Boost.Graph - algo.is_optimal()断言

Question

我正在尝试实现一个程序，使用最小成本流算法来检测套利交易机会。该算法在Boost.Graph中以boost::push_relabel_max_flow()的形式实现，然后调用boost::cycle_canceling()。

下面是我已经拥有的代码，省略了boost::cycle_canceling-part，因为我的程序在到达函数之前就死了。

    #include <boost/graph/adjacency_list.hpp>
    #include <boost/property_map/property_map.hpp>
    #include <boost/graph/push_relabel_max_flow.hpp>
    #include <boost/graph/cycle_canceling.hpp>
    #include <boost/graph/directed_graph.hpp>
    #include <boost/config.hpp>
    #include <iostream>
    #include <string>



    typedef boost::adjacency_list_traits<boost::vecS, boost::vecS, boost::directedS> Traits;

    struct st_order {
        double price;
        double amount;
        std::string type;
    };

    struct VertexProps {
        unsigned int id;
    };

    struct EdgeProps {
        double capacity;
        double residual_capacity;
        double weight;
        Traits::edge_descriptor reverse;
    };

    typedef boost::adjacency_list<boost::vecS, boost::vecS, boost::directedS, VertexProps, EdgeProps > DirectedGraph;

    int main() {


        DirectedGraph g;

        // ETH / BTC
        std::vector<st_order> trades{
            st_order{0.0101,10.0,"SELL"},
            st_order{0.01,3.0,"BUY"},
            st_order{0.0102,5.0,"SELL"},
            st_order{0.2,42.0,"BUY"},
        };


        std::vector<boost::graph_traits<DirectedGraph>::vertex_descriptor> vertices;
        for(unsigned int vertex_index = 0; vertex_index < trades.size(); vertex_index++)
        {
            vertices.push_back(boost::add_vertex({vertex_index}, g));
        }


        std::map<DirectedGraph::vertex_descriptor, std::map<DirectedGraph::vertex_descriptor, Traits::edge_descriptor>> edges;


int ifirst = 0;
for(auto& first : vertices)
{
    int isecond = 0;
    for(auto& second : vertices)
    {

        if(first == second || trades[ifirst].type.compare(trades[isecond].type) == 0)
        {
            isecond++;
            continue;
        }

        double amount = trades[isecond].amount;

        if(trades[isecond].type.compare("SELL") == 0)
            amount = amount * trades[isecond].price;

        edges[first][second] = boost::add_edge(first, second, {amount, amount, (trades[isecond].price / trades[ifirst].price)} , g).first;
        std::cout << "Add Edge: From " << first << " to " << second << std::endl;

        isecond++;
    }
    ifirst++;
}


for(auto& i : vertices)
{
    for(auto& j : vertices)
    {
        if(i == j)
            continue;

        if(edges.find(i) != edges.end() && edges[i].find(j) != edges[i].end())
        {
            if(edges.find(j) == edges.end() || edges[j].find(i) == edges[j].end())
            {
                throw std::runtime_error("No return edge found: "+std::to_string(i)+" "+std::to_string(j));
            }

            auto edge = boost::edge(i,j,g).first;
            g[edge].reverse = edges[i][j];

        }
    }
}



        double flow = boost::push_relabel_max_flow(g, vertices[0], vertices[1],
                boost::get(&EdgeProps::capacity, g),
                boost::get(&EdgeProps::residual_capacity, g),
                boost::get(&EdgeProps::reverse, g),
                boost::get(boost::vertex_index, g)
            );

// Now boost::cycle_canceling() would follow

    std::cout << "END << std::endl;
    return 0;
    };

我的程序的“正常”输出是：

Add Edge: From 0 to 1
Add Edge: From 0 to 3
Add Edge: From 1 to 0
Add Edge: From 1 to 2
Add Edge: From 2 to 1
Add Edge: From 2 to 3
Add Edge: From 3 to 0
Add Edge: From 3 to 2

作为流程图：

​

​

我的程序在push_relabel_max_flow-function中声明。以下是完整的错误代码(在运行时中打印)：

    /usr/local/include/boost/graph/push_relabel_max_flow.hpp:707: typename
 boost::property_traits<IndexMap>::value_type 
boost::push_relabel_max_flow(Graph&, typename 
boost::graph_traits<Graph>::vertex_descriptor, typename 
boost::graph_traits<Graph>::vertex_descriptor, CapacityEdgeMap, 
ResidualCapacityEdgeMap, ReverseEdgeMap, VertexIndexMap) [with Graph = 
boost::adjacency_list<boost::vecS, boost::vecS, boost::directedS, 
VertexProps, EdgeProps>; CapacityEdgeMap = 
boost::adj_list_edge_property_map<boost::directed_tag, double, double&, long 
unsigned int, EdgeProps, double EdgeProps::*>; ResidualCapacityEdgeMap = 
boost::adj_list_edge_property_map<boost::directed_tag, double, double&, long 
unsigned int, EdgeProps, double EdgeProps::*>; ReverseEdgeMap = 
boost::adj_list_edge_property_map<boost::directed_tag, 
boost::detail::edge_desc_impl<boost::directed_tag, long unsigned int>, 
boost::detail::edge_desc_impl<boost::directed_tag, long unsigned int>&, long
 unsigned int, EdgeProps, boost::detail::edge_desc_impl<boost::directed_tag, 
long unsigned int> EdgeProps::*>; VertexIndexMap = 
boost::vec_adj_list_vertex_id_map<VertexProps, long unsigned int>; typename 
boost::property_traits<IndexMap>::value_type = double; typename 
boost::graph_traits<Graph>::vertex_descriptor = long unsigned int]: Assertion
 `algo.is_optimal()' failed.

在消息的末尾，您可以看到断言: algo.is_optimal()失败了。我完全不知道这意味着什么。

在源文件(boost/graph/push_relabel_max_ file . the )中，它被定义为：

bool is_optimal() {
        // check if mincut is saturated...
        global_distance_update();
        return get(distance, src) >= n;
      }

我在谷歌上搜索过却什么都没找到。我用错误的方式传递参数了吗？这是因为我使用double作为容量(但是，如果我没有记错的话，"文档“描述了使用double作为容量的可能性)？此外，我在文档中发现了这句话：

CapacityEdgeMap参数上限必须将E中的每个边映射为正数，和E^T中的每个边映射到0。

大胆的部分意味着什么？这是否意味着我必须将从接收器顶点到0的所有输出边的容量设置为0？

Answer 1

您需要将反向边缘的容量设置为0。

所以你需要：

auto edge = boost::edge(i,j,g).first;
g[edge].reverse = edges[i][j];
g[edges[i][j]].capacity = 0;

但我不知道为什么。在查看dimacs.hpp时，我注意到它们创建了它们的反向边，并给它们提供了0的容量。约3/4的方式下一页：

capacity[e1] = cap;
capacity[e2] = 0;
reverse_edge[e1] = e2;
reverse_edge[e2] = e1;

如果没有这个约束，该算法将尝试将这些作为法线边缘处理。您引用的文档中的部分描述了这一点，但并不是完全显而易见。

该算法对输入图和属性映射参数有几个特殊的要求。首先，表示网络的有向图G=(V，E)必须扩展为包含E中每条边的反向边，即输入图应该是Gin = (V，{ E ^T})。ReverseEdgeMap自变量rev必须将原图中的每一条边映射到它的反向边，即E中所有(u，v)的所有(u，v)的(u，v) -> (v，u)。CapacityEdgeMap参数上限必须将E中的每一条边映射为正数，E^T中的每一条边映射到0。

我认为这里E^T的意思是转置而不是目标。你必须知道，有向邻接矩阵的转置实际上是所有边的反向。这就是为什么他们说输入图是G= {V，E^T}。边加上需要添加的反向边。

附带注意:在long中将double更改为推拉实例非常好。