src/dynamic_fusion/sketch/utils/DependencyGraph.h

/*
 * Copyright (c) 2022 Arm Limited.
 *
 * SPDX-License-Identifier: MIT
 *
 * Permission is hereby granted, free of charge, to any person obtaining a copy
 * of this software and associated documentation files (the "Software"), to
 * deal in the Software without restriction, including without limitation the
 * rights to use, copy, modify, merge, publish, distribute, sublicense, and/or
 * sell copies of the Software, and to permit persons to whom the Software is
 * furnished to do so, subject to the following conditions:
 *
 * The above copyright notice and this permission notice shall be included in all
 * copies or substantial portions of the Software.
 *
 * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
 * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
 * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
 * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
 * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
 * OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
 * SOFTWARE.
 */
#ifndef SRC_DYNAMIC_FUSION_SKETCH_UTILS_DEPENDENCYGRAPH
#define SRC_DYNAMIC_FUSION_SKETCH_UTILS_DEPENDENCYGRAPH

#include "arm_compute/core/Error.h"
#include <algorithm>
#include <cstdint>
#include <deque>
#include <map>
#include <set>
#include <tuple>
#include <vector>

namespace arm_compute
{
namespace experimental
{
namespace dynamic_fusion
{
namespace
{
template <typename T>
bool is_in(const T &v, const std::vector<T> &vec)
{
    return std::find(std::begin(vec), std::end(vec), v) != std::end(vec);
}
} // namespace

/** A multi-input (tensors), multi-output (tensors) acyclic directed graph
 *  Represented as a doubly-linked adjacency list with the differentiation between source and destination
 */
class DependencyGraph
{
public:
    using Id         = int32_t;
    using TensorId   = Id;
    using OperatorId = Id;
    /** Adjacency list
     *
     */
    using AdjList = std::map<Id, std::vector<Id>>;

    /** A pack of operator including its input and output tensors, used by traversing through the graph in topological order
     *
     */
    struct OpPack
    {
        OperatorId            op{};
        std::vector<TensorId> inputs{};
        std::vector<TensorId> outputs{};
        friend bool operator==(const OpPack &opp0, const OpPack &opp1)
        {
            return std::make_tuple(
                       opp0.op, opp0.inputs, opp0.outputs)
                   == std::make_tuple(
                       opp1.op, opp1.inputs, opp1.outputs);
        }
    };

public:
    DependencyGraph() = default;
    friend std::ostream &operator<<(std::ostream &os, const DependencyGraph &);

    /** Try adding an operator (without actually adding it), while keeping the graph as a "linear sequence" / list
     * @note The list is expected to only grow from head to tail
     *
     * PRECONDITION: The current graph is already linear
     *
     * @return true  If the operator can be added while keeping the graph as a linear sequence
     * @return false  Otherwise
     */
    bool try_add_operator_as_linear(OperatorId op, const std::vector<TensorId> &inputs, const std::vector<TensorId> &outputs) const
    {
        ARM_COMPUTE_UNUSED(op, outputs);
        if(all_ops().empty())
        {
            return true;
        }
        std::vector<TensorId> common_tensors{};
        auto                  existing_tensors = all_tensors();
        std::sort(existing_tensors.begin(), existing_tensors.end()); // To use std::set_intersection, both input sets must be sorted
        std::vector<TensorId> sorted_inputs{ inputs };
        std::sort(sorted_inputs.begin(), sorted_inputs.end());
        std::set_intersection(existing_tensors.begin(), existing_tensors.end(),
                              sorted_inputs.begin(), sorted_inputs.end(), std::back_inserter(common_tensors));
        if(common_tensors.size() != 1U)
        {
            return false;
        }
        const auto linked_tensor = common_tensors[0];
        const auto tail_ops      = get_dst_ops();
        ARM_COMPUTE_ERROR_ON(tail_ops.size() != 1U); // PRECONDITION
        const auto tail = tail_ops[0];

        if(!is_in(linked_tensor, dst_tensors(tail)))
        {
            return false;
        }
        return true;
    }
    /** Add an operator, while keeping the graph as a "linear sequence"
     *
     * PRECONDITION: The current graph is already linear
     * INVARIANT: The list can only grow from head to tail
     * INVARIANT: POSTCONDITION: The graph is linear
     */
    void add_operator_as_linear(OperatorId op, const std::vector<TensorId> &inputs, const std::vector<TensorId> &outputs)
    {
        ARM_COMPUTE_ERROR_ON(!try_add_operator_as_linear(op, inputs, outputs));
        auto success = add_operator(op, inputs, outputs);
        ARM_COMPUTE_UNUSED(success);
        ARM_COMPUTE_ERROR_ON(!success);
    }
    /** Add a new operator
     *  Return invalid if it violates the DAG invariant
     *  Invalid operation will not change the graph
     *
     * @param[in] op      Operator to add
     * @param[in] inputs  Input tensors to the operator
     * @param[in] outputs Output tensors to the operator
     */
    bool add_operator(OperatorId op, const std::vector<TensorId> &inputs, const std::vector<TensorId> &outputs)
    {
        if(operator_exists(op))
        {
            return false;
        }
        _adj_src_tensors[op] = {};
        _adj_dst_tensors[op] = {};
        for(auto in_tensor : inputs)
        {
            // Linking input tensor to operator node will never create a cycle / loop because we guarantee
            // each op is newly created, so every <input, op> pair / edge is new
            link_input(op, in_tensor);
        }
        for(auto out_tensor : outputs)
        {
            // If there exists a back path from op's output tensor to op already, then linking the two will create a loop / cycle
            if(path_exists_from_tensor_to_op(out_tensor, op))
            {
                remove_operator(op);
                return false;
            }
            else
            {
                link_output(op, out_tensor);
            }
        }

        return true;
    }

    /** Sort the graph in a topological order
     *
     * @return std::vector<OpPack>
     */
    std::vector<OpPack> topological_sort() const
    {
        // Incident degree (number of source operators to an op)
        std::map<OperatorId, unsigned int> in_degree{};
        std::set<OperatorId>   visited_ops{};
        std::deque<OperatorId> zero_in_degree_ops{};
        std::vector<OpPack>    sorted_op_packs{};
        for(auto op : all_ops())
        {
            const auto degree = src_ops(op).size();
            in_degree[op]     = degree;
            if(degree == 0)
            {
                zero_in_degree_ops.push_back(op);
                visited_ops.insert(op);
            }
        }

        while(!zero_in_degree_ops.empty())
        {
            const OperatorId op = zero_in_degree_ops.front();
            zero_in_degree_ops.pop_front();
            sorted_op_packs.push_back(OpPack{ op, src_tensors(op), dst_tensors(op) });

            for(const auto next_op : dst_ops(op))
            {
                if(in_degree[next_op] > 0)
                {
                    in_degree[next_op]--;
                }
                if(in_degree[next_op] == 0 && visited_ops.find(next_op) == visited_ops.end())
                {
                    zero_in_degree_ops.push_back(next_op);
                    visited_ops.insert(op);
                }
            }
        }

        return sorted_op_packs;
    }

    void find_independent_paths_util(OperatorId op, std::vector<std::vector<OperatorId>> &paths, std::vector<OperatorId> cur_path,
                                     const std::map<OperatorId, unsigned int> &in_degree) const
    {
        // We have found an unresolved dependency
        if(in_degree.at(op) > 1)
        {
            paths.push_back(cur_path);
            return;
        }
        const auto child_ops = dst_ops(op);

        cur_path.push_back(op);
        // Hit the leaf op
        if(child_ops.empty())
        {
            paths.push_back(cur_path);
            return;
        }
        for(const auto child_op : child_ops)
        {
            find_independent_paths_util(child_op, paths, cur_path, in_degree);
        }
    }
    /** Find all independent linear paths from op, which doesn't depend on any other op
     *
     * @return std::vector<OpPack>
     */
    std::vector<std::vector<OperatorId>> find_independent_paths(OperatorId op,
                                                                const std::map<OperatorId, unsigned int> &in_degree) const
    {
        std::vector<std::vector<OperatorId>> paths;
        std::vector<OperatorId>              cur_path;
        find_independent_paths_util(op, paths, cur_path, in_degree);
        return paths;
    }
    /** Find a longest linear path from op, which doesn't depend on any other op
     *
     * @return std::vector<OpPack>
     */
    std::vector<OperatorId> find_longest_independent_path(OperatorId op,
                                                          const std::map<OperatorId, unsigned int> &in_degree) const
    {
        const auto &paths = find_independent_paths(op, in_degree);
        ARM_COMPUTE_ERROR_ON(paths.empty());
        size_t                         max_len  = 0;
        const std::vector<OperatorId> *max_path = nullptr;

        for(const auto &path : paths)
        {
            if(path.size() >= max_len)
            {
                max_path = &path;
                max_len  = path.size();
            }
        }
        return *max_path;
    }
    std::vector<OperatorId> propose_next_path(std::set<OperatorId> &candidate_ops,
                                              const std::map<OperatorId, unsigned int> &in_degree) const
    {
        if(candidate_ops.empty())
        {
            return {};
        }
        size_t                  max_len = 0;
        std::vector<OperatorId> max_path;
        OperatorId              chosen_op{};
        for(auto op : candidate_ops)
        {
            const auto path = find_longest_independent_path(op, in_degree);
            if(path.size() >= max_len)
            {
                chosen_op = op;
                max_path  = path;
                max_len   = path.size();
            }
        }
        candidate_ops.erase(chosen_op);
        return max_path;
    }
    /** Partition the graph into a list of linear sub-"graphs", while preserving the topological order, and trying to minimize
     *  the number of partitions
     */
    std::vector<std::vector<OpPack>> topological_partition() const
    {
        // Initialize zero incident degree and zero in degree ops
        std::map<OperatorId, unsigned int> in_degree{};
        std::set<OperatorId> candidate_ops{};
        for(auto op : all_ops())
        {
            const auto degree = src_ops(op).size();
            in_degree[op]     = degree;
            if(degree == 0)
            {
                candidate_ops.insert(op);
            }
        }

        std::vector<std::vector<OpPack>> sorted_partitions{};
        while(!candidate_ops.empty())
        {
            // generate_longest_path_from_zero_indegree_ops(in_degree, visited_ops, candidate_ops)
            const auto path = propose_next_path(candidate_ops, in_degree);

            // Append to sorted_partitions
            std::vector<OpPack> path_op_pack{};
            for(auto op : path)
            {
                path_op_pack.push_back(OpPack{ op, src_tensors(op), dst_tensors(op) });
            }
            sorted_partitions.push_back(path_op_pack);
            // Remove whole path (Update in_degree, visited_ops, candidate_ops)
            for(auto op : path)
            {
                for(const auto next_op_child : dst_ops(op))
                {
                    if(in_degree[next_op_child] > 0)
                    {
                        in_degree[next_op_child]--;
                    }
                    if(in_degree[next_op_child] == 0 && !is_in(next_op_child, path)) // We do not want to put the proposed path back into candidates
                    {
                        candidate_ops.insert(next_op_child);
                    }
                }
            }
        }
        return sorted_partitions;
    }

    /** Strict equality comparison (all internal ids and order of insertion matter).
     *        In the future this may be replaced with a topological comparison, allowing equivalent graphs with different internal ids to be equal
     *
     *
     * @param[in] g0
     * @param[in] g1
     * @return true  If the same
     * @return false Otherwise
     */
    friend bool operator==(const DependencyGraph &g0, const DependencyGraph &g1)
    {
        // Do not compare id allocators
        return std::make_tuple(
                   g0._adj_src_tensors, g0._adj_dst_tensors, g0._adj_src_ops, g0._adj_dst_ops)
               == std::make_tuple(
                   g1._adj_src_tensors, g1._adj_dst_tensors, g1._adj_src_ops, g1._adj_dst_ops);
    }
    std::vector<OperatorId> src_ops_from_tensor(TensorId tensor) const
    {
        return _adj_src_ops.at(tensor);
    }
    std::vector<OperatorId> dst_ops_from_tensor(TensorId tensor) const
    {
        return _adj_dst_ops.at(tensor);
    }
    /** Get all tensors
     *
     * @return std::vector<TensorId>
     */
    std::vector<TensorId> all_tensors() const
    {
        std::vector<TensorId> tensors{};
        std::transform(std::begin(_adj_src_ops), std::end(_adj_src_ops), std::back_inserter(tensors), [](const auto & it)
        {
            return it.first;
        });
        return tensors;
    }
    /** Get source tensors of the whole graph
     *
     * @return std::vector<TensorId>
     */
    std::vector<TensorId> global_src_tensors() const
    {
        std::vector<TensorId> tensors;
        for(auto tensor_src_ops : _adj_src_ops)
        {
            if(tensor_src_ops.second.empty())
            {
                tensors.push_back(tensor_src_ops.first);
            }
        }
        return tensors;
    }
    /** Get destination tensors of the whole graph
     *
     * @return std::vector<TensorId>
     */
    std::vector<TensorId> global_dst_tensors() const
    {
        std::vector<TensorId> tensors;
        for(auto tensor_dst_ops : _adj_dst_ops)
        {
            if(tensor_dst_ops.second.empty())
            {
                tensors.push_back(tensor_dst_ops.first);
            }
        }
        return tensors;
    }
    /** Get intermediate tensors of the whole graph.
     *
     * @return std::vector<TensorId>
     */
    std::vector<TensorId> intermediate_tensors() const
    {
        std::vector<TensorId> tensors;

        // If a tensor is used to connect the input of an operator and the output of another operator,
        // it is not allocated in the memory. The tensor exists as a temporary variable only.
        for(auto src_tensor : _adj_src_ops)
        {
            if(!src_tensor.second.empty())
            {
                const auto dst_tensor = _adj_dst_ops.find(src_tensor.first);
                if(dst_tensor != _adj_dst_ops.end())
                {
                    if(!dst_tensor->second.empty())
                    {
                        tensors.push_back(src_tensor.first);
                    }
                }
            }
        }

        return tensors;
    }
    /** Get all root ops. Root ops can also be referred to as "src ops" of the whole graph
     *
     * @return std::vector<OperatorId>
     */
    std::vector<OperatorId> get_root_ops() const
    {
        std::vector<OperatorId> ops{};
        const auto              op_list = all_ops();

        for(auto op : op_list)
        {
            if(src_ops(op).empty())
            {
                ops.emplace_back(op);
            }
        }
        return ops;
    }

private:
    void link_input(OperatorId op, TensorId in_tensor)
    {
        ARM_COMPUTE_ERROR_ON(!operator_exists(op));
        if(!tensor_exists(in_tensor))
        {
            insert_new_tensor(in_tensor);
        }
        ARM_COMPUTE_ERROR_ON(are_connected(op, in_tensor)); // Prevent repetitive linking
        _adj_src_tensors[op].push_back(in_tensor);
        _adj_dst_ops[in_tensor].push_back(op);
    }
    void link_output(OperatorId op, TensorId out_tensor)
    {
        ARM_COMPUTE_ERROR_ON(!operator_exists(op));
        if(!tensor_exists(out_tensor))
        {
            insert_new_tensor(out_tensor);
        }
        ARM_COMPUTE_ERROR_ON(are_connected(op, out_tensor)); // Prevent repetitive linking
        _adj_dst_tensors[op].push_back(out_tensor);
        _adj_src_ops[out_tensor].push_back(op);
    }

    std::vector<OperatorId> src_ops(OperatorId op) const
    {
        ARM_COMPUTE_ERROR_ON(!operator_exists(op));
        std::vector<OperatorId> ops{};
        for(TensorId src_tensor : src_tensors(op))
        {
            ops.insert(ops.end(), std::begin(_adj_src_ops.at(src_tensor)), std::end(_adj_src_ops.at(src_tensor)));
        }
        return ops;
    }
    std::vector<OperatorId> dst_ops(OperatorId op) const
    {
        ARM_COMPUTE_ERROR_ON(!operator_exists(op));
        std::vector<OperatorId> ops{};
        for(TensorId dst_tensor : _adj_dst_tensors.at(op))
        {
            ops.insert(ops.end(), std::begin(_adj_dst_ops.at(dst_tensor)), std::end(_adj_dst_ops.at(dst_tensor)));
        }
        return ops;
    }

    /** Get source tensors to an operator
     *
     * @param[in] op
     * @return std::vector<TensorId>
     */
    std::vector<TensorId> src_tensors(OperatorId op) const
    {
        ARM_COMPUTE_ERROR_ON(!operator_exists(op));
        return _adj_src_tensors.at(op);
    }
    /** Get destination tensors to an operator
     *
     * @param[in] op
     * @return std::vector<TensorId>
     */
    std::vector<TensorId> dst_tensors(OperatorId op) const
    {
        ARM_COMPUTE_ERROR_ON(!operator_exists(op));
        return _adj_dst_tensors.at(op);
    }
    /** Get all operators
     *
     * @return std::vector<OperatorId>
     */
    std::vector<OperatorId> all_ops() const
    {
        std::vector<OperatorId> ops{};
        std::transform(std::begin(_adj_src_tensors), std::end(_adj_src_tensors), std::back_inserter(ops), [](const auto & it)
        {
            return it.first;
        });
        return ops;
    }
    /** Remove an operator from graph.
     *
     * @param[in] op
     */
    void remove_operator(OperatorId op)
    {
        for(auto src_tensor : _adj_src_tensors.at(op))
        {
            auto &dst_ops = _adj_dst_ops.at(src_tensor);
            dst_ops.erase(
                std::remove(std::begin(dst_ops), std::end(dst_ops), op),
                std::end(dst_ops));
        }
        for(auto dst_tensor : _adj_dst_tensors.at(op))
        {
            auto &src_ops = _adj_src_ops.at(dst_tensor);
            src_ops.erase(
                std::remove(std::begin(src_ops), std::end(src_ops), op),
                std::end(src_ops));
        }
        // Remove any isolated tensors
        // An isolated tensor is one where both its _adj_src_ops and _adj_dst_ops are empty
        for(auto t : all_tensors())
        {
            if(_adj_src_ops.at(t).empty() && _adj_dst_ops.at(t).empty())
            {
                _adj_src_ops.erase(t);
                _adj_dst_ops.erase(t);
            }
        }
        _adj_src_tensors.erase(op);
        _adj_dst_tensors.erase(op);
    }
    void insert_new_tensor(TensorId tensor)
    {
        _adj_src_ops[tensor] = {};
        _adj_dst_ops[tensor] = {};
    }
    bool tensor_exists(TensorId tensor) const
    {
        return _adj_src_ops.find(tensor) != _adj_src_ops.end() && _adj_dst_ops.find(tensor) != _adj_dst_ops.end();
    }
    bool operator_exists(OperatorId op) const
    {
        return _adj_src_tensors.find(op) != _adj_src_tensors.end() && _adj_dst_tensors.find(op) != _adj_dst_tensors.end();
    }
    bool is_src_tensor_of(OperatorId op, TensorId tensor) const
    {
        if(!operator_exists(op) || !tensor_exists(tensor))
        {
            return false;
        }
        const auto op_inputs = src_tensors(op);
        return std::find(op_inputs.begin(), op_inputs.end(), tensor) != op_inputs.end();
    }
    bool is_dst_tensor_of(OperatorId op, TensorId tensor) const
    {
        if(!operator_exists(op) || !tensor_exists(tensor))
        {
            return false;
        }
        const auto op_outputs = dst_tensors(op);
        return std::find(op_outputs.begin(), op_outputs.end(), tensor) != op_outputs.end();
    }
    bool are_connected(OperatorId op, TensorId tensor) const
    {
        return is_src_tensor_of(op, tensor) || is_dst_tensor_of(op, tensor);
    }
    /** If op is the destination / leaf operator of the whole graph
     *
     * @param[in] op
     * @return true
     * @return false
     */
    bool is_dst_op(OperatorId op) const
    {
        return dst_ops(op).empty();
    }
    std::vector<OperatorId> get_dst_ops() const
    {
        std::vector<OperatorId> ops{};
        const auto              op_list = all_ops();

        for(auto op : op_list)
        {
            if(is_dst_op(op))
            {
                ops.emplace_back(op);
            }
        }
        return ops;
    }
    bool path_exists_from_tensor_to_op(TensorId src_tensor, OperatorId dst_op) const
    {
        if(!tensor_exists(src_tensor) || !operator_exists(dst_op))
        {
            return false;
        }
        for(auto child_op : dst_ops_from_tensor(src_tensor))
        {
            if(path_exists_from_op_to_op(child_op, dst_op))
            {
                return true;
            }
        }
        return false;
    }

    bool path_exists_from_op_to_op(OperatorId src_op, OperatorId dst_op) const
    {
        if(!operator_exists(src_op) || !operator_exists(dst_op))
        {
            return false;
        }
        if(src_op == dst_op)
        {
            return true;
        }
        if(is_in(src_op, get_dst_ops()))
        {
            return false;
        }
        for(auto child_tensor : dst_tensors(src_op))
        {
            if(path_exists_from_tensor_to_op(child_tensor, dst_op))
            {
                return true;
            }
        }
        return false;
    }

private:
    AdjList _adj_src_tensors{};
    AdjList _adj_dst_tensors{};
    AdjList _adj_src_ops{};
    AdjList _adj_dst_ops{};
};

} // namespace dynamic_fusion
} // namespace experimental
} // namespace arm_compute
#endif /* SRC_DYNAMIC_FUSION_SKETCH_UTILS_DEPENDENCYGRAPH */