->min_vals_.HostVector();
-    auto& thread_cuts = cuts[t]->p_cuts_->cut_values_.HostVector();
-    auto& thread_ptrs = cuts[t]->p_cuts_->cut_ptrs_.HostVector();
-
-    // concat csc pointers.
-    size_t const old_ptr_size = local_ptrs.size();
-    local_ptrs.resize(
-        thread_ptrs.size() + local_ptrs.size() - 1);
-    size_t const new_icp_size = local_ptrs.size();
-    auto tail = local_ptrs[old_ptr_size-1];
-    for (size_t j = old_ptr_size; j < new_icp_size; ++j) {
-      local_ptrs[j] = tail + thread_ptrs[j-old_ptr_size+1];
-    }
-    // concat csc values
-    size_t const old_iv_size = local_cuts.size();
-    local_cuts.resize(
-        thread_cuts.size() + local_cuts.size());
-    size_t const new_iv_size = local_cuts.size();
-    for (size_t j = old_iv_size; j < new_iv_size; ++j) {
-      local_cuts[j] = thread_cuts[j-old_iv_size];
-    }
-    // merge min values
-    for (size_t j = 0; j < thread_min_vals.size(); ++j) {
-       local_min_vals.at(min_vals_tail + j) =
-          std::min(local_min_vals.at(min_vals_tail + j), thread_min_vals.at(j));
-    }
-    min_vals_tail += thread_min_vals.size();
-  }
-  monitor_.Stop(__FUNCTION__);
-}
-
-void DenseCuts::Build(DMatrix* p_fmat, uint32_t max_num_bins) {
-  monitor_.Start(__FUNCTION__);
-  const MetaInfo& info = p_fmat->Info();
-
-  // safe factor for better accuracy
-  std::vector<WQSketch> sketchs;
-
-  const int nthread = omp_get_max_threads();
-
-  unsigned const nstep =
-      static_cast<unsigned>((info.num_col_ + nthread - 1) / nthread);
-  unsigned const ncol = static_cast<unsigned>(info.num_col_);
-  sketchs.resize(info.num_col_);
-  for (auto& s : sketchs) {
-    s.Init(info.num_row_, 1.0 / (max_num_bins * WQSketch::kFactor));
-  }
-
-  // Data groups, used in ranking.
-  std::vector<bst_uint> const& group_ptr = info.group_ptr_;
-  size_t const num_groups = group_ptr.size() == 0 ? 0 : group_ptr.size() - 1;
-  // Use group index for weights?
-  bool const use_group = UseGroup(p_fmat);
-  const bool isDense = p_fmat->IsDense();
-  for (const auto &batch : p_fmat->GetBatches<SparsePage>()) {
-    size_t group_ind = 0;
-    if (use_group) {
-      group_ind = this->SearchGroupIndFromRow(group_ptr, batch.base_rowid);
-    }
-#pragma omp parallel num_threads(nthread) firstprivate(group_ind, use_group)
-    {
-      CHECK_EQ(nthread, omp_get_num_threads());
-      auto tid = static_cast<unsigned>(omp_get_thread_num());
-      unsigned begin = std::min(nstep * tid, ncol);
-      unsigned end = std::min(nstep * (tid + 1), ncol);
-
-      // do not iterate if no columns are assigned to the thread
-      if (begin < end && end <= ncol) {
-        for (size_t i = 0; i < batch.Size(); ++i) { // NOLINT(*)
-          size_t const ridx = batch.base_rowid + i;
-          SparsePage::Inst const inst = batch[i];
-          if (use_group &&
-              group_ptr[group_ind] == ridx &&
-              // maximum equals to weights.size() - 1
-              group_ind < num_groups - 1) {
-            // move to next group
-            group_ind++;
-          }
-          size_t w_idx = use_group ? group_ind : ridx;
-          auto w = info.GetWeight(w_idx);
-          if (isDense) {
-            auto data = inst.data();
-            for (size_t ii = begin; ii < end; ii++) {
-              sketchs[ii].Push(data[ii].fvalue, w);
-            }
-          } else {
-            for (auto const& entry : inst) {
-              if (entry.index >= begin && entry.index < end) {
-                sketchs[entry.index].Push(entry.fvalue, w);
-              }
-            }
-          }
-        }
-      }
-    }
-  }
-
-  Init(&sketchs, max_num_bins, info.num_row_);
-  monitor_.Stop(__FUNCTION__);
-}
-
-/**
- * \param [in,out]  in_sketchs
- * \param           max_num_bins  The maximum number bins.
- * \param           max_rows      Number of rows in this DMatrix.
- */
-void DenseCuts::Init
-(std::vector<WQSketch>* in_sketchs, uint32_t max_num_bins, size_t max_rows) {
-  monitor_.Start(__func__);
-  std::vector<WQSketch>& sketchs = *in_sketchs;
-
-  // Compute how many cuts samples we need at each node
-  // Do not require more than the number of total rows  in training data
-  // This allows efficient training on wide data
-  size_t global_max_rows = max_rows;
-  rabit::Allreduce<rabit::op::Sum>(&global_max_rows, 1);
-  size_t intermediate_num_cuts =
-      std::min(global_max_rows, static_cast<size_t>(max_num_bins * WQSketch::kFactor));
-  // gather the histogram data
-  rabit::SerializeReducer<WQSketch::SummaryContainer> sreducer;
-  std::vector<WQSketch::SummaryContainer> summary_array;
-  summary_array.resize(sketchs.size());
-  for (size_t i = 0; i < sketchs.size(); ++i) {
-    WQSketch::SummaryContainer out;
-    sketchs[i].GetSummary(&out);
-    summary_array[i].Reserve(intermediate_num_cuts);
-    summary_array[i].SetPrune(out, intermediate_num_cuts);
-  }
-  CHECK_EQ(summary_array.size(), in_sketchs->size());
-  size_t nbytes = WQSketch::SummaryContainer::CalcMemCost(intermediate_num_cuts);
-  // TODO(chenqin): rabit failure recovery assumes no boostrap onetime call after loadcheckpoint
-  // we need to move this allreduce before loadcheckpoint call in future
-  sreducer.Allreduce(dmlc::BeginPtr(summary_array), nbytes, summary_array.size());
-  p_cuts_->min_vals_.HostVector().resize(sketchs.size());
-
-  for (size_t fid = 0; fid < summary_array.size(); ++fid) {
-    WQSketch::SummaryContainer a;
-    a.Reserve(max_num_bins + 1);
-    a.SetPrune(summary_array[fid], max_num_bins + 1);
-    const bst_float mval = a.data[0].value;
-    p_cuts_->min_vals_.HostVector()[fid] = mval - (fabs(mval) + 1e-5);
-    AddCutPoint(a, max_num_bins);
-    // push a value that is greater than anything
-    const bst_float cpt
-      = (a.size > 0) ? a.data[a.size - 1].value : p_cuts_->min_vals_.HostVector()[fid];
-    // this must be bigger than last value in a scale
-    const bst_float last = cpt + (fabs(cpt) + 1e-5);
-    p_cuts_->cut_values_.HostVector().push_back(last);
-
-    // Ensure that every feature gets at least one quantile point
-    CHECK_LE(p_cuts_->cut_values_.HostVector().size(), std::numeric_limits<uint32_t>::max());
-    auto cut_size = static_cast<uint32_t>(p_cuts_->cut_values_.HostVector().size());
-    CHECK_GT(cut_size, p_cuts_->cut_ptrs_.HostVector().back());
-    p_cuts_->cut_ptrs_.HostVector().push_back(cut_size);
-  }
-  monitor_.Stop(__func__);
-}
-
 void GHistIndexMatrix::Init(DMatrix* p_fmat, int max_bins) {
-  cut.Build(p_fmat, max_bins);
+  cut = SketchOnDMatrix(p_fmat, max_bins);
+
   max_num_bins = max_bins;
   const int32_t nthread = omp_get_max_threads();
   const uint32_t nbins = cut.Ptrs().back();
@@ -1048,12 +714,11 @@ void BuildHistKernel(const std::vector<GradientPair>& gpair,
   }
 }
 
-template<typename GradientSumT>
-void GHistBuilder<GradientSumT>::BuildHist(const std::vector<GradientPair>& gpair,
-                             const RowSetCollection::Elem row_indices,
-                             const GHistIndexMatrix& gmat,
-                             GHistRowT hist,
-                             bool isDense) {
+template <typename GradientSumT>
+void GHistBuilder<GradientSumT>::BuildHist(
+    const std::vector<GradientPair> &gpair,
+    const RowSetCollection::Elem row_indices, const GHistIndexMatrix &gmat,
+    GHistRowT hist, bool isDense) {
   const size_t nrows = row_indices.Size();
   const size_t no_prefetch_size = Prefetch::NoPrefetchSize(nrows);
 
diff --git a/src/common/hist_util.cu b/src/common/hist_util.cu
index 6953a556b939..ebd38b7aecd9 100644
--- a/src/common/hist_util.cu
+++ b/src/common/hist_util.cu
@@ -313,7 +313,6 @@ HistogramCuts DeviceSketch(int device, DMatrix* dmat, int max_bins,
       device, num_cuts_per_feature, has_weights);
 
   HistogramCuts cuts;
-  DenseCuts dense_cuts(&cuts);
   SketchContainer sketch_container(max_bins, dmat->Info().num_col_,
                                    dmat->Info().num_row_, device);
 
@@ -324,7 +323,7 @@ HistogramCuts DeviceSketch(int device, DMatrix* dmat, int max_bins,
     for (auto begin = 0ull; begin < batch_nnz; begin += sketch_batch_num_elements) {
       size_t end = std::min(batch_nnz, size_t(begin + sketch_batch_num_elements));
       if (has_weights) {
-        bool is_ranking = CutsBuilder::UseGroup(dmat);
+        bool is_ranking = HostSketchContainer::UseGroup(dmat->Info());
         dh::caching_device_vector<uint32_t> groups(info.group_ptr_.cbegin(),
                                                    info.group_ptr_.cend());
         ProcessWeightedBatch(
diff --git a/src/common/hist_util.cuh b/src/common/hist_util.cuh
index 8dca9fdb9bef..f1034040c1ab 100644
--- a/src/common/hist_util.cuh
+++ b/src/common/hist_util.cuh
@@ -306,7 +306,7 @@ void AdapterDeviceSketch(Batch batch, int num_bins,
       size_t end = std::min(batch.Size(), size_t(begin + sketch_batch_num_elements));
       ProcessWeightedSlidingWindow(batch, info,
                                    num_cuts_per_feature,
-                                   CutsBuilder::UseGroup(info), missing, device, num_cols, begin, end,
+                                   HostSketchContainer::UseGroup(info), missing, device, num_cols, begin, end,
                                    sketch_container);
     }
   } else {
diff --git a/src/common/hist_util.h b/src/common/hist_util.h
index dbb0b35e4cea..d86b73135f34 100644
--- a/src/common/hist_util.h
+++ b/src/common/hist_util.h
@@ -17,6 +17,7 @@
 #include <map>
 
 #include "row_set.h"
+#include "common.h"
 #include "threading_utils.h"
 #include "../tree/param.h"
 #include "./quantile.h"
@@ -34,15 +35,8 @@ using GHistIndexRow = Span<uint32_t const>;
 // A CSC matrix representing histogram cuts, used in CPU quantile hist.
 // The cut values represent upper bounds of bins containing approximately equal numbers of elements
 class HistogramCuts {
-  // Using friends to avoid creating a virtual class, since HistogramCuts is used as value
-  // object in many places.
-  friend class SparseCuts;
-  friend class DenseCuts;
-  friend class CutsBuilder;
-
  protected:
   using BinIdx = uint32_t;
-  common::Monitor monitor_;
 
  public:
   HostDeviceVector<bst_float> cut_values_;  // NOLINT
@@ -75,16 +69,12 @@ class HistogramCuts {
   }
 
   HistogramCuts& operator=(HistogramCuts&& that) noexcept(true) {
-    monitor_ = std::move(that.monitor_);
     cut_ptrs_ = std::move(that.cut_ptrs_);
     cut_values_ = std::move(that.cut_values_);
     min_vals_ = std::move(that.min_vals_);
     return *this;
   }
 
-  /* \brief Build histogram cuts. */
-  void Build(DMatrix* dmat, uint32_t const max_num_bins);
-  /* \brief How many bins a feature has. */
   uint32_t FeatureBins(uint32_t feature) const {
     return cut_ptrs_.ConstHostVector().at(feature + 1) -
            cut_ptrs_.ConstHostVector()[feature];
@@ -118,86 +108,42 @@ class HistogramCuts {
   }
 };
 
-/* \brief An interface for building quantile cuts.
- *
- * `DenseCuts' always assumes there are `max_bins` for each feature, which makes it not
- * suitable for sparse dataset.  On the other hand `SparseCuts' uses `GetColumnBatches',
- * which doubles the memory usage, hence can not be applied to dense dataset.
- */
-class CutsBuilder {
- public:
-  using WQSketch = common::WQuantileSketch<bst_float, bst_float>;
-  /* \brief return whether group for ranking is used. */
-  static bool UseGroup(DMatrix* dmat);
-  static bool UseGroup(MetaInfo const& info);
-
- protected:
-  HistogramCuts* p_cuts_;
-
- public:
-  explicit CutsBuilder(HistogramCuts* p_cuts) : p_cuts_{p_cuts} {}
-  virtual ~CutsBuilder() = default;
-
-  static uint32_t SearchGroupIndFromRow(std::vector<bst_uint> const &group_ptr,
-                                        size_t const base_rowid) {
-    CHECK_LT(base_rowid, group_ptr.back())
-        << "Row: " << base_rowid << " is not found in any group.";
-    auto it =
-        std::upper_bound(group_ptr.cbegin(), group_ptr.cend() - 1, base_rowid);
-    bst_group_t group_ind = it - group_ptr.cbegin() - 1;
-    return group_ind;
-  }
-
-  void AddCutPoint(WQSketch::SummaryContainer const& summary, int max_bin) {
-    size_t required_cuts = std::min(summary.size, static_cast<size_t>(max_bin));
-    for (size_t i = 1; i < required_cuts; ++i) {
-      bst_float cpt = summary.data[i].value;
-      if (i == 1 || cpt > p_cuts_->cut_values_.ConstHostVector().back()) {
-        p_cuts_->cut_values_.HostVector().push_back(cpt);
+inline HistogramCuts SketchOnDMatrix(DMatrix *m, int32_t max_bins) {
+  HistogramCuts out;
+  auto const& info = m->Info();
+  const auto threads = omp_get_max_threads();
+  std::vector<std::vector<bst_row_t>> column_sizes(threads);
+  for (auto& column : column_sizes) {
+    column.resize(info.num_col_, 0);
+  }
+  for (auto const& page : m->GetBatches<SparsePage>()) {
+    page.data.HostVector();
+    page.offset.HostVector();
+    ParallelFor(page.Size(), threads, [&](size_t i) {
+      auto &local_column_sizes = column_sizes.at(omp_get_thread_num());
+      auto row = page[i];
+      auto const *p_row = row.data();
+      for (size_t j = 0; j < row.size(); ++j) {
+        local_column_sizes.at(p_row[j].index)++;
       }
-    }
+    });
   }
+  std::vector<bst_row_t> reduced(info.num_col_, 0);
 
-  /* \brief Build histogram indices. */
-  virtual void Build(DMatrix* dmat, uint32_t const max_num_bins) = 0;
-};
-
-/*! \brief Cut configuration for sparse dataset. */
-class SparseCuts : public CutsBuilder {
-  /* \brief Distribute columns to each thread according to number of entries. */
-  static std::vector<size_t> LoadBalance(SparsePage const& page, size_t const nthreads);
-  Monitor monitor_;
-
- public:
-  explicit SparseCuts(HistogramCuts* container) :
-      CutsBuilder(container) {
-    monitor_.Init(__FUNCTION__);
-  }
-
-  /* \brief Concatonate the built cuts in each thread. */
-  void Concat(std::vector<std::unique_ptr<SparseCuts>> const& cuts, uint32_t n_cols);
-  /* \brief Build histogram indices in single thread. */
-  void SingleThreadBuild(SparsePage const& page, MetaInfo const& info,
-                         uint32_t max_num_bins,
-                         bool const use_group_ind,
-                         uint32_t beg, uint32_t end, uint32_t thread_id);
-  void Build(DMatrix* dmat, uint32_t const max_num_bins) override;
-};
-
-/*! \brief Cut configuration for dense dataset. */
-class DenseCuts  : public CutsBuilder {
- protected:
-  Monitor monitor_;
+  ParallelFor(info.num_col_, threads, [&](size_t i) {
+    for (auto const &thread : column_sizes) {
+      reduced[i] += thread[i];
+    }
+  });
 
- public:
-  explicit DenseCuts(HistogramCuts* container) :
-      CutsBuilder(container) {
-    monitor_.Init(__FUNCTION__);
+  HostSketchContainer container(reduced, max_bins,
+                                HostSketchContainer::UseGroup(info));
+  for (auto const &page : m->GetBatches<SparsePage>()) {
+    container.PushRowPage(page, info);
   }
-  void Init(std::vector<WQSketch>* sketchs, uint32_t max_num_bins, size_t max_rows);
-  void Build(DMatrix* p_fmat, uint32_t max_num_bins) override;
-};
-
+  container.MakeCuts(&out);
+  return out;
+}
 
 enum BinTypeSize {
   kUint8BinsTypeSize  = 1,
diff --git a/src/common/quantile.cc b/src/common/quantile.cc
new file mode 100644
index 000000000000..374864c8f4b0
--- /dev/null
+++ b/src/common/quantile.cc
@@ -0,0 +1,193 @@
+/*!
+ * Copyright 2020 by XGBoost Contributors
+ */
+#include <limits>
+#include <utility>
+#include "quantile.h"
+#include "hist_util.h"
+
+namespace xgboost {
+namespace common {
+
+HostSketchContainer::HostSketchContainer(std::vector<bst_row_t> columns_size,
+                                         int32_t max_bins, bool use_group)
+    : columns_size_{std::move(columns_size)}, max_bins_{max_bins},
+      use_group_ind_{use_group} {
+  monitor_.Init(__func__);
+  CHECK_NE(columns_size_.size(), 0);
+  sketches_.resize(columns_size_.size());
+  for (size_t i = 0; i < sketches_.size(); ++i) {
+    auto n_bins = std::min(static_cast<size_t>(max_bins_), columns_size_[i]);
+    n_bins = std::max(n_bins, static_cast<decltype(n_bins)>(1));
+    auto eps = 1.0 / (static_cast<float>(n_bins) * WQSketch::kFactor);
+    sketches_[i].Init(columns_size_[i], eps);
+    sketches_[i].inqueue.queue.resize(sketches_[i].limit_size * 2);
+  }
+}
+
+std::vector<bst_feature_t> LoadBalance(SparsePage const &page,
+                                       std::vector<size_t> columns_size,
+                                       size_t const nthreads) {
+  /* Some sparse datasets have their mass concentrating on small
+   * number of features.  To avoid wating for a few threads running
+   * forever, we here distirbute different number of columns to
+   * different threads according to number of entries. */
+  size_t const total_entries = page.data.Size();
+  size_t const entries_per_thread = common::DivRoundUp(total_entries, nthreads);
+
+  std::vector<bst_feature_t> cols_ptr(nthreads+1, 0);
+  size_t count {0};
+  size_t current_thread {1};
+
+  for (auto col : columns_size) {
+    cols_ptr[current_thread]++;  // add one column to thread
+    count += col;
+    if (count > entries_per_thread + 1) {
+      current_thread++;
+      count = 0;
+      cols_ptr[current_thread] = cols_ptr[current_thread-1];
+    }
+  }
+  // Idle threads.
+  for (; current_thread < cols_ptr.size() - 1; ++current_thread) {
+    cols_ptr[current_thread+1] = cols_ptr[current_thread];
+  }
+
+  return cols_ptr;
+}
+
+void HostSketchContainer::PushRowPage(SparsePage const &page,
+                                      MetaInfo const &info) {
+  monitor_.Start(__func__);
+  int nthread = omp_get_max_threads();
+  CHECK_EQ(sketches_.size(), info.num_col_);
+
+  // Data groups, used in ranking.
+  std::vector<bst_uint> const &group_ptr = info.group_ptr_;
+  // Use group index for weights?
+  auto batch = page.GetView();
+  dmlc::OMPException exec;
+  // Parallel over columns.  Asumming the data is dense, each thread owns a set of
+  // consecutive columns.
+  auto const ncol = static_cast<uint32_t>(info.num_col_);
+  auto const is_dense = info.num_nonzero_ == info.num_col_ * info.num_row_;
+  auto thread_columns_ptr = LoadBalance(page, columns_size_, nthread);
+
+#pragma omp parallel num_threads(nthread)
+  {
+    exec.Run([&]() {
+      auto tid = static_cast<uint32_t>(omp_get_thread_num());
+      auto const begin = thread_columns_ptr[tid];
+      auto const end = thread_columns_ptr[tid + 1];
+      size_t group_ind = 0;
+
+      // do not iterate if no columns are assigned to the thread
+      if (begin < end && end <= ncol) {
+        for (size_t i = 0; i < batch.Size(); ++i) {
+          size_t const ridx = page.base_rowid + i;
+          SparsePage::Inst const inst = batch[i];
+          if (use_group_ind_) {
+            group_ind = this->SearchGroupIndFromRow(group_ptr, i + page.base_rowid);
+          }
+          size_t w_idx = use_group_ind_ ? group_ind : ridx;
+          auto w = info.GetWeight(w_idx);
+          auto p_inst = inst.data();
+          if (is_dense) {
+            for (size_t ii = begin; ii < end; ii++) {
+              sketches_[ii].Push(p_inst[ii].fvalue, w);
+            }
+          } else {
+            for (size_t i = 0; i < inst.size(); ++i) {
+              auto const& entry = p_inst[i];
+              if (entry.index >= begin && entry.index < end) {
+                sketches_[entry.index].Push(entry.fvalue, w);
+              }
+            }
+          }
+        }
+      }
+    });
+  }
+  exec.Rethrow();
+  monitor_.Stop(__func__);
+}
+
+void AddCutPoint(WQuantileSketch<float, float>::SummaryContainer const &summary,
+                 int max_bin, HistogramCuts *cuts) {
+  size_t required_cuts = std::min(summary.size, static_cast<size_t>(max_bin));
+  auto& cut_values = cuts->cut_values_.HostVector();
+  for (size_t i = 1; i < required_cuts; ++i) {
+    bst_float cpt = summary.data[i].value;
+    if (i == 1 || cpt > cuts->cut_values_.ConstHostVector().back()) {
+      cut_values.push_back(cpt);
+    }
+  }
+}
+
+void HostSketchContainer::MakeCuts(HistogramCuts* cuts) {
+  monitor_.Start(__func__);
+  rabit::Allreduce<rabit::op::Sum>(columns_size_.data(), columns_size_.size());
+  std::vector<WQSketch::SummaryContainer> reduced(sketches_.size());
+  std::vector<int32_t> num_cuts;
+  size_t nbytes = 0;
+  for (size_t i = 0; i < sketches_.size(); ++i) {
+    int32_t intermediate_num_cuts =  static_cast<int32_t>(std::min(
+        columns_size_[i], static_cast<size_t>(max_bins_ * WQSketch::kFactor)));
+    if (columns_size_[i] != 0) {
+      WQSketch::SummaryContainer out;
+      sketches_[i].GetSummary(&out);
+      reduced[i].Reserve(intermediate_num_cuts);
+      CHECK(reduced[i].data);
+      reduced[i].SetPrune(out, intermediate_num_cuts);
+    }
+    num_cuts.push_back(intermediate_num_cuts);
+    nbytes = std::max(
+        WQSketch::SummaryContainer::CalcMemCost(intermediate_num_cuts), nbytes);
+  }
+
+  if (rabit::IsDistributed()) {
+    // FIXME(trivialfis): This call will allocate nbytes * num_columns on rabit, which
+    // may generate oom error when data is sparse.  To fix it, we need to:
+    //   - gather the column offsets over all workers.
+    //   - run rabit::allgather on sketch data to collect all data.
+    //   - merge all gathered sketches based on worker offsets and column offsets of data
+    //     from each worker.
+    // See GPU implementation for details.
+    rabit::SerializeReducer<WQSketch::SummaryContainer> sreducer;
+    sreducer.Allreduce(dmlc::BeginPtr(reduced), nbytes, reduced.size());
+  }
+
+  cuts->min_vals_.HostVector().resize(sketches_.size(), 0.0f);
+  for (size_t fid = 0; fid < reduced.size(); ++fid) {
+    WQSketch::SummaryContainer a;
+    size_t max_num_bins = std::min(num_cuts[fid], max_bins_);
+    a.Reserve(max_num_bins + 1);
+    CHECK(a.data);
+    if (columns_size_[fid] != 0) {
+      a.SetPrune(reduced[fid], max_num_bins + 1);
+      CHECK(a.data && reduced[fid].data);
+      const bst_float mval = a.data[0].value;
+      cuts->min_vals_.HostVector()[fid] = mval - fabs(mval) - 1e-5f;
+    } else {
+      // Empty column.
+      const float mval = 1e-5f;
+      cuts->min_vals_.HostVector()[fid] = mval;
+    }
+    AddCutPoint(a, max_num_bins, cuts);
+    // push a value that is greater than anything
+    const bst_float cpt
+      = (a.size > 0) ? a.data[a.size - 1].value : cuts->min_vals_.HostVector()[fid];
+    // this must be bigger than last value in a scale
+    const bst_float last = cpt + (fabs(cpt) + 1e-5f);
+    cuts->cut_values_.HostVector().push_back(last);
+
+    // Ensure that every feature gets at least one quantile point
+    CHECK_LE(cuts->cut_values_.HostVector().size(), std::numeric_limits<uint32_t>::max());
+    auto cut_size = static_cast<uint32_t>(cuts->cut_values_.HostVector().size());
+    CHECK_GT(cut_size, cuts->cut_ptrs_.HostVector().back());
+    cuts->cut_ptrs_.HostVector().push_back(cut_size);
+  }
+  monitor_.Stop(__func__);
+}
+}  // namespace common
+}  // namespace xgboost
diff --git a/src/common/quantile.cu b/src/common/quantile.cu
index 8910e41cd2e5..52d0e37e97be 100644
--- a/src/common/quantile.cu
+++ b/src/common/quantile.cu
@@ -20,7 +20,7 @@
 namespace xgboost {
 namespace common {
 
-using WQSketch = DenseCuts::WQSketch;
+using WQSketch = HostSketchContainer::WQSketch;
 using SketchEntry = WQSketch::Entry;
 
 // Algorithm 4 in XGBoost's paper, using binary search to find i.
diff --git a/src/common/quantile.h b/src/common/quantile.h
index 49345d13f406..11e2530f748e 100644
--- a/src/common/quantile.h
+++ b/src/common/quantile.h
@@ -9,12 +9,15 @@
 
 #include <dmlc/base.h>
 #include <xgboost/logging.h>
+#include <xgboost/data.h>
 #include <cmath>
 #include <vector>
 #include <cstring>
 #include <algorithm>
 #include <iostream>
 
+#include "timer.h"
+
 namespace xgboost {
 namespace common {
 /*!
@@ -682,6 +685,57 @@ template<typename DType, typename RType = unsigned>
 class WXQuantileSketch :
       public QuantileSketchTemplate<DType, RType, WXQSummary<DType, RType> > {
 };
+
+class HistogramCuts;
+
+/*!
+ * A sketch matrix storing sketches for each feature.
+ */
+class HostSketchContainer {
+ public:
+  using WQSketch = WQuantileSketch<float, float>;
+
+ private:
+  std::vector<WQSketch> sketches_;
+  std::vector<bst_row_t> columns_size_;
+  int32_t max_bins_;
+  bool use_group_ind_{false};
+  Monitor monitor_;
+
+ public:
+  /* \brief Initialize necessary info.
+   *
+   * \param columns_size Size of each column.
+   * \param max_bins maximum number of bins for each feature.
+   * \param use_group whether is assigned to group to data instance.
+   */
+  HostSketchContainer(std::vector<bst_row_t> columns_size, int32_t max_bins,
+                      bool use_group);
+
+  static bool UseGroup(MetaInfo const &info) {
+    size_t const num_groups =
+        info.group_ptr_.size() == 0 ? 0 : info.group_ptr_.size() - 1;
+    // Use group index for weights?
+    bool const use_group_ind =
+        num_groups != 0 && (info.weights_.Size() != info.num_row_);
+    return use_group_ind;
+  }
+
+  static uint32_t SearchGroupIndFromRow(std::vector<bst_uint> const &group_ptr,
+                                        size_t const base_rowid) {
+    CHECK_LT(base_rowid, group_ptr.back())
+        << "Row: " << base_rowid << " is not found in any group.";
+    bst_group_t group_ind =
+        std::upper_bound(group_ptr.cbegin(), group_ptr.cend() - 1, base_rowid) -
+        group_ptr.cbegin() - 1;
+    return group_ind;
+  }
+
+  /* \brief Push a CSR matrix. */
+  void PushRowPage(SparsePage const& page, MetaInfo const& info);
+
+  void MakeCuts(HistogramCuts* cuts);
+};
 }  // namespace common
 }  // namespace xgboost
 #endif  // XGBOOST_COMMON_QUANTILE_H_
diff --git a/src/common/threading_utils.h b/src/common/threading_utils.h
index 3f0519b054c6..2c6f5ba11e90 100644
--- a/src/common/threading_utils.h
+++ b/src/common/threading_utils.h
@@ -6,9 +6,9 @@
 #ifndef XGBOOST_COMMON_THREADING_UTILS_H_
 #define XGBOOST_COMMON_THREADING_UTILS_H_
 
+#include <dmlc/common.h>
 #include <vector>
 #include <algorithm>
-
 #include "xgboost/logging.h"
 
 namespace xgboost {
@@ -115,17 +115,32 @@ void ParallelFor2d(const BlockedSpace2d& space, int nthreads, Func func) {
   nthreads = std::min(nthreads, omp_get_max_threads());
   nthreads = std::max(nthreads, 1);
 
+  dmlc::OMPException omp_exc;
 #pragma omp parallel num_threads(nthreads)
   {
-    size_t tid = omp_get_thread_num();
-    size_t chunck_size = num_blocks_in_space / nthreads + !!(num_blocks_in_space % nthreads);
+    omp_exc.Run([&]() {
+      size_t tid = omp_get_thread_num();
+      size_t chunck_size =
+          num_blocks_in_space / nthreads + !!(num_blocks_in_space % nthreads);
+
+      size_t begin = chunck_size * tid;
+      size_t end = std::min(begin + chunck_size, num_blocks_in_space);
+      for (auto i = begin; i < end; i++) {
+        func(space.GetFirstDimension(i), space.GetRange(i));
+      }
+    });
+  }
+  omp_exc.Rethrow();
+}
 
-    size_t begin = chunck_size * tid;
-    size_t end   = std::min(begin + chunck_size, num_blocks_in_space);
-    for (auto i = begin; i < end; i++) {
-      func(space.GetFirstDimension(i), space.GetRange(i));
-    }
+template <typename Func>
+void ParallelFor(size_t size, size_t nthreads, Func fn) {
+  dmlc::OMPException omp_exc;
+#pragma omp parallel for num_threads(nthreads)
+  for (omp_ulong i = 0; i < size; ++i) {
+    omp_exc.Run(fn, i);
   }
+  omp_exc.Rethrow();
 }
 
 }  // namespace common
diff --git a/src/predictor/cpu_predictor.cc b/src/predictor/cpu_predictor.cc
index 1c84f4947514..8d116999e62c 100644
--- a/src/predictor/cpu_predictor.cc
+++ b/src/predictor/cpu_predictor.cc
@@ -44,18 +44,16 @@ bst_float PredValue(const SparsePage::Inst &inst,
 
 template <size_t kUnrollLen = 8>
 struct SparsePageView {
-  SparsePage const* page;
   bst_row_t base_rowid;
+  HostSparsePageView view;
   static size_t constexpr kUnroll = kUnrollLen;
 
   explicit SparsePageView(SparsePage const *p)
-      : page{p}, base_rowid{page->base_rowid} {
-    // Pull to host before entering omp block, as this is not thread safe.
-    page->data.HostVector();
-    page->offset.HostVector();
+      : base_rowid{p->base_rowid} {
+    view = p->GetView();
   }
-  SparsePage::Inst operator[](size_t i) { return (*page)[i]; }
-  size_t Size() const { return page->Size(); }
+  SparsePage::Inst operator[](size_t i) { return view[i]; }
+  size_t Size() const { return view.Size(); }
 };
 
 template <typename Adapter, size_t kUnrollLen = 8>
diff --git a/tests/cpp/common/test_hist_util.cc b/tests/cpp/common/test_hist_util.cc
index 7a0ff9a47215..0fad360f4298 100644
--- a/tests/cpp/common/test_hist_util.cc
+++ b/tests/cpp/common/test_hist_util.cc
@@ -158,86 +158,20 @@ TEST(CutsBuilder, SearchGroupInd) {
 
   HistogramCuts hmat;
 
-  size_t group_ind = CutsBuilder::SearchGroupIndFromRow(p_mat->Info().group_ptr_, 0);
+  size_t group_ind = HostSketchContainer::SearchGroupIndFromRow(p_mat->Info().group_ptr_, 0);
   ASSERT_EQ(group_ind, 0);
 
-  group_ind = CutsBuilder::SearchGroupIndFromRow(p_mat->Info().group_ptr_, 5);
+  group_ind = HostSketchContainer::SearchGroupIndFromRow(p_mat->Info().group_ptr_, 5);
   ASSERT_EQ(group_ind, 2);
 
+  EXPECT_ANY_THROW(HostSketchContainer::SearchGroupIndFromRow(p_mat->Info().group_ptr_, 17));
+
   p_mat->Info().Validate(-1);
-  EXPECT_THROW(CutsBuilder::SearchGroupIndFromRow(p_mat->Info().group_ptr_, 17),
+  EXPECT_THROW(HostSketchContainer::SearchGroupIndFromRow(p_mat->Info().group_ptr_, 17),
                dmlc::Error);
 
   std::vector<bst_uint> group_ptr {0, 1, 2};
-  CHECK_EQ(CutsBuilder::SearchGroupIndFromRow(group_ptr, 1), 1);
-}
-
-TEST(SparseCuts, SingleThreadedBuild) {
-  size_t constexpr kRows = 267;
-  size_t constexpr kCols = 31;
-  size_t constexpr kBins = 256;
-
-  auto p_fmat = RandomDataGenerator(kRows, kCols, 0).GenerateDMatrix();
-
-  common::GHistIndexMatrix hmat;
-  hmat.Init(p_fmat.get(), kBins);
-
-  HistogramCuts cuts;
-  SparseCuts indices(&cuts);
-  auto const& page = *(p_fmat->GetBatches<xgboost::CSCPage>().begin());
-  indices.SingleThreadBuild(page, p_fmat->Info(), kBins, false, 0, page.Size(), 0);
-
-  ASSERT_EQ(hmat.cut.Ptrs().size(), cuts.Ptrs().size());
-  ASSERT_EQ(hmat.cut.Ptrs(), cuts.Ptrs());
-  ASSERT_EQ(hmat.cut.Values(), cuts.Values());
-  ASSERT_EQ(hmat.cut.MinValues(), cuts.MinValues());
-}
-
-TEST(SparseCuts, MultiThreadedBuild) {
-  size_t constexpr kRows = 17;
-  size_t constexpr kCols = 15;
-  size_t constexpr kBins = 255;
-
-  omp_ulong ori_nthreads = omp_get_max_threads();
-  omp_set_num_threads(16);
-
-  auto Compare =
-#if defined(_MSC_VER)  // msvc fails to capture
-      [kBins](DMatrix* p_fmat) {
-#else
-      [](DMatrix* p_fmat) {
-#endif
-        HistogramCuts threaded_container;
-        SparseCuts threaded_indices(&threaded_container);
-        threaded_indices.Build(p_fmat, kBins);
-
-        HistogramCuts container;
-        SparseCuts indices(&container);
-        auto const& page = *(p_fmat->GetBatches<xgboost::CSCPage>().begin());
-        indices.SingleThreadBuild(page, p_fmat->Info(), kBins, false, 0, page.Size(), 0);
-
-        ASSERT_EQ(container.Ptrs().size(), threaded_container.Ptrs().size());
-        ASSERT_EQ(container.Values().size(), threaded_container.Values().size());
-
-        for (uint32_t i = 0; i < container.Ptrs().size(); ++i) {
-          ASSERT_EQ(container.Ptrs()[i], threaded_container.Ptrs()[i]);
-        }
-        for (uint32_t i = 0; i < container.Values().size(); ++i) {
-          ASSERT_EQ(container.Values()[i], threaded_container.Values()[i]);
-        }
-      };
-
-  {
-    auto p_fmat = RandomDataGenerator(kRows, kCols, 0).GenerateDMatrix();
-    Compare(p_fmat.get());
-  }
-
-  {
-    auto p_fmat = RandomDataGenerator(kRows, kCols, 0.0001).GenerateDMatrix();
-    Compare(p_fmat.get());
-  }
-
-  omp_set_num_threads(ori_nthreads);
+  CHECK_EQ(HostSketchContainer::SearchGroupIndFromRow(group_ptr, 1), 1);
 }
 
 TEST(HistUtil, DenseCutsCategorical) {
@@ -250,9 +184,7 @@ TEST(HistUtil, DenseCutsCategorical) {
        std::vector<float> x_sorted(x);
        std::sort(x_sorted.begin(), x_sorted.end());
        auto dmat = GetDMatrixFromData(x, n, 1);
-       HistogramCuts cuts;
-       DenseCuts dense(&cuts);
-       dense.Build(dmat.get(), num_bins);
+       HistogramCuts cuts = SketchOnDMatrix(dmat.get(), num_bins);
        auto cuts_from_sketch = cuts.Values();
        EXPECT_LT(cuts.MinValues()[0], x_sorted.front());
        EXPECT_GT(cuts_from_sketch.front(), x_sorted.front());
@@ -264,15 +196,14 @@ TEST(HistUtil, DenseCutsCategorical) {
 
 TEST(HistUtil, DenseCutsAccuracyTest) {
   int bin_sizes[] = {2, 16, 256, 512};
-  int sizes[] = {100, 1000, 1500};
+  int sizes[] = {100};
+  // omp_set_num_threads(1);
   int num_columns = 5;
   for (auto num_rows : sizes) {
     auto x = GenerateRandom(num_rows, num_columns);
     auto dmat = GetDMatrixFromData(x, num_rows, num_columns);
     for (auto num_bins : bin_sizes) {
-      HistogramCuts cuts;
-      DenseCuts dense(&cuts);
-      dense.Build(dmat.get(), num_bins);
+      HistogramCuts cuts = SketchOnDMatrix(dmat.get(), num_bins);
       ValidateCuts(cuts, dmat.get(), num_bins);
     }
   }
@@ -288,9 +219,7 @@ TEST(HistUtil, DenseCutsAccuracyTestWeights) {
     auto w = GenerateRandomWeights(num_rows);
     dmat->Info().weights_.HostVector() = w;
     for (auto num_bins : bin_sizes) {
-      HistogramCuts cuts;
-      DenseCuts dense(&cuts);
-      dense.Build(dmat.get(), num_bins);
+      HistogramCuts cuts = SketchOnDMatrix(dmat.get(), num_bins);
       ValidateCuts(cuts, dmat.get(), num_bins);
     }
   }
@@ -306,65 +235,7 @@ TEST(HistUtil, DenseCutsExternalMemory) {
     auto dmat =
         GetExternalMemoryDMatrixFromData(x, num_rows, num_columns, 50, tmpdir);
     for (auto num_bins : bin_sizes) {
-      HistogramCuts cuts;
-      DenseCuts dense(&cuts);
-      dense.Build(dmat.get(), num_bins);
-      ValidateCuts(cuts, dmat.get(), num_bins);
-    }
-  }
-}
-
-TEST(HistUtil, SparseCutsAccuracyTest) {
-  int bin_sizes[] = {2, 16, 256, 512};
-  int sizes[] = {100, 1000, 1500};
-  int num_columns = 5;
-  for (auto num_rows : sizes) {
-    auto x = GenerateRandom(num_rows, num_columns);
-    auto dmat = GetDMatrixFromData(x, num_rows, num_columns);
-    for (auto num_bins : bin_sizes) {
-      HistogramCuts cuts;
-      SparseCuts sparse(&cuts);
-      sparse.Build(dmat.get(), num_bins);
-      ValidateCuts(cuts, dmat.get(), num_bins);
-    }
-  }
-}
-
-TEST(HistUtil, SparseCutsCategorical) {
-  int categorical_sizes[] = {2, 6, 8, 12};
-  int num_bins = 256;
-  int sizes[] = {25, 100, 1000};
-  for (auto n : sizes) {
-    for (auto num_categories : categorical_sizes) {
-      auto x = GenerateRandomCategoricalSingleColumn(n, num_categories);
-      std::vector<float> x_sorted(x);
-      std::sort(x_sorted.begin(), x_sorted.end());
-      auto dmat = GetDMatrixFromData(x, n, 1);
-      HistogramCuts cuts;
-      SparseCuts sparse(&cuts);
-      sparse.Build(dmat.get(), num_bins);
-      auto cuts_from_sketch = cuts.Values();
-      EXPECT_LT(cuts.MinValues()[0], x_sorted.front());
-      EXPECT_GT(cuts_from_sketch.front(), x_sorted.front());
-      EXPECT_GE(cuts_from_sketch.back(), x_sorted.back());
-      EXPECT_EQ(cuts_from_sketch.size(), num_categories);
-    }
-  }
-}
-
-TEST(HistUtil, SparseCutsExternalMemory) {
-  int bin_sizes[] = {2, 16, 256, 512};
-  int sizes[] = {100, 1000, 1500};
-  int num_columns = 5;
-  for (auto num_rows : sizes) {
-    auto x = GenerateRandom(num_rows, num_columns);
-    dmlc::TemporaryDirectory tmpdir;
-    auto dmat =
-        GetExternalMemoryDMatrixFromData(x, num_rows, num_columns, 50, tmpdir);
-    for (auto num_bins : bin_sizes) {
-      HistogramCuts cuts;
-      SparseCuts dense(&cuts);
-      dense.Build(dmat.get(), num_bins);
+      HistogramCuts cuts = SketchOnDMatrix(dmat.get(), num_bins);
       ValidateCuts(cuts, dmat.get(), num_bins);
     }
   }
@@ -391,25 +262,6 @@ TEST(HistUtil, IndexBinBound) {
   }
 }
 
-TEST(HistUtil, SparseIndexBinBound) {
-  uint64_t bin_sizes[] = { static_cast<uint64_t>(std::numeric_limits<uint8_t>::max()) + 1,
-                           static_cast<uint64_t>(std::numeric_limits<uint16_t>::max()) + 1,
-                           static_cast<uint64_t>(std::numeric_limits<uint16_t>::max()) + 2 };
-  BinTypeSize expected_bin_type_sizes[] = { kUint32BinsTypeSize,
-                                            kUint32BinsTypeSize,
-                                            kUint32BinsTypeSize };
-  size_t constexpr kRows = 100;
-  size_t constexpr kCols = 10;
-
-  size_t bin_id = 0;
-  for (auto max_bin : bin_sizes) {
-    auto p_fmat = RandomDataGenerator(kRows, kCols, 0.2).GenerateDMatrix();
-    common::GHistIndexMatrix hmat;
-    hmat.Init(p_fmat.get(), max_bin);
-    EXPECT_EQ(expected_bin_type_sizes[bin_id++], hmat.index.GetBinTypeSize());
-  }
-}
-
 template <typename T>
 void CheckIndexData(T* data_ptr, uint32_t* offsets,
                     const common::GHistIndexMatrix& hmat, size_t n_cols) {
@@ -448,25 +300,61 @@ TEST(HistUtil, IndexBinData) {
   }
 }
 
-TEST(HistUtil, SparseIndexBinData) {
-  uint64_t bin_sizes[] = { static_cast<uint64_t>(std::numeric_limits<uint8_t>::max()) + 1,
-                           static_cast<uint64_t>(std::numeric_limits<uint16_t>::max()) + 1,
-                           static_cast<uint64_t>(std::numeric_limits<uint16_t>::max()) + 2 };
-  size_t constexpr kRows = 100;
-  size_t constexpr kCols = 10;
+void TestSketchFromWeights(bool with_group) {
+  size_t constexpr kRows = 300, kCols = 20, kBins = 256;
+  size_t constexpr kGroups = 10;
+  auto m =
+      RandomDataGenerator{kRows, kCols, 0}.Device(0).GenerateDMatrix();
+  common::HistogramCuts cuts = SketchOnDMatrix(m.get(), kBins);
+
+  MetaInfo info;
+  auto& h_weights = info.weights_.HostVector();
+  if (with_group) {
+    h_weights.resize(kGroups);
+  } else {
+    h_weights.resize(kRows);
+  }
+  std::fill(h_weights.begin(), h_weights.end(), 1.0f);
 
-  for (auto max_bin : bin_sizes) {
-    auto p_fmat = RandomDataGenerator(kRows, kCols, 0.2).GenerateDMatrix();
-    common::GHistIndexMatrix hmat;
-    hmat.Init(p_fmat.get(), max_bin);
-    EXPECT_EQ(hmat.index.Offset(), nullptr);
+  std::vector<bst_group_t> groups(kGroups);
+  if (with_group) {
+    for (size_t i = 0; i < kGroups; ++i) {
+      groups[i] = kRows / kGroups;
+    }
+    info.SetInfo("group", groups.data(), DataType::kUInt32, kGroups);
+  }
+
+  info.num_row_ = kRows;
+  info.num_col_ = kCols;
+
+  // Assign weights.
+  if (with_group) {
+    m->Info().SetInfo("group", groups.data(), DataType::kUInt32, kGroups);
+  }
+
+  m->Info().SetInfo("weight", h_weights.data(), DataType::kFloat32, h_weights.size());
+  m->Info().num_col_ = kCols;
+  m->Info().num_row_ = kRows;
+  ASSERT_EQ(cuts.Ptrs().size(), kCols + 1);
+  ValidateCuts(cuts, m.get(), kBins);
 
-    uint32_t* data_ptr = hmat.index.data<uint32_t>();
-    for (size_t i = 0; i < hmat.index.Size(); ++i) {
-      EXPECT_EQ(data_ptr[i], hmat.index[i]);
+  if (with_group) {
+    HistogramCuts non_weighted = SketchOnDMatrix(m.get(), kBins);
+    for (size_t i = 0; i < cuts.Values().size(); ++i) {
+      EXPECT_EQ(cuts.Values()[i], non_weighted.Values()[i]);
+    }
+    for (size_t i = 0; i < cuts.MinValues().size(); ++i) {
+      ASSERT_EQ(cuts.MinValues()[i], non_weighted.MinValues()[i]);
+    }
+    for (size_t i = 0; i < cuts.Ptrs().size(); ++i) {
+      ASSERT_EQ(cuts.Ptrs().at(i), non_weighted.Ptrs().at(i));
     }
   }
 }
 
+TEST(HistUtil, SketchFromWeights) {
+  TestSketchFromWeights(true);
+  TestSketchFromWeights(false);
+}
 }  // namespace common
 }  // namespace xgboost
diff --git a/tests/cpp/common/test_hist_util.cu b/tests/cpp/common/test_hist_util.cu
index 83e9595f75f1..b225acb2039d 100644
--- a/tests/cpp/common/test_hist_util.cu
+++ b/tests/cpp/common/test_hist_util.cu
@@ -24,10 +24,8 @@ namespace common {
 
 template <typename AdapterT>
 HistogramCuts GetHostCuts(AdapterT *adapter, int num_bins, float missing) {
-  HistogramCuts cuts;
-  DenseCuts builder(&cuts);
   data::SimpleDMatrix dmat(adapter, missing, 1);
-  builder.Build(&dmat, num_bins);
+  HistogramCuts cuts = SketchOnDMatrix(&dmat, num_bins);
   return cuts;
 }
 
@@ -39,9 +37,7 @@ TEST(HistUtil, DeviceSketch) {
   auto dmat = GetDMatrixFromData(x, num_rows, num_columns);
 
   auto device_cuts = DeviceSketch(0, dmat.get(), num_bins);
-  HistogramCuts host_cuts;
-  DenseCuts builder(&host_cuts);
-  builder.Build(dmat.get(), num_bins);
+  HistogramCuts host_cuts = SketchOnDMatrix(dmat.get(), num_bins);
 
   EXPECT_EQ(device_cuts.Values(), host_cuts.Values());
   EXPECT_EQ(device_cuts.Ptrs(), host_cuts.Ptrs());
@@ -460,7 +456,11 @@ void TestAdapterSketchFromWeights(bool with_group) {
           &storage);
   MetaInfo info;
   auto& h_weights = info.weights_.HostVector();
-  h_weights.resize(kRows);
+  if (with_group) {
+    h_weights.resize(kGroups);
+  } else {
+    h_weights.resize(kRows);
+  }
   std::fill(h_weights.begin(), h_weights.end(), 1.0f);
 
   std::vector<bst_group_t> groups(kGroups);
diff --git a/tests/cpp/common/test_quantile.cc b/tests/cpp/common/test_quantile.cc
new file mode 100644
index 000000000000..c273658e54cb
--- /dev/null
+++ b/tests/cpp/common/test_quantile.cc
@@ -0,0 +1,77 @@
+#include <gtest/gtest.h>
+#include "test_quantile.h"
+#include "../../../src/common/quantile.h"
+#include "../../../src/common/hist_util.h"
+
+namespace xgboost {
+namespace common {
+TEST(Quantile, SameOnAllWorkers) {
+  std::string msg{"Skipping Quantile AllreduceBasic test"};
+  size_t constexpr kWorkers = 4;
+  InitRabitContext(msg, kWorkers);
+  auto world = rabit::GetWorldSize();
+  if (world != 1) {
+    CHECK_EQ(world, kWorkers);
+  } else {
+    return;
+  }
+
+  constexpr size_t kRows = 1000, kCols = 100;
+  RunWithSeedsAndBins(
+      kRows, [=](int32_t seed, size_t n_bins, MetaInfo const &info) {
+        auto rank = rabit::GetRank();
+        HostDeviceVector<float> storage;
+        auto m = RandomDataGenerator{kRows, kCols, 0}
+                     .Device(0)
+                     .Seed(rank + seed)
+                     .GenerateDMatrix();
+        auto cuts = SketchOnDMatrix(m.get(), n_bins);
+        std::vector<float> cut_values(cuts.Values().size() * world, 0);
+        std::vector<
+            typename std::remove_reference_t<decltype(cuts.Ptrs())>::value_type>
+            cut_ptrs(cuts.Ptrs().size() * world, 0);
+        std::vector<float> cut_min_values(cuts.MinValues().size() * world, 0);
+
+        size_t value_size = cuts.Values().size();
+        rabit::Allreduce<rabit::op::Max>(&value_size, 1);
+        size_t ptr_size = cuts.Ptrs().size();
+        rabit::Allreduce<rabit::op::Max>(&ptr_size, 1);
+        CHECK_EQ(ptr_size, kCols + 1);
+        size_t min_value_size = cuts.MinValues().size();
+        rabit::Allreduce<rabit::op::Max>(&min_value_size, 1);
+        CHECK_EQ(min_value_size, kCols);
+
+        size_t value_offset = value_size * rank;
+        std::copy(cuts.Values().begin(), cuts.Values().end(),
+                  cut_values.begin() + value_offset);
+        size_t ptr_offset = ptr_size * rank;
+        std::copy(cuts.Ptrs().cbegin(), cuts.Ptrs().cend(),
+                  cut_ptrs.begin() + ptr_offset);
+        size_t min_values_offset = min_value_size * rank;
+        std::copy(cuts.MinValues().cbegin(), cuts.MinValues().cend(),
+                  cut_min_values.begin() + min_values_offset);
+
+        rabit::Allreduce<rabit::op::Sum>(cut_values.data(), cut_values.size());
+        rabit::Allreduce<rabit::op::Sum>(cut_ptrs.data(), cut_ptrs.size());
+        rabit::Allreduce<rabit::op::Sum>(cut_min_values.data(), cut_min_values.size());
+
+        for (int32_t i = 0; i < world; i++) {
+          for (size_t j = 0; j < value_size; ++j) {
+            size_t idx = i * value_size + j;
+            ASSERT_NEAR(cuts.Values().at(j), cut_values.at(idx), kRtEps);
+          }
+
+          for (size_t j = 0; j < ptr_size; ++j) {
+            size_t idx = i * ptr_size + j;
+            ASSERT_EQ(cuts.Ptrs().at(j), cut_ptrs.at(idx));
+          }
+
+          for (size_t j = 0; j < min_value_size; ++j) {
+            size_t idx = i * min_value_size + j;
+            ASSERT_EQ(cuts.MinValues().at(j), cut_min_values.at(idx));
+          }
+        }
+      });
+}
+}  // namespace common
+}  // namespace xgboost
diff --git a/tests/cpp/common/test_quantile.cu b/tests/cpp/common/test_quantile.cu
index e16edfef06b7..f7c7e22e3650 100644
--- a/tests/cpp/common/test_quantile.cu
+++ b/tests/cpp/common/test_quantile.cu
@@ -1,4 +1,5 @@
 #include <gtest/gtest.h>
+#include "test_quantile.h"
 #include "../helpers.h"
 #include "../../../src/common/hist_util.cuh"
 #include "../../../src/common/quantile.cuh"
@@ -16,32 +17,6 @@ TEST(GPUQuantile, Basic) {
   ASSERT_EQ(sketch.Data().size(), 0);
 }
 
-template <typename Fn> void RunWithSeedsAndBins(size_t rows, Fn fn) {
-  std::vector<int32_t> seeds(4);
-  SimpleLCG lcg;
-  SimpleRealUniformDistribution<float> dist(3, 1000);
-  std::generate(seeds.begin(), seeds.end(), [&](){ return dist(&lcg); });
-
-  std::vector<size_t> bins(8);
-  for (size_t i = 0; i < bins.size() - 1; ++i) {
-    bins[i] = i * 35 + 2;
-  }
-  bins.back() = rows + 80;  // provide a bin number greater than rows.
-
-  std::vector<MetaInfo> infos(2);
-  auto& h_weights = infos.front().weights_.HostVector();
-  h_weights.resize(rows);
-  std::generate(h_weights.begin(), h_weights.end(), [&]() { return dist(&lcg); });
-
-  for (auto seed : seeds) {
-    for (auto n_bin : bins) {
-      for (auto const& info : infos) {
-        fn(seed, n_bin, info);
-      }
-    }
-  }
-}
-
 void TestSketchUnique(float sparsity) {
   constexpr size_t kRows = 1000, kCols = 100;
   RunWithSeedsAndBins(kRows, [kRows, kCols, sparsity](int32_t seed, size_t n_bins, MetaInfo const& info) {
@@ -297,31 +272,12 @@ TEST(GPUQuantile, MergeDuplicated) {
   }
 }
 
-void InitRabitContext(std::string msg) {
-  auto n_gpus = AllVisibleGPUs();
-  auto port = std::getenv("DMLC_TRACKER_PORT");
-  std::string port_str;
-  if (port) {
-    port_str = port;
-  } else {
-    LOG(WARNING) << msg << " as `DMLC_TRACKER_PORT` is not set up.";
-    return;
-  }
-
-  std::vector<std::string> envs{
-      "DMLC_TRACKER_PORT=" + port_str,
-      "DMLC_TRACKER_URI=127.0.0.1",
-      "DMLC_NUM_WORKER=" + std::to_string(n_gpus)};
-  char* c_envs[] {&(envs[0][0]), &(envs[1][0]), &(envs[2][0])};
-  rabit::Init(3, c_envs);
-}
-
 TEST(GPUQuantile, AllReduceBasic) {
   // This test is supposed to run by a python test that setups the environment.
   std::string msg {"Skipping AllReduce test"};
 #if defined(__linux__) && defined(XGBOOST_USE_NCCL)
-  InitRabitContext(msg);
   auto n_gpus = AllVisibleGPUs();
+  InitRabitContext(msg, n_gpus);
   auto world = rabit::GetWorldSize();
   if (world != 1) {
     ASSERT_EQ(world, n_gpus);
@@ -407,9 +363,9 @@ TEST(GPUQuantile, AllReduceBasic) {
 TEST(GPUQuantile, SameOnAllWorkers) {
   std::string msg {"Skipping SameOnAllWorkers test"};
 #if defined(__linux__) && defined(XGBOOST_USE_NCCL)
-  InitRabitContext(msg);
-  auto world = rabit::GetWorldSize();
   auto n_gpus = AllVisibleGPUs();
+  InitRabitContext(msg, n_gpus);
+  auto world = rabit::GetWorldSize();
   if (world != 1) {
     ASSERT_EQ(world, n_gpus);
   } else {
diff --git a/tests/cpp/common/test_quantile.h b/tests/cpp/common/test_quantile.h
new file mode 100644
index 000000000000..7dea0b17deb3
--- /dev/null
+++ b/tests/cpp/common/test_quantile.h
@@ -0,0 +1,54 @@
+#include <rabit/rabit.h>
+#include <algorithm>
+#include <string>
+#include <vector>
+
+#include "../helpers.h"
+
+namespace xgboost {
+namespace common {
+inline void InitRabitContext(std::string msg, size_t n_workers) {
+  auto port = std::getenv("DMLC_TRACKER_PORT");
+  std::string port_str;
+  if (port) {
+    port_str = port;
+  } else {
+    LOG(WARNING) << msg << " as `DMLC_TRACKER_PORT` is not set up.";
+    return;
+  }
+
+  std::vector<std::string> envs{
+      "DMLC_TRACKER_PORT=" + port_str,
+      "DMLC_TRACKER_URI=127.0.0.1",
+      "DMLC_NUM_WORKER=" + std::to_string(n_workers)};
+  char* c_envs[] {&(envs[0][0]), &(envs[1][0]), &(envs[2][0])};
+  rabit::Init(3, c_envs);
+}
+
+template <typename Fn> void RunWithSeedsAndBins(size_t rows, Fn fn) {
+  std::vector<int32_t> seeds(4);
+  SimpleLCG lcg;
+  SimpleRealUniformDistribution<float> dist(3, 1000);
+  std::generate(seeds.begin(), seeds.end(), [&](){ return dist(&lcg); });
+
+  std::vector<size_t> bins(8);
+  for (size_t i = 0; i < bins.size() - 1; ++i) {
+    bins[i] = i * 35 + 2;
+  }
+  bins.back() = rows + 80;  // provide a bin number greater than rows.
+
+  std::vector<MetaInfo> infos(2);
+  auto& h_weights = infos.front().weights_.HostVector();
+  h_weights.resize(rows);
+  std::generate(h_weights.begin(), h_weights.end(), [&]() { return dist(&lcg); });
+
+  for (auto seed : seeds) {
+    for (auto n_bin : bins) {
+      for (auto const& info : infos) {
+        fn(seed, n_bin, info);
+      }
+    }
+  }
+}
+}  // namespace common
+}  // namespace xgboost
diff --git a/tests/python-gpu/test_gpu_with_dask.py b/tests/python-gpu/test_gpu_with_dask.py
index f118c7188528..e5c90181373f 100644
--- a/tests/python-gpu/test_gpu_with_dask.py
+++ b/tests/python-gpu/test_gpu_with_dask.py
@@ -233,12 +233,14 @@ def runit(worker_addr, rabit_args):
                     assert ret.returncode == 0, msg
 
     @pytest.mark.skipif(**tm.no_dask())
+    @pytest.mark.skipif(**tm.no_dask_cuda())
     @pytest.mark.mgpu
     @pytest.mark.gtest
     def test_quantile_basic(self):
         self.run_quantile('AllReduceBasic')
 
     @pytest.mark.skipif(**tm.no_dask())
+    @pytest.mark.skipif(**tm.no_dask_cuda())
     @pytest.mark.mgpu
     @pytest.mark.gtest
     def test_quantile_same_on_all_workers(self):
diff --git a/tests/python/test_with_dask.py b/tests/python/test_with_dask.py
index 66336c47ac3a..a92dc351e46f 100644
--- a/tests/python/test_with_dask.py
+++ b/tests/python/test_with_dask.py
@@ -1,11 +1,16 @@
 import testing as tm
 import pytest
+import unittest
 import xgboost as xgb
 import sys
 import numpy as np
 import json
 import asyncio
 from sklearn.datasets import make_classification
+import os
+import subprocess
+from hypothesis import given, strategies, settings, note
+from test_updaters import hist_parameter_strategy, exact_parameter_strategy
 
 if sys.platform.startswith("win"):
     pytest.skip("Skipping dask tests on Windows", allow_module_level=True)
@@ -14,12 +19,16 @@
 
 try:
     from distributed import LocalCluster, Client
+    from distributed.utils_test import client, loop, cluster_fixture
     import dask.dataframe as dd
     import dask.array as da
     from xgboost.dask import DaskDMatrix
 except ImportError:
     LocalCluster = None
     Client = None
+    client = None
+    loop = None
+    cluster_fixture = None
     dd = None
     da = None
     DaskDMatrix = None
@@ -445,3 +454,97 @@ def test_with_asyncio():
 
             asyncio.run(run_dask_regressor_asyncio(address))
             asyncio.run(run_dask_classifier_asyncio(address))
+
+
+class TestWithDask:
+    def run_updater_test(self, client, params, num_rounds, dataset,
+                         tree_method):
+        params['tree_method'] = tree_method
+        params = dataset.set_params(params)
+        # multi class doesn't handle empty dataset well (empty
+        # means at least 1 worker has data).
+        if params['objective'] == "multi:softmax":
+            return
+        # It doesn't make sense to distribute a completely
+        # empty dataset.
+        if dataset.X.shape[0] == 0:
+            return
+
+        chunk = 128
+        X = da.from_array(dataset.X,
+                          chunks=(chunk, dataset.X.shape[1]))
+        y = da.from_array(dataset.y, chunks=(chunk, ))
+        if dataset.w is not None:
+            w = da.from_array(dataset.w, chunks=(chunk, ))
+        else:
+            w = None
+
+        m = xgb.dask.DaskDMatrix(
+            client, data=X, label=y, weight=w)
+        history = xgb.dask.train(client, params=params, dtrain=m,
+                                 num_boost_round=num_rounds,
+                                 evals=[(m, 'train')])['history']
+        note(history)
+        assert tm.non_increasing(history['train'][dataset.metric])
+
+    @given(params=hist_parameter_strategy,
+           num_rounds=strategies.integers(10, 20),
+           dataset=tm.dataset_strategy)
+    @settings(deadline=None)
+    def test_hist(self, params, num_rounds, dataset, client):
+        self.run_updater_test(client, params, num_rounds, dataset, 'hist')
+
+    @given(params=exact_parameter_strategy,
+           num_rounds=strategies.integers(10, 20),
+           dataset=tm.dataset_strategy)
+    @settings(deadline=None)
+    def test_approx(self, client, params, num_rounds, dataset):
+        self.run_updater_test(client, params, num_rounds, dataset, 'approx')
+
+    def run_quantile(self, name):
+        if sys.platform.startswith("win"):
+            pytest.skip("Skipping dask tests on Windows")
+
+        exe = None
+        for possible_path in {'./testxgboost', './build/testxgboost',
+                              '../build/testxgboost',
+                              '../cpu-build/testxgboost',
+                              '../gpu-build/testxgboost'}:
+            if os.path.exists(possible_path):
+                exe = possible_path
+        if exe is None:
+            return
+
+        test = "--gtest_filter=Quantile." + name
+
+        def runit(worker_addr, rabit_args):
+            port = None
+            # setup environment for running the c++ part.
+            for arg in rabit_args:
+                if arg.decode('utf-8').startswith('DMLC_TRACKER_PORT'):
+                    port = arg.decode('utf-8')
+            port = port.split('=')
+            env = os.environ.copy()
+            env[port[0]] = port[1]
+            return subprocess.run([exe, test], env=env, stdout=subprocess.PIPE)
+
+        with LocalCluster(n_workers=4) as cluster:
+            with Client(cluster) as client:
+                workers = list(xgb.dask._get_client_workers(client).keys())
+                rabit_args = client.sync(
+                    xgb.dask._get_rabit_args, workers, client)
+                futures = client.map(runit,
+                                     workers,
+                                     pure=False,
+                                     workers=workers,
+                                     rabit_args=rabit_args)
+                results = client.gather(futures)
+                for ret in results:
+                    msg = ret.stdout.decode('utf-8')
+                    assert msg.find('1 test from Quantile') != -1, msg
+                    assert ret.returncode == 0, msg
+
+    @pytest.mark.skipif(**tm.no_dask())
+    @pytest.mark.gtest
+    def test_quantile_basic(self):
+        self.run_quantile('SameOnAllWorkers')