fused_csc_sampling_graph.cc

/**
 *  Copyright (c) 2023 by Contributors
 * @file fused_csc_sampling_graph.cc
 * @brief Source file of sampling graph.
 */

#include <graphbolt/fused_csc_sampling_graph.h>
#include <graphbolt/serialize.h>
#include <torch/torch.h>

#include <algorithm>
#include <array>
#include <cmath>
#include <limits>
#include <numeric>
#include <tuple>
#include <vector>

#include "./random.h"
#include "./shared_memory_helper.h"

namespace {
torch::optional<torch::Dict<std::string, torch::Tensor>> TensorizeDict(
    const torch::optional<torch::Dict<std::string, int64_t>>& dict) {
  if (!dict.has_value()) {
    return torch::nullopt;
  }
  torch::Dict<std::string, torch::Tensor> result;
  for (const auto& pair : dict.value()) {
    result.insert(pair.key(), torch::tensor(pair.value(), torch::kInt64));
  }
  return result;
}

torch::optional<torch::Dict<std::string, int64_t>> DetensorizeDict(
    const torch::optional<torch::Dict<std::string, torch::Tensor>>& dict) {
  if (!dict.has_value()) {
    return torch::nullopt;
  }
  torch::Dict<std::string, int64_t> result;
  for (const auto& pair : dict.value()) {
    result.insert(pair.key(), pair.value().item<int64_t>());
  }
  return result;
}
}  // namespace

namespace graphbolt {
namespace sampling {

static const int kPickleVersion = 6199;

FusedCSCSamplingGraph::FusedCSCSamplingGraph(
    const torch::Tensor& indptr, const torch::Tensor& indices,
    const torch::optional<torch::Tensor>& node_type_offset,
    const torch::optional<torch::Tensor>& type_per_edge,
    const torch::optional<NodeTypeToIDMap>& node_type_to_id,
    const torch::optional<EdgeTypeToIDMap>& edge_type_to_id,
    const torch::optional<EdgeAttrMap>& edge_attributes)
    : indptr_(indptr),
      indices_(indices),
      node_type_offset_(node_type_offset),
      type_per_edge_(type_per_edge),
      node_type_to_id_(node_type_to_id),
      edge_type_to_id_(edge_type_to_id),
      edge_attributes_(edge_attributes) {
  TORCH_CHECK(indptr.dim() == 1);
  TORCH_CHECK(indices.dim() == 1);
  TORCH_CHECK(indptr.device() == indices.device());
}

c10::intrusive_ptr<FusedCSCSamplingGraph> FusedCSCSamplingGraph::FromCSC(
    const torch::Tensor& indptr, const torch::Tensor& indices,
    const torch::optional<torch::Tensor>& node_type_offset,
    const torch::optional<torch::Tensor>& type_per_edge,
    const torch::optional<NodeTypeToIDMap>& node_type_to_id,
    const torch::optional<EdgeTypeToIDMap>& edge_type_to_id,
    const torch::optional<EdgeAttrMap>& edge_attributes) {
  if (node_type_offset.has_value()) {
    auto& offset = node_type_offset.value();
    TORCH_CHECK(offset.dim() == 1);
    TORCH_CHECK(node_type_to_id.has_value());
    TORCH_CHECK(
        offset.size(0) ==
        static_cast<int64_t>(node_type_to_id.value().size() + 1));
  }
  if (type_per_edge.has_value()) {
    TORCH_CHECK(type_per_edge.value().dim() == 1);
    TORCH_CHECK(type_per_edge.value().size(0) == indices.size(0));
    TORCH_CHECK(edge_type_to_id.has_value());
  }
  if (edge_attributes.has_value()) {
    for (const auto& pair : edge_attributes.value()) {
      TORCH_CHECK(pair.value().size(0) == indices.size(0));
    }
  }
  return c10::make_intrusive<FusedCSCSamplingGraph>(
      indptr, indices, node_type_offset, type_per_edge, node_type_to_id,
      edge_type_to_id, edge_attributes);
}

void FusedCSCSamplingGraph::Load(torch::serialize::InputArchive& archive) {
  const int64_t magic_num =
      read_from_archive(archive, "FusedCSCSamplingGraph/magic_num").toInt();
  TORCH_CHECK(
      magic_num == kCSCSamplingGraphSerializeMagic,
      "Magic numbers mismatch when loading FusedCSCSamplingGraph.");
  indptr_ =
      read_from_archive(archive, "FusedCSCSamplingGraph/indptr").toTensor();
  indices_ =
      read_from_archive(archive, "FusedCSCSamplingGraph/indices").toTensor();
  if (read_from_archive(archive, "FusedCSCSamplingGraph/has_node_type_offset")
          .toBool()) {
    node_type_offset_ =
        read_from_archive(archive, "FusedCSCSamplingGraph/node_type_offset")
            .toTensor();
  }
  if (read_from_archive(archive, "FusedCSCSamplingGraph/has_type_per_edge")
          .toBool()) {
    type_per_edge_ =
        read_from_archive(archive, "FusedCSCSamplingGraph/type_per_edge")
            .toTensor();
  }

  if (read_from_archive(archive, "FusedCSCSamplingGraph/has_node_type_to_id")
          .toBool()) {
    torch::Dict<torch::IValue, torch::IValue> generic_dict =
        read_from_archive(archive, "FusedCSCSamplingGraph/node_type_to_id")
            .toGenericDict();
    NodeTypeToIDMap node_type_to_id;
    for (const auto& pair : generic_dict) {
      std::string key = pair.key().toStringRef();
      int64_t value = pair.value().toInt();
      node_type_to_id.insert(std::move(key), value);
    }
    node_type_to_id_ = std::move(node_type_to_id);
  }

  if (read_from_archive(archive, "FusedCSCSamplingGraph/has_edge_type_to_id")
          .toBool()) {
    torch::Dict<torch::IValue, torch::IValue> generic_dict =
        read_from_archive(archive, "FusedCSCSamplingGraph/edge_type_to_id")
            .toGenericDict();
    EdgeTypeToIDMap edge_type_to_id;
    for (const auto& pair : generic_dict) {
      std::string key = pair.key().toStringRef();
      int64_t value = pair.value().toInt();
      edge_type_to_id.insert(std::move(key), value);
    }
    edge_type_to_id_ = std::move(edge_type_to_id);
  }

  // Optional edge attributes.
  torch::IValue has_edge_attributes;
  if (archive.try_read(
          "FusedCSCSamplingGraph/has_edge_attributes", has_edge_attributes) &&
      has_edge_attributes.toBool()) {
    torch::Dict<torch::IValue, torch::IValue> generic_dict =
        read_from_archive(archive, "FusedCSCSamplingGraph/edge_attributes")
            .toGenericDict();
    EdgeAttrMap target_dict;
    for (const auto& pair : generic_dict) {
      std::string key = pair.key().toStringRef();
      torch::Tensor value = pair.value().toTensor();
      // Use move to avoid copy.
      target_dict.insert(std::move(key), std::move(value));
    }
    // Same as above.
    edge_attributes_ = std::move(target_dict);
  }
}

void FusedCSCSamplingGraph::Save(
    torch::serialize::OutputArchive& archive) const {
  archive.write(
      "FusedCSCSamplingGraph/magic_num", kCSCSamplingGraphSerializeMagic);
  archive.write("FusedCSCSamplingGraph/indptr", indptr_);
  archive.write("FusedCSCSamplingGraph/indices", indices_);
  archive.write(
      "FusedCSCSamplingGraph/has_node_type_offset",
      node_type_offset_.has_value());
  if (node_type_offset_) {
    archive.write(
        "FusedCSCSamplingGraph/node_type_offset", node_type_offset_.value());
  }
  archive.write(
      "FusedCSCSamplingGraph/has_type_per_edge", type_per_edge_.has_value());
  if (type_per_edge_) {
    archive.write(
        "FusedCSCSamplingGraph/type_per_edge", type_per_edge_.value());
  }
  archive.write(
      "FusedCSCSamplingGraph/has_node_type_to_id",
      node_type_to_id_.has_value());
  if (node_type_to_id_) {
    archive.write(
        "FusedCSCSamplingGraph/node_type_to_id", node_type_to_id_.value());
  }
  archive.write(
      "FusedCSCSamplingGraph/has_edge_type_to_id",
      edge_type_to_id_.has_value());
  if (edge_type_to_id_) {
    archive.write(
        "FusedCSCSamplingGraph/edge_type_to_id", edge_type_to_id_.value());
  }
  archive.write(
      "FusedCSCSamplingGraph/has_edge_attributes",
      edge_attributes_.has_value());
  if (edge_attributes_) {
    archive.write(
        "FusedCSCSamplingGraph/edge_attributes", edge_attributes_.value());
  }
}

void FusedCSCSamplingGraph::SetState(
    const torch::Dict<std::string, torch::Dict<std::string, torch::Tensor>>&
        state) {
  // State is a dict of dicts. The tensor-type attributes are stored in the dict
  // with key "independent_tensors". The dict-type attributes (edge_attributes)
  // are stored directly with the their name as the key.
  const auto& independent_tensors = state.at("independent_tensors");
  TORCH_CHECK(
      independent_tensors.at("version_number")
          .equal(torch::tensor({kPickleVersion})),
      "Version number mismatches when loading pickled FusedCSCSamplingGraph.")
  indptr_ = independent_tensors.at("indptr");
  indices_ = independent_tensors.at("indices");
  if (independent_tensors.find("node_type_offset") !=
      independent_tensors.end()) {
    node_type_offset_ = independent_tensors.at("node_type_offset");
  }
  if (independent_tensors.find("type_per_edge") != independent_tensors.end()) {
    type_per_edge_ = independent_tensors.at("type_per_edge");
  }
  if (state.find("node_type_to_id") != state.end()) {
    node_type_to_id_ = DetensorizeDict(state.at("node_type_to_id"));
  }
  if (state.find("edge_type_to_id") != state.end()) {
    edge_type_to_id_ = DetensorizeDict(state.at("edge_type_to_id"));
  }
  if (state.find("edge_attributes") != state.end()) {
    edge_attributes_ = state.at("edge_attributes");
  }
}

torch::Dict<std::string, torch::Dict<std::string, torch::Tensor>>
FusedCSCSamplingGraph::GetState() const {
  // State is a dict of dicts. The tensor-type attributes are stored in the dict
  // with key "independent_tensors". The dict-type attributes (edge_attributes)
  // are stored directly with the their name as the key.
  torch::Dict<std::string, torch::Dict<std::string, torch::Tensor>> state;
  torch::Dict<std::string, torch::Tensor> independent_tensors;
  // Serialization version number. It indicates the serialization method of the
  // whole state.
  independent_tensors.insert("version_number", torch::tensor({kPickleVersion}));
  independent_tensors.insert("indptr", indptr_);
  independent_tensors.insert("indices", indices_);
  if (node_type_offset_.has_value()) {
    independent_tensors.insert("node_type_offset", node_type_offset_.value());
  }
  if (type_per_edge_.has_value()) {
    independent_tensors.insert("type_per_edge", type_per_edge_.value());
  }
  state.insert("independent_tensors", independent_tensors);
  if (node_type_to_id_.has_value()) {
    state.insert("node_type_to_id", TensorizeDict(node_type_to_id_).value());
  }
  if (edge_type_to_id_.has_value()) {
    state.insert("edge_type_to_id", TensorizeDict(edge_type_to_id_).value());
  }
  if (edge_attributes_.has_value()) {
    state.insert("edge_attributes", edge_attributes_.value());
  }
  return state;
}

c10::intrusive_ptr<FusedSampledSubgraph> FusedCSCSamplingGraph::InSubgraph(
    const torch::Tensor& nodes) const {
  using namespace torch::indexing;
  const int32_t kDefaultGrainSize = 100;
  const auto num_seeds = nodes.size(0);
  torch::Tensor indptr = torch::zeros({num_seeds + 1}, indptr_.dtype());
  std::vector<torch::Tensor> indices_arr(num_seeds);
  torch::Tensor original_column_node_ids =
      torch::zeros({num_seeds}, indptr_.dtype());
  std::vector<torch::Tensor> edge_ids_arr(num_seeds);
  std::vector<torch::Tensor> type_per_edge_arr(num_seeds);

  AT_DISPATCH_INTEGRAL_TYPES(
      indptr_.scalar_type(), "InSubgraph", ([&] {
        torch::parallel_for(
            0, num_seeds, kDefaultGrainSize, [&](size_t start, size_t end) {
              for (size_t i = start; i < end; ++i) {
                const auto node_id = nodes[i].item<scalar_t>();
                const auto start_idx = indptr_[node_id].item<scalar_t>();
                const auto end_idx = indptr_[node_id + 1].item<scalar_t>();
                indptr[i + 1] = end_idx - start_idx;
                original_column_node_ids[i] = node_id;
                indices_arr[i] = indices_.slice(0, start_idx, end_idx);
                edge_ids_arr[i] = torch::arange(start_idx, end_idx);
                if (type_per_edge_) {
                  type_per_edge_arr[i] =
                      type_per_edge_.value().slice(0, start_idx, end_idx);
                }
              }
            });
      }));

  return c10::make_intrusive<FusedSampledSubgraph>(
      indptr.cumsum(0), torch::cat(indices_arr), original_column_node_ids,
      torch::arange(0, NumNodes()), torch::cat(edge_ids_arr),
      type_per_edge_
          ? torch::optional<torch::Tensor>{torch::cat(type_per_edge_arr)}
          : torch::nullopt);
}

/**
 * @brief Get a lambda function which counts the number of the neighbors to be
 * sampled.
 *
 * @param fanouts The number of edges to be sampled for each node with or
 * without considering edge types.
 * @param replace Boolean indicating whether the sample is performed with or
 * without replacement. If True, a value can be selected multiple times.
 * Otherwise, each value can be selected only once.
 * @param type_per_edge A tensor representing the type of each edge, if
 * present.
 * @param probs_or_mask Optional tensor containing the (unnormalized)
 * probabilities associated with each neighboring edge of a node in the original
 * graph. It must be a 1D floating-point tensor with the number of elements
 * equal to the number of edges in the graph.
 *
 * @return A lambda function (int64_t offset, int64_t num_neighbors) ->
 * torch::Tensor, which takes offset (the starting edge ID of the given node)
 * and num_neighbors (number of neighbors) as params and returns the pick number
 * of the given node.
 */
auto GetNumPickFn(
    const std::vector<int64_t>& fanouts, bool replace,
    const torch::optional<torch::Tensor>& type_per_edge,
    const torch::optional<torch::Tensor>& probs_or_mask) {
  // If fanouts.size() > 1, returns the total number of all edge types of the
  // given node.
  return [&fanouts, replace, &probs_or_mask, &type_per_edge](
             int64_t offset, int64_t num_neighbors) {
    if (fanouts.size() > 1) {
      return NumPickByEtype(
          fanouts, replace, type_per_edge.value(), probs_or_mask, offset,
          num_neighbors);
    } else {
      return NumPick(fanouts[0], replace, probs_or_mask, offset, num_neighbors);
    }
  };
}

/**
 * @brief Get a lambda function which contains the sampling process.
 *
 * @param fanouts The number of edges to be sampled for each node with or
 * without considering edge types.
 * @param replace Boolean indicating whether the sample is performed with or
 * without replacement. If True, a value can be selected multiple times.
 * Otherwise, each value can be selected only once.
 * @param options Tensor options specifying the desired data type of the result.
 * @param type_per_edge A tensor representing the type of each edge, if
 * present.
 * @param probs_or_mask Optional tensor containing the (unnormalized)
 * probabilities associated with each neighboring edge of a node in the original
 * graph. It must be a 1D floating-point tensor with the number of elements
 * equal to the number of edges in the graph.
 * @param args Contains sampling algorithm specific arguments.
 *
 * @return A lambda function: (int64_t offset, int64_t num_neighbors,
 * PickedType* picked_data_ptr) -> torch::Tensor, which takes offset (the
 * starting edge ID of the given node) and num_neighbors (number of neighbors)
 * as params and puts the picked neighbors at the address specified by
 * picked_data_ptr.
 */
template <SamplerType S>
auto GetPickFn(
    const std::vector<int64_t>& fanouts, bool replace,
    const torch::TensorOptions& options,
    const torch::optional<torch::Tensor>& type_per_edge,
    const torch::optional<torch::Tensor>& probs_or_mask, SamplerArgs<S> args) {
  return [&fanouts, replace, &options, &type_per_edge, &probs_or_mask, args](
             int64_t offset, int64_t num_neighbors, auto picked_data_ptr) {
    // If fanouts.size() > 1, perform sampling for each edge type of each
    // node; otherwise just sample once for each node with no regard of edge
    // types.
    if (fanouts.size() > 1) {
      return PickByEtype(
          offset, num_neighbors, fanouts, replace, options,
          type_per_edge.value(), probs_or_mask, args, picked_data_ptr);
    } else {
      int64_t num_sampled = Pick(
          offset, num_neighbors, fanouts[0], replace, options, probs_or_mask,
          args, picked_data_ptr);
      if (type_per_edge) {
        std::sort(picked_data_ptr, picked_data_ptr + num_sampled);
      }
      return num_sampled;
    }
  };
}

template <typename NumPickFn, typename PickFn>
c10::intrusive_ptr<FusedSampledSubgraph>
FusedCSCSamplingGraph::SampleNeighborsImpl(
    const torch::Tensor& nodes, bool return_eids, NumPickFn num_pick_fn,
    PickFn pick_fn) const {
  const int64_t num_nodes = nodes.size(0);
  const auto indptr_options = indptr_.options();
  torch::Tensor num_picked_neighbors_per_node =
      torch::empty({num_nodes + 1}, indptr_options);

  // Calculate GrainSize for parallel_for.
  // Set the default grain size to 64.
  const int64_t grain_size = 64;
  torch::Tensor picked_eids;
  torch::Tensor subgraph_indptr;
  torch::Tensor subgraph_indices;
  torch::optional<torch::Tensor> subgraph_type_per_edge = torch::nullopt;

  AT_DISPATCH_INTEGRAL_TYPES(
      indptr_.scalar_type(), "SampleNeighborsImplWrappedWithIndptr", ([&] {
        using indptr_t = scalar_t;
        AT_DISPATCH_INTEGRAL_TYPES(
            nodes.scalar_type(), "SampleNeighborsImplWrappedWithNodes", ([&] {
              using nodes_t = scalar_t;
              const auto indptr_data = indptr_.data_ptr<indptr_t>();
              auto num_picked_neighbors_data_ptr =
                  num_picked_neighbors_per_node.data_ptr<indptr_t>();
              num_picked_neighbors_data_ptr[0] = 0;
              const auto nodes_data_ptr = nodes.data_ptr<nodes_t>();

              // Step 1. Calculate pick number of each node.
              torch::parallel_for(
                  0, num_nodes, grain_size, [&](int64_t begin, int64_t end) {
                    for (int64_t i = begin; i < end; ++i) {
                      const auto nid = nodes_data_ptr[i];
                      TORCH_CHECK(
                          nid >= 0 && nid < NumNodes(),
                          "The seed nodes' IDs should fall within the range of "
                          "the "
                          "graph's node IDs.");
                      const auto offset = indptr_data[nid];
                      const auto num_neighbors = indptr_data[nid + 1] - offset;

                      num_picked_neighbors_data_ptr[i + 1] =
                          num_neighbors == 0
                              ? 0
                              : num_pick_fn(offset, num_neighbors);
                    }
                  });

              // Step 2. Calculate prefix sum to get total length and offsets of
              // each node. It's also the indptr of the generated subgraph.
              subgraph_indptr = num_picked_neighbors_per_node.cumsum(
                  0, indptr_.scalar_type());

              // Step 3. Allocate the tensor for picked neighbors.
              const auto total_length =
                  subgraph_indptr.data_ptr<indptr_t>()[num_nodes];
              picked_eids = torch::empty({total_length}, indptr_options);
              subgraph_indices =
                  torch::empty({total_length}, indices_.options());
              if (type_per_edge_.has_value()) {
                subgraph_type_per_edge = torch::empty(
                    {total_length}, type_per_edge_.value().options());
              }

              // Step 4. Pick neighbors for each node.
              auto picked_eids_data_ptr = picked_eids.data_ptr<indptr_t>();
              auto subgraph_indptr_data_ptr =
                  subgraph_indptr.data_ptr<indptr_t>();
              torch::parallel_for(
                  0, num_nodes, grain_size, [&](int64_t begin, int64_t end) {
                    for (int64_t i = begin; i < end; ++i) {
                      const auto nid = nodes_data_ptr[i];
                      const auto offset = indptr_data[nid];
                      const auto num_neighbors = indptr_data[nid + 1] - offset;
                      const auto picked_number =
                          num_picked_neighbors_data_ptr[i + 1];
                      const auto picked_offset = subgraph_indptr_data_ptr[i];
                      if (picked_number > 0) {
                        auto actual_picked_count = pick_fn(
                            offset, num_neighbors,
                            picked_eids_data_ptr + picked_offset);
                        TORCH_CHECK(
                            actual_picked_count == picked_number,
                            "Actual picked count doesn't match the calculated "
                            "pick "
                            "number.");

                        // Step 5. Calculate other attributes and return the
                        // subgraph.
                        AT_DISPATCH_INTEGRAL_TYPES(
                            subgraph_indices.scalar_type(),
                            "IndexSelectSubgraphIndices", ([&] {
                              auto subgraph_indices_data_ptr =
                                  subgraph_indices.data_ptr<scalar_t>();
                              auto indices_data_ptr =
                                  indices_.data_ptr<scalar_t>();
                              for (auto i = picked_offset;
                                   i < picked_offset + picked_number; ++i) {
                                subgraph_indices_data_ptr[i] =
                                    indices_data_ptr[picked_eids_data_ptr[i]];
                              }
                            }));
                        if (type_per_edge_.has_value()) {
                          AT_DISPATCH_INTEGRAL_TYPES(
                              subgraph_type_per_edge.value().scalar_type(),
                              "IndexSelectTypePerEdge", ([&] {
                                auto subgraph_type_per_edge_data_ptr =
                                    subgraph_type_per_edge.value()
                                        .data_ptr<scalar_t>();
                                auto type_per_edge_data_ptr =
                                    type_per_edge_.value().data_ptr<scalar_t>();
                                for (auto i = picked_offset;
                                     i < picked_offset + picked_number; ++i) {
                                  subgraph_type_per_edge_data_ptr[i] =
                                      type_per_edge_data_ptr
                                          [picked_eids_data_ptr[i]];
                                }
                              }));
                        }
                      }
                    }
                  });
            }));
      }));

  torch::optional<torch::Tensor> subgraph_reverse_edge_ids = torch::nullopt;
  if (return_eids) subgraph_reverse_edge_ids = std::move(picked_eids);

  return c10::make_intrusive<FusedSampledSubgraph>(
      subgraph_indptr, subgraph_indices, nodes, torch::nullopt,
      subgraph_reverse_edge_ids, subgraph_type_per_edge);
}

c10::intrusive_ptr<FusedSampledSubgraph> FusedCSCSamplingGraph::SampleNeighbors(
    const torch::Tensor& nodes, const std::vector<int64_t>& fanouts,
    bool replace, bool layer, bool return_eids,
    torch::optional<std::string> probs_name) const {
  torch::optional<torch::Tensor> probs_or_mask = torch::nullopt;
  if (probs_name.has_value() && !probs_name.value().empty()) {
    probs_or_mask = edge_attributes_.value().at(probs_name.value());
    // Note probs will be passed as input for 'torch.multinomial' in deeper
    // stack, which doesn't support 'torch.half' and 'torch.bool' data types. To
    // avoid crashes, convert 'probs_or_mask' to 'float32' data type.
    if (probs_or_mask.value().dtype() == torch::kBool ||
        probs_or_mask.value().dtype() == torch::kFloat16) {
      probs_or_mask = probs_or_mask.value().to(torch::kFloat32);
    }
  }

  if (layer) {
    const int64_t random_seed = RandomEngine::ThreadLocal()->RandInt(
        static_cast<int64_t>(0), std::numeric_limits<int64_t>::max());
    SamplerArgs<SamplerType::LABOR> args{indices_, random_seed, NumNodes()};
    return SampleNeighborsImpl(
        nodes, return_eids,
        GetNumPickFn(fanouts, replace, type_per_edge_, probs_or_mask),
        GetPickFn(
            fanouts, replace, indptr_.options(), type_per_edge_, probs_or_mask,
            args));
  } else {
    SamplerArgs<SamplerType::NEIGHBOR> args;
    return SampleNeighborsImpl(
        nodes, return_eids,
        GetNumPickFn(fanouts, replace, type_per_edge_, probs_or_mask),
        GetPickFn(
            fanouts, replace, indptr_.options(), type_per_edge_, probs_or_mask,
            args));
  }
}

std::tuple<torch::Tensor, torch::Tensor>
FusedCSCSamplingGraph::SampleNegativeEdgesUniform(
    const std::tuple<torch::Tensor, torch::Tensor>& node_pairs,
    int64_t negative_ratio, int64_t max_node_id) const {
  torch::Tensor pos_src;
  std::tie(pos_src, std::ignore) = node_pairs;
  auto neg_len = pos_src.size(0) * negative_ratio;
  auto neg_src = pos_src.repeat(negative_ratio);
  auto neg_dst = torch::randint(0, max_node_id, {neg_len}, pos_src.options());
  return std::make_tuple(neg_src, neg_dst);
}

static c10::intrusive_ptr<FusedCSCSamplingGraph>
BuildGraphFromSharedMemoryHelper(SharedMemoryHelper&& helper) {
  helper.InitializeRead();
  auto indptr = helper.ReadTorchTensor();
  auto indices = helper.ReadTorchTensor();
  auto node_type_offset = helper.ReadTorchTensor();
  auto type_per_edge = helper.ReadTorchTensor();
  auto node_type_to_id = DetensorizeDict(helper.ReadTorchTensorDict());
  auto edge_type_to_id = DetensorizeDict(helper.ReadTorchTensorDict());
  auto edge_attributes = helper.ReadTorchTensorDict();
  auto graph = c10::make_intrusive<FusedCSCSamplingGraph>(
      indptr.value(), indices.value(), node_type_offset, type_per_edge,
      node_type_to_id, edge_type_to_id, edge_attributes);
  auto shared_memory = helper.ReleaseSharedMemory();
  graph->HoldSharedMemoryObject(
      std::move(shared_memory.first), std::move(shared_memory.second));
  return graph;
}

c10::intrusive_ptr<FusedCSCSamplingGraph>
FusedCSCSamplingGraph::CopyToSharedMemory(
    const std::string& shared_memory_name) {
  SharedMemoryHelper helper(shared_memory_name, SERIALIZED_METAINFO_SIZE_MAX);
  helper.WriteTorchTensor(indptr_);
  helper.WriteTorchTensor(indices_);
  helper.WriteTorchTensor(node_type_offset_);
  helper.WriteTorchTensor(type_per_edge_);
  helper.WriteTorchTensorDict(TensorizeDict(node_type_to_id_));
  helper.WriteTorchTensorDict(TensorizeDict(edge_type_to_id_));
  helper.WriteTorchTensorDict(edge_attributes_);
  helper.Flush();
  return BuildGraphFromSharedMemoryHelper(std::move(helper));
}

c10::intrusive_ptr<FusedCSCSamplingGraph>
FusedCSCSamplingGraph::LoadFromSharedMemory(
    const std::string& shared_memory_name) {
  SharedMemoryHelper helper(shared_memory_name, SERIALIZED_METAINFO_SIZE_MAX);
  return BuildGraphFromSharedMemoryHelper(std::move(helper));
}

void FusedCSCSamplingGraph::HoldSharedMemoryObject(
    SharedMemoryPtr tensor_metadata_shm, SharedMemoryPtr tensor_data_shm) {
  tensor_metadata_shm_ = std::move(tensor_metadata_shm);
  tensor_data_shm_ = std::move(tensor_data_shm);
}

int64_t NumPick(
    int64_t fanout, bool replace,
    const torch::optional<torch::Tensor>& probs_or_mask, int64_t offset,
    int64_t num_neighbors) {
  int64_t num_valid_neighbors = num_neighbors;
  if (probs_or_mask.has_value()) {
    // Subtract the count of zeros in probs_or_mask.
    AT_DISPATCH_ALL_TYPES(
        probs_or_mask.value().scalar_type(), "CountZero", ([&] {
          scalar_t* probs_data_ptr = probs_or_mask.value().data_ptr<scalar_t>();
          num_valid_neighbors -= std::count(
              probs_data_ptr + offset, probs_data_ptr + offset + num_neighbors,
              0);
        }));
  }
  if (num_valid_neighbors == 0 || fanout == -1) return num_valid_neighbors;
  return replace ? fanout : std::min(fanout, num_valid_neighbors);
}

int64_t NumPickByEtype(
    const std::vector<int64_t>& fanouts, bool replace,
    const torch::Tensor& type_per_edge,
    const torch::optional<torch::Tensor>& probs_or_mask, int64_t offset,
    int64_t num_neighbors) {
  int64_t etype_begin = offset;
  const int64_t end = offset + num_neighbors;
  int64_t total_count = 0;
  AT_DISPATCH_INTEGRAL_TYPES(
      type_per_edge.scalar_type(), "NumPickFnByEtype", ([&] {
        const scalar_t* type_per_edge_data = type_per_edge.data_ptr<scalar_t>();
        while (etype_begin < end) {
          scalar_t etype = type_per_edge_data[etype_begin];
          TORCH_CHECK(
              etype >= 0 && etype < (int64_t)fanouts.size(),
              "Etype values exceed the number of fanouts.");
          auto etype_end_it = std::upper_bound(
              type_per_edge_data + etype_begin, type_per_edge_data + end,
              etype);
          int64_t etype_end = etype_end_it - type_per_edge_data;
          // Do sampling for one etype.
          total_count += NumPick(
              fanouts[etype], replace, probs_or_mask, etype_begin,
              etype_end - etype_begin);
          etype_begin = etype_end;
        }
      }));
  return total_count;
}

/**
 * @brief Perform uniform sampling of elements and return the sampled indices.
 *
 * @param offset The starting edge ID for the connected neighbors of the sampled
 * node.
 * @param num_neighbors The number of neighbors to pick.
 * @param fanout The number of edges to be sampled for each node. It should be
 * >= 0 or -1.
 *  - When the value is -1, all neighbors will be sampled once regardless of
 * replacement. It is equivalent to selecting all neighbors when the fanout is
 * >= the number of neighbors (and replacement is set to false).
 *  - When the value is a non-negative integer, it serves as a minimum
 * threshold for selecting neighbors.
 * @param replace Boolean indicating whether the sample is performed with or
 * without replacement. If True, a value can be selected multiple times.
 * Otherwise, each value can be selected only once.
 * @param options Tensor options specifying the desired data type of the result.
 * @param picked_data_ptr The destination address where the picked neighbors
 * should be put. Enough memory space should be allocated in advance.
 */
template <typename PickedType>
inline int64_t UniformPick(
    int64_t offset, int64_t num_neighbors, int64_t fanout, bool replace,
    const torch::TensorOptions& options, PickedType* picked_data_ptr) {
  if ((fanout == -1) || (num_neighbors <= fanout && !replace)) {
    std::iota(picked_data_ptr, picked_data_ptr + num_neighbors, offset);
    return num_neighbors;
  } else if (replace) {
    std::memcpy(
        picked_data_ptr,
        torch::randint(offset, offset + num_neighbors, {fanout}, options)
            .data_ptr<PickedType>(),
        fanout * sizeof(PickedType));
    return fanout;
  } else {
    // We use different sampling strategies for different sampling case.
    if (fanout >= num_neighbors / 10) {
      // [Algorithm]
      // This algorithm is conceptually related to the Fisher-Yates
      // shuffle.
      //
      // [Complexity Analysis]
      // This algorithm's memory complexity is O(num_neighbors), but
      // it generates fewer random numbers (O(fanout)).
      //
      // (Compare) Reservoir algorithm is one of the most classical
      // sampling algorithms. Both the reservoir algorithm and our
      // algorithm offer distinct advantages, we need to compare to
      // illustrate our trade-offs.
      // The reservoir algorithm is memory-efficient (O(fanout)) but
      // creates many random numbers (O(num_neighbors)), which is
      // costly.
      //
      // [Practical Consideration]
      // Use this algorithm when `fanout >= num_neighbors / 10` to
      // reduce computation.
      // In this scenarios above, memory complexity is not a concern due
      // to the small size of both `fanout` and `num_neighbors`. And it
      // is efficient to allocate a small amount of memory. So the
      // algorithm performence is great in this case.
      std::vector<PickedType> seq(num_neighbors);
      // Assign the seq with [offset, offset + num_neighbors].
      std::iota(seq.begin(), seq.end(), offset);
      for (int64_t i = 0; i < fanout; ++i) {
        auto j = RandomEngine::ThreadLocal()->RandInt(i, num_neighbors);
        std::swap(seq[i], seq[j]);
      }
      // Save the randomly sampled fanout elements to the output tensor.
      std::copy(seq.begin(), seq.begin() + fanout, picked_data_ptr);
      return fanout;
    } else if (fanout < 64) {
      // [Algorithm]
      // Use linear search to verify uniqueness.
      //
      // [Complexity Analysis]
      // Since the set of numbers is small (up to 64), so it is more
      // cost-effective for the CPU to use this algorithm.
      auto begin = picked_data_ptr;
      auto end = picked_data_ptr + fanout;

      while (begin != end) {
        // Put the new random number in the last position.
        *begin = RandomEngine::ThreadLocal()->RandInt(
            offset, offset + num_neighbors);
        // Check if a new value doesn't exist in current
        // range(picked_data_ptr, begin). Otherwise get a new
        // value until we haven't unique range of elements.
        auto it = std::find(picked_data_ptr, begin, *begin);
        if (it == begin) ++begin;
      }
      return fanout;
    } else {
      // [Algorithm]
      // Use hash-set to verify uniqueness. In the best scenario, the
      // time complexity is O(fanout), assuming no conflicts occur.
      //
      // [Complexity Analysis]
      // Let K = (fanout / num_neighbors), the expected number of extra
      // sampling steps is roughly K^2 / (1-K) * num_neighbors, which
      // means in the worst case scenario, the time complexity is
      // O(num_neighbors^2).
      //
      // [Practical Consideration]
      // In practice, we set the threshold K to 1/10. This trade-off is
      // due to the slower performance of std::unordered_set, which
      // would otherwise increase the sampling cost. By doing so, we
      // achieve a balance between theoretical efficiency and practical
      // performance.
      std::unordered_set<PickedType> picked_set;
      while (static_cast<int64_t>(picked_set.size()) < fanout) {
        picked_set.insert(RandomEngine::ThreadLocal()->RandInt(
            offset, offset + num_neighbors));
      }
      std::copy(picked_set.begin(), picked_set.end(), picked_data_ptr);
      return picked_set.size();
    }
  }
}

/**
 * @brief Perform non-uniform sampling of elements based on probabilities and
 * return the sampled indices.
 *
 * If 'probs_or_mask' is provided, it indicates that the sampling is
 * non-uniform. In such cases:
 * - When the number of neighbors with non-zero probability is less than or
 * equal to fanout, all neighbors with non-zero probability will be selected.
 * - When the number of neighbors with non-zero probability exceeds fanout, the
 * sampling process will select 'fanout' elements based on their respective
 * probabilities. Higher probabilities will increase the chances of being chosen
 * during the sampling process.
 *
 * @param offset The starting edge ID for the connected neighbors of the sampled
 * node.
 * @param num_neighbors The number of neighbors to pick.
 * @param fanout The number of edges to be sampled for each node. It should be
 * >= 0 or -1.
 *  - When the value is -1, all neighbors with non-zero probability will be
 * sampled once regardless of replacement. It is equivalent to selecting all
 * neighbors with non-zero probability when the fanout is >= the number of
 * neighbors (and replacement is set to false).
 *  - When the value is a non-negative integer, it serves as a minimum
 * threshold for selecting neighbors.
 * @param replace Boolean indicating whether the sample is performed with or
 * without replacement. If True, a value can be selected multiple times.
 * Otherwise, each value can be selected only once.
 * @param options Tensor options specifying the desired data type of the result.
 * @param probs_or_mask Optional tensor containing the (unnormalized)
 * probabilities associated with each neighboring edge of a node in the original
 * graph. It must be a 1D floating-point tensor with the number of elements
 * equal to the number of edges in the graph.
 * @param picked_data_ptr The destination address where the picked neighbors
 * should be put. Enough memory space should be allocated in advance.
 */
template <typename PickedType>
inline int64_t NonUniformPick(
    int64_t offset, int64_t num_neighbors, int64_t fanout, bool replace,
    const torch::TensorOptions& options,
    const torch::optional<torch::Tensor>& probs_or_mask,
    PickedType* picked_data_ptr) {
  auto local_probs =
      probs_or_mask.value().slice(0, offset, offset + num_neighbors);
  auto positive_probs_indices = local_probs.nonzero().squeeze(1);
  auto num_positive_probs = positive_probs_indices.size(0);
  if (num_positive_probs == 0) return 0;
  if ((fanout == -1) || (num_positive_probs <= fanout && !replace)) {
    std::memcpy(
        picked_data_ptr,
        (positive_probs_indices + offset).data_ptr<PickedType>(),
        num_positive_probs * sizeof(PickedType));
    return num_positive_probs;
  } else {
    if (!replace) fanout = std::min(fanout, num_positive_probs);
    if (fanout == 0) return 0;
    AT_DISPATCH_FLOATING_TYPES(
        local_probs.scalar_type(), "MultinomialSampling", ([&] {
          auto local_probs_data_ptr = local_probs.data_ptr<scalar_t>();
          auto positive_probs_indices_ptr =
              positive_probs_indices.data_ptr<PickedType>();

          if (!replace) {
            // The algorithm is from gumbel softmax.
            // s = argmax( logp - log(-log(eps)) ) where eps ~ U(0, 1).
            // Here we can apply exp to the formula which will not affect result
            // of argmax or topk. Then we have
            // s = argmax( p / (-log(eps)) ) where eps ~ U(0, 1).
            // We can also simplify the formula above by
            // s = argmax( p / q ) where q ~ Exp(1).
            if (fanout == 1) {
              // Return argmax(p / q).
              scalar_t max_prob = 0;
              PickedType max_prob_index = -1;
              // We only care about the neighbors with non-zero probability.
              for (auto i = 0; i < num_positive_probs; ++i) {
                // Calculate (p / q) for the current neighbor.
                scalar_t current_prob =
                    local_probs_data_ptr[positive_probs_indices_ptr[i]] /
                    RandomEngine::ThreadLocal()->Exponential(1.);
                if (current_prob > max_prob) {
                  max_prob = current_prob;
                  max_prob_index = positive_probs_indices_ptr[i];
                }
              }
              *picked_data_ptr = max_prob_index + offset;
            } else {
              // Return topk(p / q).
              std::vector<std::pair<scalar_t, PickedType>> q(
                  num_positive_probs);
              for (auto i = 0; i < num_positive_probs; ++i) {
                q[i].first =
                    local_probs_data_ptr[positive_probs_indices_ptr[i]] /
                    RandomEngine::ThreadLocal()->Exponential(1.);
                q[i].second = positive_probs_indices_ptr[i];
              }
              if (fanout < num_positive_probs / 64) {
                // Use partial_sort.
                std::partial_sort(
                    q.begin(), q.begin() + fanout, q.end(), std::greater{});
                for (auto i = 0; i < fanout; ++i) {
                  picked_data_ptr[i] = q[i].second + offset;
                }
              } else {
                // Use nth_element.
                std::nth_element(
                    q.begin(), q.begin() + fanout - 1, q.end(), std::greater{});
                for (auto i = 0; i < fanout; ++i) {
                  picked_data_ptr[i] = q[i].second + offset;
                }
              }
            }
          } else {
            // Calculate cumulative sum of probabilities.
            std::vector<scalar_t> prefix_sum_probs(num_positive_probs);
            scalar_t sum_probs = 0;
            for (auto i = 0; i < num_positive_probs; ++i) {
              sum_probs += local_probs_data_ptr[positive_probs_indices_ptr[i]];
              prefix_sum_probs[i] = sum_probs;
            }
            // Normalize.
            if ((sum_probs > 1.00001) || (sum_probs < 0.99999)) {
              for (auto i = 0; i < num_positive_probs; ++i) {
                prefix_sum_probs[i] /= sum_probs;
              }
            }
            for (auto i = 0; i < fanout; ++i) {
              // Sample a probability mass from a uniform distribution.
              double uniform_sample =
                  RandomEngine::ThreadLocal()->Uniform(0., 1.);
              // Use a binary search to find the index.
              int sampled_index = std::lower_bound(
                                      prefix_sum_probs.begin(),
                                      prefix_sum_probs.end(), uniform_sample) -
                                  prefix_sum_probs.begin();
              picked_data_ptr[i] =
                  positive_probs_indices_ptr[sampled_index] + offset;
            }
          }
        }));
    return fanout;
  }
}

template <typename PickedType>
int64_t Pick(
    int64_t offset, int64_t num_neighbors, int64_t fanout, bool replace,
    const torch::TensorOptions& options,
    const torch::optional<torch::Tensor>& probs_or_mask,
    SamplerArgs<SamplerType::NEIGHBOR> args, PickedType* picked_data_ptr) {
  if (probs_or_mask.has_value()) {
    return NonUniformPick(
        offset, num_neighbors, fanout, replace, options, probs_or_mask,
        picked_data_ptr);
  } else {
    return UniformPick(
        offset, num_neighbors, fanout, replace, options, picked_data_ptr);
  }
}

template <SamplerType S, typename PickedType>
int64_t PickByEtype(
    int64_t offset, int64_t num_neighbors, const std::vector<int64_t>& fanouts,
    bool replace, const torch::TensorOptions& options,
    const torch::Tensor& type_per_edge,
    const torch::optional<torch::Tensor>& probs_or_mask, SamplerArgs<S> args,
    PickedType* picked_data_ptr) {
  int64_t etype_begin = offset;
  int64_t etype_end = offset;
  int64_t pick_offset = 0;
  AT_DISPATCH_INTEGRAL_TYPES(
      type_per_edge.scalar_type(), "PickByEtype", ([&] {
        const scalar_t* type_per_edge_data = type_per_edge.data_ptr<scalar_t>();
        const auto end = offset + num_neighbors;
        while (etype_begin < end) {
          scalar_t etype = type_per_edge_data[etype_begin];
          TORCH_CHECK(
              etype >= 0 && etype < (int64_t)fanouts.size(),
              "Etype values exceed the number of fanouts.");
          int64_t fanout = fanouts[etype];
          auto etype_end_it = std::upper_bound(
              type_per_edge_data + etype_begin, type_per_edge_data + end,
              etype);
          etype_end = etype_end_it - type_per_edge_data;
          // Do sampling for one etype.
          if (fanout != 0) {
            int64_t picked_count = Pick(
                etype_begin, etype_end - etype_begin, fanout, replace, options,
                probs_or_mask, args, picked_data_ptr + pick_offset);
            pick_offset += picked_count;
          }
          etype_begin = etype_end;
        }
      }));
  return pick_offset;
}

template <typename PickedType>
int64_t Pick(
    int64_t offset, int64_t num_neighbors, int64_t fanout, bool replace,
    const torch::TensorOptions& options,
    const torch::optional<torch::Tensor>& probs_or_mask,
    SamplerArgs<SamplerType::LABOR> args, PickedType* picked_data_ptr) {
  if (fanout == 0) return 0;
  if (probs_or_mask.has_value()) {
    if (fanout < 0) {
      return NonUniformPick(
          offset, num_neighbors, fanout, replace, options, probs_or_mask,
          picked_data_ptr);
    } else {
      int64_t picked_count;
      AT_DISPATCH_FLOATING_TYPES(
          probs_or_mask.value().scalar_type(), "LaborPickFloatType", ([&] {
            if (replace) {
              picked_count = LaborPick<true, true, scalar_t>(
                  offset, num_neighbors, fanout, options, probs_or_mask, args,
                  picked_data_ptr);
            } else {
              picked_count = LaborPick<true, false, scalar_t>(
                  offset, num_neighbors, fanout, options, probs_or_mask, args,
                  picked_data_ptr);
            }
          }));
      return picked_count;
    }
  } else if (fanout < 0) {
    return UniformPick(
        offset, num_neighbors, fanout, replace, options, picked_data_ptr);
  } else if (replace) {
    return LaborPick<false, true, float>(
        offset, num_neighbors, fanout, options,
        /* probs_or_mask= */ torch::nullopt, args, picked_data_ptr);
  } else {  // replace = false
    return LaborPick<false, false, float>(
        offset, num_neighbors, fanout, options,
        /* probs_or_mask= */ torch::nullopt, args, picked_data_ptr);
  }
}

template <typename T, typename U>
inline void safe_divide(T& a, U b) {
  a = b > 0 ? (T)(a / b) : std::numeric_limits<T>::infinity();
}

/**
 * @brief Perform uniform-nonuniform sampling of elements depending on the
 * template parameter NonUniform and return the sampled indices.
 *
 * @param offset The starting edge ID for the connected neighbors of the sampled
 * node.
 * @param num_neighbors The number of neighbors to pick.
 * @param fanout The number of edges to be sampled for each node. It should be
 * >= 0 or -1.
 *  - When the value is -1, all neighbors (with non-zero probability, if
 * weighted) will be sampled once regardless of replacement. It is equivalent to
 * selecting all neighbors with non-zero probability when the fanout is >= the
 * number of neighbors (and replacement is set to false).
 *  - When the value is a non-negative integer, it serves as a minimum
 * threshold for selecting neighbors.
 * @param options Tensor options specifying the desired data type of the result.
 * @param probs_or_mask Optional tensor containing the (unnormalized)
 * probabilities associated with each neighboring edge of a node in the original
 * graph. It must be a 1D floating-point tensor with the number of elements
 * equal to the number of edges in the graph.
 * @param args Contains labor specific arguments.
 * @param picked_data_ptr The destination address where the picked neighbors
 * should be put. Enough memory space should be allocated in advance.
 */
template <
    bool NonUniform, bool Replace, typename ProbsType, typename PickedType,
    int StackSize>
inline int64_t LaborPick(
    int64_t offset, int64_t num_neighbors, int64_t fanout,
    const torch::TensorOptions& options,
    const torch::optional<torch::Tensor>& probs_or_mask,
    SamplerArgs<SamplerType::LABOR> args, PickedType* picked_data_ptr) {
  fanout = Replace ? fanout : std::min(fanout, num_neighbors);
  if (!NonUniform && !Replace && fanout >= num_neighbors) {
    std::iota(picked_data_ptr, picked_data_ptr + num_neighbors, offset);
    return num_neighbors;
  }
  // Assuming max_degree of a vertex is <= 4 billion.
  std::array<std::pair<float, uint32_t>, StackSize> heap;
  auto heap_data = heap.data();
  torch::Tensor heap_tensor;
  if (fanout > StackSize) {
    constexpr int factor = sizeof(heap_data[0]) / sizeof(int32_t);
    heap_tensor = torch::empty({fanout * factor}, torch::kInt32);
    heap_data = reinterpret_cast<std::pair<float, uint32_t>*>(
        heap_tensor.data_ptr<int32_t>());
  }
  const ProbsType* local_probs_data =
      NonUniform ? probs_or_mask.value().data_ptr<ProbsType>() + offset
                 : nullptr;
  AT_DISPATCH_INTEGRAL_TYPES(
      args.indices.scalar_type(), "LaborPickMain", ([&] {
        const scalar_t* local_indices_data =
            args.indices.data_ptr<scalar_t>() + offset;
        if constexpr (Replace) {
          // [Algorithm] @mfbalin
          // Use a max-heap to get rid of the big random numbers and filter the
          // smallest fanout of them. Implements arXiv:2210.13339 Section A.3.
          // Unlike sampling without replacement below, the same item can be
          // included fanout times in our sample. Thus, we sort and pick the
          // smallest fanout random numbers out of num_neighbors * fanout of
          // them. Each item has fanout many random numbers in the race and the
          // smallest fanout of them get picked. Instead of generating
          // fanout * num_neighbors random numbers and increase the complexity,
          // I devised an algorithm to generate the fanout numbers for an item
          // in a sorted manner on demand, meaning we continue generating random
          // numbers for an item only if it has been sampled that many times
          // already.
          // https://gist.github.com/mfbalin/096dcad5e3b1f6a59ff7ff2f9f541618
          //
          // [Complexity Analysis]
          // Will modify the heap at most linear in O(num_neighbors + fanout)
          // and each modification takes O(log(fanout)). So the total complexity
          // is O((fanout + num_neighbors) log(fanout)). It is possible to
          // decrease the logarithmic factor down to
          // O(log(min(fanout, num_neighbors))).
          std::array<float, StackSize> remaining;
          auto remaining_data = remaining.data();
          torch::Tensor remaining_tensor;
          if (num_neighbors > StackSize) {
            remaining_tensor = torch::empty({num_neighbors}, torch::kFloat32);
            remaining_data = remaining_tensor.data_ptr<float>();
          }
          std::fill_n(remaining_data, num_neighbors, 1.f);
          auto heap_end = heap_data;
          const auto init_count = (num_neighbors + fanout - 1) / num_neighbors;
          auto sample_neighbor_i_with_index_t_jth_time =
              [&](scalar_t t, int64_t j, uint32_t i) {
                auto rnd = labor::jth_sorted_uniform_random(
                    args.random_seed, t, args.num_nodes, j, remaining_data[i],
                    fanout - j);  // r_t
                if constexpr (NonUniform) {
                  safe_divide(rnd, local_probs_data[i]);
                }  // r_t / \pi_t
                if (heap_end < heap_data + fanout) {
                  heap_end[0] = std::make_pair(rnd, i);
                  if (++heap_end >= heap_data + fanout) {
                    std::make_heap(heap_data, heap_data + fanout);
                  }
                  return false;
                } else if (rnd < heap_data[0].first) {
                  std::pop_heap(heap_data, heap_data + fanout);
                  heap_data[fanout - 1] = std::make_pair(rnd, i);
                  std::push_heap(heap_data, heap_data + fanout);
                  return false;
                } else {
                  remaining_data[i] = -1;
                  return true;
                }
              };
          for (uint32_t i = 0; i < num_neighbors; ++i) {
            const auto t = local_indices_data[i];
            for (int64_t j = 0; j < init_count; j++) {
              sample_neighbor_i_with_index_t_jth_time(t, j, i);
            }
          }
          for (uint32_t i = 0; i < num_neighbors; ++i) {
            if (remaining_data[i] == -1) continue;
            const auto t = local_indices_data[i];
            for (int64_t j = init_count; j < fanout; ++j) {
              if (sample_neighbor_i_with_index_t_jth_time(t, j, i)) break;
            }
          }
        } else {
          // [Algorithm]
          // Use a max-heap to get rid of the big random numbers and filter the
          // smallest fanout of them. Implements arXiv:2210.13339 Section A.3.
          //
          // [Complexity Analysis]
          // the first for loop and std::make_heap runs in time O(fanouts).
          // The next for loop compares each random number to the current
          // minimum fanout numbers. For any given i, the probability that the
          // current random number will replace any number in the heap is fanout
          // / i. Summing from i=fanout to num_neighbors, we get f * (H_n -
          // H_f), where n is num_neighbors and f is fanout, H_f is \sum_j=1^f
          // 1/j. In the end H_n - H_f = O(log n/f), there are n - f iterations,
          // each heap operation takes time log f, so the total complexity is
          // O(f + (n - f)
          // + f log(n/f) log f) = O(n + f log(f) log(n/f)). If f << n (f is a
          // constant in almost all cases), then the average complexity is
          // O(num_neighbors).
          for (uint32_t i = 0; i < fanout; ++i) {
            const auto t = local_indices_data[i];
            auto rnd =
                labor::uniform_random<float>(args.random_seed, t);  // r_t
            if constexpr (NonUniform) {
              safe_divide(rnd, local_probs_data[i]);
            }  // r_t / \pi_t
            heap_data[i] = std::make_pair(rnd, i);
          }
          if (!NonUniform || fanout < num_neighbors) {
            std::make_heap(heap_data, heap_data + fanout);
          }
          for (uint32_t i = fanout; i < num_neighbors; ++i) {
            const auto t = local_indices_data[i];
            auto rnd =
                labor::uniform_random<float>(args.random_seed, t);  // r_t
            if constexpr (NonUniform) {
              safe_divide(rnd, local_probs_data[i]);
            }  // r_t / \pi_t
            if (rnd < heap_data[0].first) {
              std::pop_heap(heap_data, heap_data + fanout);
              heap_data[fanout - 1] = std::make_pair(rnd, i);
              std::push_heap(heap_data, heap_data + fanout);
            }
          }
        }
      }));
  int64_t num_sampled = 0;
  for (int64_t i = 0; i < fanout; ++i) {
    const auto [rnd, j] = heap_data[i];
    if (!NonUniform || rnd < std::numeric_limits<float>::infinity()) {
      picked_data_ptr[num_sampled++] = offset + j;
    }
  }
  return num_sampled;
}

}  // namespace sampling
}  // namespace graphbolt