如何有效地随机排列图形中的边缘

在没有太多指导的情况下，我去创建了一些比较基准。具有90个顶点和120个边的时间：

完整的样本详细信息（单击以获取交互式图表）：

事实证明，我对邻接矩阵更快的直觉恰恰相反：

我认为可以通过创建选择随机边缘的专门方法来解决¹。我现在将其留给读者作为练习。

基准代码

使用https://github.com/rmartinho/nonius

#include <boost/graph/adjacency_list.hpp>
#include <boost/graph/adjacency_matrix.hpp>
#include <boost/graph/edge_list.hpp>
#include <boost/graph/random.hpp>
#include <boost/graph/graphviz.hpp>
#include <boost/container/flat_set.hpp>
#include <nonius/benchmark.h++>

namespace edge_list_detail {
    struct edge { 
        using first_type = size_t;
        using second_type = size_t;
        first_type  s;
        second_type t;

        edge(first_type s, second_type t) : s(std::min(s,t)), t(std::max(s,t)) { assert(s!=t); }
        bool operator<(edge const& other) const { return std::tie(s,t) < std::tie(other.s, other.t); }
    };

    using node_based_set = std::set<edge>;
    using flat_set       = boost::container::flat_set<edge>;

    void reserve(node_based_set const&, size_t) {}
    void reserve(flat_set& c, size_t n) { c.reserve(n); }

    void erase_two(node_based_set& from, node_based_set::iterator e1, node_based_set::iterator e2) {
        from.erase(e1);
        from.erase(e2);
    }

    void erase_two(flat_set& from, flat_set::iterator e1, flat_set::iterator e2) {
        if (e2<e1) std::swap(e1, e2);
        from.erase(e2); // invalidates higher iterators
        from.erase(e1);
    }
}

typedef boost::adjacency_list   < boost::setS, boost::vecS, boost::undirectedS > adj_list_t;
typedef boost::adjacency_matrix < boost::undirectedS                           > adj_mat_t;

static std::mt19937 engine(std::random_device{}());

static auto const sample_adj_list = [] {
    using namespace boost;
    adj_list_t graph(90);
    generate_random_graph(graph, 90, 120, engine);
    {
        std::ofstream ofs("/tmp/raw.dot");
        write_graphviz(ofs, graph);
    }

    return graph;
}();

static auto const sample_adj_mat = [] {
    using namespace boost;
    adj_mat_t graph(num_vertices(sample_adj_list));
    for (auto e : make_iterator_range(edges(sample_adj_list))) {
        add_edge(source(e, sample_adj_list), target(e, sample_adj_list), graph);
    }
    return graph;
}();

template <typename graph_t> auto nth_edge(graph_t& graph, size_t n) {
    return std::next(boost::edges(graph).first, n);
}
auto nth_edge(edge_list_detail::node_based_set& lst, size_t n) {
    return std::next(lst.begin(), n);
}
auto nth_edge(edge_list_detail::flat_set& lst, size_t n) {
    return std::next(lst.begin(), n);
}

template <typename graph_t> void OP_algo(nonius::chronometer& cm, graph_t graph) {
    // Number of edges.
    cm.measure([&] {
        unsigned int nb_edges = boost::num_edges(graph);

        // Defines a function that give a random edge.
        std::uniform_int_distribution<int> get_rand_edge(0, nb_edges - 1);

        // Descriptors and iterators.
        typename graph_t::vertex_descriptor v1, v2, v3, v4;
        typename graph_t::edge_iterator e1_it, e2_it, e_end;

        // Shuffles the edges, with the condition of not creating multiple edges or self-loops.
        unsigned int nb_edge_swaps(0);
        while(nb_edge_swaps < 10 * nb_edges)
        {
            {
                e1_it = nth_edge(graph, get_rand_edge(engine));
                v1 = boost::source(*e1_it, graph);
                v2 = boost::target(*e1_it, graph);

                e2_it = nth_edge(graph, get_rand_edge(engine));
                v3 = boost::source(*e2_it, graph);
                v4 = boost::target(*e2_it, graph);
            }

            // Avoids self-loops.
            if((v1 != v3) && (v2 != v4))
            {
                // Avoids multiple edge.
                if(boost::edge(v1, v3, graph).second == false)
                {
                    // Avoids multiple edge.
                    if(boost::edge(v2, v4, graph).second == false)
                    {
                        // Destroys the old edges.
                        boost::remove_edge(*e1_it, graph);
                        boost::remove_edge(boost::edge(v3, v4, graph).first, graph);
                        // Creates the new edges.
                        boost::add_edge(v1, v3, graph);
                        boost::add_edge(v2, v4, graph);
                        // Counts the number of changes.
                        ++nb_edge_swaps;
                    }
                }
            }
        }
        return;
        {
            std::ofstream ofs("/tmp/shuffled.dot");
            boost::write_graphviz(ofs, graph);
        }
    });

}

template <typename list_t> void edge_list_algo(nonius::chronometer& cm, list_t& lst) {
    cm.measure([&] {
        unsigned int nb_edges = lst.size();

        // Defines a function that give a random edge.
        std::uniform_int_distribution<int> get_rand_edge(0, nb_edges - 1);

        // Shuffles the edges, with the condition of not creating multiple edges or self-loops.
        unsigned int nb_edge_swaps(0);
        while(nb_edge_swaps < 10 * nb_edges)
        {
            auto e1 = nth_edge(lst, get_rand_edge(engine));
            auto v1 = e1->s;
            auto v2 = e1->t;

            auto e2 = nth_edge(lst, get_rand_edge(engine));
            auto v3 = e2->s;
            auto v4 = e2->t;

            // Avoids self-loops.
            // Avoids multiple edge.
            if ((v1 == v3) || (v2 == v4) || lst.count({v1,v3}) || lst.count({v2,v4}))
                continue;

            // swap edges
            edge_list_detail::erase_two(lst, e1, e2);
            lst.emplace(v1, v3);
            lst.emplace(v2, v4);

            // Counts the number of changes.
            ++nb_edge_swaps;
        }
        return;
    });

}

template <typename edge_list>
void edge_list_config(nonius::chronometer& cm) {
        using namespace boost;
        edge_list lst;
        {
            edge_list_detail::reserve(lst, num_edges(sample_adj_list));
            for (auto e : make_iterator_range(edges(sample_adj_list))) {
                lst.emplace(source(e, sample_adj_list), target(e, sample_adj_list));
            }
        }
        edge_list_algo(cm, lst); 

        typedef boost::edge_list<typename edge_list::iterator> graph_t;
        graph_t graph(lst.begin(), lst.end());
        {
            std::ofstream ofs("/tmp/edge_list.dot");
            //boost::write_graphviz(ofs, graph);
        }
}

NONIUS_BENCHMARK("original_adj_list",   [](nonius::chronometer cm) { OP_algo(cm,        sample_adj_list);        });
NONIUS_BENCHMARK("original_adj_matrix", [](nonius::chronometer cm) { OP_algo(cm,        sample_adj_mat);         });
NONIUS_BENCHMARK("node_based_edge_list",[](nonius::chronometer cm) { edge_list_config<edge_list_detail::node_based_set>(cm); });
NONIUS_BENCHMARK("flat_edge_list",      [](nonius::chronometer cm) { edge_list_config<edge_list_detail::flat_set>(cm); });

#define NONIUS_RUNNER
#include <nonius/main.h++>

要创建图：

./test -r html -o stats.html

¹（nth_edge以下为通用代码，对于adjacency_matrix而言效率不高）。