提升图相等和子图

Question

我正在使用 boost 库编写图挖掘代码，我想知道如何测试：

• 如果两个图使用同构相等（仅当图具有相同的结构和相同的标签时才返回真）

• 如果一个图是另一个图的子图？

这是图表文件：3test.txt

这是我制作的部分源代码：

#include <boost/graph/adjacency_list.hpp>
#include <boost/graph/vf2_sub_graph_iso.hpp>
#include <boost/algorithm/string/split.hpp>
#include <boost/algorithm/string/classification.hpp>
#include <boost/config.hpp>
#include <boost/graph/isomorphism.hpp>
#include <boost/graph/graph_utility.hpp>

#include <fstream>
#include <iostream>
#include <vector>


//for mmap:
#include <sys/mman.h>
#include <sys/stat.h>
#include <fcntl.h>

using namespace std;
using namespace boost;


//==========STRUCTURES==========
// vertex
struct VertexProperties {
    int id;
    int label;
    VertexProperties(unsigned i = 0, unsigned l = 0) : id(i), label(l) {}
};

// edge
struct EdgeProperties {
    unsigned label;
    EdgeProperties(unsigned l = 0) :label(l) {}
};

// Graph
struct GraphProperties {
    unsigned id;
    unsigned label;
    GraphProperties(unsigned i = 0, unsigned l = 0) : id(i), label(l) {}
};

// adjency list
typedef boost::adjacency_list<boost::vecS, boost::vecS, boost::undirectedS, VertexProperties, EdgeProperties,
GraphProperties> Graph;

// descriptors

typedef boost::graph_traits<Graph>::vertex_descriptor vertex_t;
typedef std::pair<boost::graph_traits<Graph>::edge_descriptor, bool> edge_t;
// iterators
typedef graph_traits<Graph>::vertex_iterator vertex_iter;
typedef graph_traits<Graph>::edge_iterator edge_iter;
typedef std::pair<edge_iter, edge_iter> edge_pair;


//*********global variables*************


vector<Graph> dataG;



//=================callback used fro subgraph_iso=================================================================
// Default print_callback
template <typename Graph1,typename Graph2>

  struct my_callback {

    my_callback(const Graph1& graph1, const Graph2& graph2)
      : graph1_(graph1), graph2_(graph2) {}

    template <typename CorrespondenceMap1To2,
              typename CorrespondenceMap2To1>
    bool operator()(CorrespondenceMap1To2 f, CorrespondenceMap2To1) const {

      return true;
    }

  private:
    const Graph1& graph1_;
    const Graph2& graph2_;
  };


//==========handle_error==========
void handle_error(const char *msg) {
    perror(msg);
    exit(255);
}


//============READ ALL THE FILE AND RETURN A STRING===================
const char *readfromfile(const char *fname, size_t &length) {
    int fd = open(fname, O_RDONLY);
    if (fd == -1)
        handle_error("open");

    // obtain file size
    struct stat sb;
    if (fstat(fd, &sb) == -1)
        handle_error("fstat");

    length = sb.st_size;

    const char *addr = static_cast<const char *>(mmap(NULL, length, PROT_READ, MAP_PRIVATE, fd, 0u));
    if (addr == MAP_FAILED)
        handle_error("mmap");

    // TODO close fd at some point in time, call munmap(...)
    return addr;
}
//==========SPLIT THE STRING BY NEWLINE (\n) ==========
vector<string> splitstringtolines(string const& str) {

    std::vector<string> split_vector;
    split(split_vector, str, is_any_of("\n"));

    return split_vector;
}

//============Get a string starting from pos============
string getpos(int const& pos, string const& yy) {
    size_t i = pos;
    string str;
    for (; ((yy[i] != ' ') && (i < yy.length())); i++) {str += yy[i];}
    return str;
}
//==================read string vector and return graphs vector===================
std::vector<Graph> creategraphs(std::vector<string> const& fichlines) {

    for (string yy : fichlines) {
        switch (yy[0]) {
            case 't': {
                string str2 = getpos(4, yy);
                unsigned gid = atoi(str2.c_str());
                dataG.emplace_back(GraphProperties(gid, gid));

            } break;
            case 'v': {
                assert(!dataG.empty()); // assert will terminate the program  if its argument turns out to be false
                // cout<<yy<<endl;
                int vId, vLabel;
                string vvv = getpos(2, yy);
                vId = atoi(vvv.c_str());
                string vvvv = getpos((int)vvv.length() + 3, yy);
                // cout<<vvvv<<endl;
                vLabel = atoi(vvvv.c_str());
                boost::add_vertex(VertexProperties(vId, vLabel), dataG.back());
            }

                break;

            case 'e': { // cout<<yy<<endl;
                assert(!dataG.empty()); // assert will terminate the program  if its argument turns out to be false

                int fromId, toId, eLabel;
                string eee = getpos(2, yy);
                // cout<<eee<<endl;
                fromId = atoi(eee.c_str());
                string eee2 = getpos((int)eee.length() + 3, yy);
                // cout<<eee2<<endl;
                toId = atoi(eee2.c_str());
                int c = (int)eee.length() + (int)eee2.length() + 4;
                //    cout<<c<<endl;
                string eee3 = getpos(c, yy);
                //  cout<<eee3<<endl;
                eLabel = atoi(eee3.c_str());
                for (size_t i = 0; i < num_vertices(dataG.back()); ++i) // size_t vertice number in the graph
                {
                    if(dataG.back()[i].id==fromId) fromId=i;
                    else if(dataG.back()[i].id==toId) toId=i;
                }

                boost::add_edge(fromId, toId, EdgeProperties(eLabel), dataG.back());

            } break;
        }
    }

    return dataG;
}

//==============================M A I N   P R O G R A M =======================================
int main()
{

    size_t length;


    std::vector<Graph> dataG =creategraphs(splitstringtolines(readfromfile("3test.txt", length)));

    cout<<"***PS***\n dataG[0] is a subgraph of dataG[1]\n dataG[2] is the same as dataG[0]\n dataG[3] is the same as dataG[0] but with other labels.\n"<<endl;


    my_callback<Graph, Graph> my_callback(dataG[0], dataG[3]);
  cout<<"equal(dataG[0], dataG[3],my_callback)="<<vf2_graph_iso(dataG[0], dataG[3],my_callback)<<endl;
 mcgregor_common_subgraphs(dataG[0], dataG[3], true, my_callback);


}

不幸的是，当我运行它时，我得到了这些错误：

/usr/include/boost/graph/mcgregor_common_subgraphs.hpp||In instantiation of ‘bool boost::detail::mcgregor_common_subgraphs_internal(const GraphFirst&, const GraphSecond&, const VertexIndexMapFirst&, const VertexIndexMapSecond&, CorrespondenceMapFirstToSecond, CorrespondenceMapSecondToFirst, VertexStackFirst&, EdgeEquivalencePredicate, VertexEquivalencePredicate, bool, SubGraphInternalCallback) [with GraphFirst = boost::adjacency_list<boost::vecS, boost::vecS, boost::undirectedS, VertexProperties, EdgeProperties, GraphProperties>; GraphSecond = boost::adjacency_list<boost::vecS, boost::vecS, boost::undirectedS, VertexProperties, EdgeProperties, GraphProperties>; VertexIndexMapFirst = boost::vec_adj_list_vertex_id_map<VertexProperties, unsigned int>; VertexIndexMapSecond = boost::vec_adj_list_vertex_id_map<VertexProperties, unsigned int>; CorrespondenceMapFirstToSecond = boost::shared_array_property_map<unsigned int, boost::vec_adj_list_vertex_id_map<VertexProperties, unsigned int> >; CorrespondenceMapSecondToFirst = boost::shared_array_property_map<unsigned int, boost::vec_adj_list_vertex_id_map<VertexProperties, unsigned int> >; VertexStackFirst = std::stack<unsigned int, std::deque<unsigned int, std::allocator<unsigned int> > >; EdgeEquivalencePredicate = boost::always_equivalent; VertexEquivalencePredicate = boost::always_equivalent; SubGraphInternalCallback = my_callback<boost::adjacency_list<boost::vecS, boost::vecS, boost::undirectedS, VertexProperties, EdgeProperties, GraphProperties>, boost::adjacency_list<boost::vecS, boost::vecS, boost::undirectedS, VertexProperties, EdgeProperties, GraphProperties> >]’:|
/usr/include/boost/graph/mcgregor_common_subgraphs.hpp|433|required from ‘void boost::detail::mcgregor_common_subgraphs_internal_init(const GraphFirst&, const GraphSecond&, VertexIndexMapFirst, VertexIndexMapSecond, EdgeEquivalencePredicate, VertexEquivalencePredicate, bool, SubGraphInternalCallback) [with GraphFirst = boost::adjacency_list<boost::vecS, boost::vecS, boost::undirectedS, VertexProperties, EdgeProperties, GraphProperties>; GraphSecond = boost::adjacency_list<boost::vecS, boost::vecS, boost::undirectedS, VertexProperties, EdgeProperties, GraphProperties>; VertexIndexMapFirst = boost::vec_adj_list_vertex_id_map<VertexProperties, unsigned int>; VertexIndexMapSecond = boost::vec_adj_list_vertex_id_map<VertexProperties, unsigned int>; EdgeEquivalencePredicate = boost::always_equivalent; VertexEquivalencePredicate = boost::always_equivalent; SubGraphInternalCallback = my_callback<boost::adjacency_list<boost::vecS, boost::vecS, boost::undirectedS, VertexProperties, EdgeProperties, GraphProperties>, boost::adjacency_list<boost::vecS, boost::vecS, boost::undirectedS, VertexProperties, EdgeProperties, GraphProperties> >]’|
/usr/include/boost/graph/mcgregor_common_subgraphs.hpp|484|required from ‘void boost::mcgregor_common_subgraphs(const GraphFirst&, const GraphSecond&, bool, SubGraphCallback) [with GraphFirst = boost::adjacency_list<boost::vecS, boost::vecS, boost::undirectedS, VertexProperties, EdgeProperties, GraphProperties>; GraphSecond = boost::adjacency_list<boost::vecS, boost::vecS, boost::undirectedS, VertexProperties, EdgeProperties, GraphProperties>; SubGraphCallback = my_callback<boost::adjacency_list<boost::vecS, boost::vecS, boost::undirectedS, VertexProperties, EdgeProperties, GraphProperties>, boost::adjacency_list<boost::vecS, boost::vecS, boost::undirectedS, VertexProperties, EdgeProperties, GraphProperties> >]’|
/home/mohsenuss91/Bureau/NouvelleApprocheBOOST/stackoverflow.cpp|211|required from here|
/usr/include/boost/graph/mcgregor_common_subgraphs.hpp|337|error: no match for call to ‘(my_callback<boost::adjacency_list<boost::vecS, boost::vecS, boost::undirectedS, VertexProperties, EdgeProperties, GraphProperties>, boost::adjacency_list<boost::vecS, boost::vecS, boost::undirectedS, VertexProperties, EdgeProperties, GraphProperties> >) (boost::shared_array_property_map<unsigned int, boost::vec_adj_list_vertex_id_map<VertexProperties, unsigned int> >&, boost::shared_array_property_map<unsigned int, boost::vec_adj_list_vertex_id_map<VertexProperties, unsigned int> >&, VertexSizeFirst&)’|
/home/mohsenuss91/Bureau/NouvelleApprocheBOOST/stackoverflow.cpp|69|note: candidate is:|
/home/mohsenuss91/Bureau/NouvelleApprocheBOOST/stackoverflow.cpp|76|note: template<class CorrespondenceMap1To2, class CorrespondenceMap2To1> bool my_callback<Graph1, Graph2>::operator()(CorrespondenceMap1To2, CorrespondenceMap2To1) const [with CorrespondenceMap1To2 = CorrespondenceMap1To2; CorrespondenceMap2To1 = CorrespondenceMap2To1; Graph1 = boost::adjacency_list<boost::vecS, boost::vecS, boost::undirectedS, VertexProperties, EdgeProperties, GraphProperties>; Graph2 = boost::adjacency_list<boost::vecS, boost::vecS, boost::undirectedS, VertexProperties, EdgeProperties, GraphProperties>]|
/home/mohsenuss91/Bureau/NouvelleApprocheBOOST/stackoverflow.cpp|76|note:   template argument deduction/substitution failed:|
/usr/include/boost/graph/mcgregor_common_subgraphs.hpp|337|note:   candidate expects 2 arguments, 3 provided|
||=== Build failed: 1 error(s), 4 warning(s) (0 minute(s), 6 second(s)) ===|

Answer 1

文档：

输出： SubGraphCallback user_callback

发现子图时将调用的函数对象。 operator() 必须具有以下形式：

template <typename CorrespondenceMapFirstToSecond,
          typename CorrespondenceMapSecondToFirst>
    bool operator()(
           CorrespondenceMapFirstToSecond correspondence_map_1_to_2,
           CorrespondenceMapSecondToFirst correspondence_map_2_to_1,
           typename graph_traits<GraphFirst>::vertices_size_type subgraph_size
   );

所以至少让函子接受额外的参数：

template <typename Graph1, typename Graph2>
struct my_callback {

    my_callback(const Graph1 &graph1, const Graph2 &graph2) : graph1_(graph1), graph2_(graph2) {}

    template <typename CorrespondenceMap1To2, typename CorrespondenceMap2To1>
    bool operator()(CorrespondenceMap1To2 f, CorrespondenceMap2To1) const {
        // vf2_graph_iso
        return true;
    }

    template <typename CorrespondenceMap1To2, typename CorrespondenceMap2To1, typename X>
    bool operator()(CorrespondenceMap1To2 f, CorrespondenceMap2To1, X) const {
        // mcgregor_common_subgraphs
        return true;
    }

private:
    const Graph1 &graph1_;
    const Graph2 &graph2_;
};

当然，这个 /just/ 修复了编译错误。回调看起来没有什么用处。

输出：

***PS***
 dataG[0] is a subgraph of dataG[1]
 dataG[2] is the same as dataG[0]
 dataG[3] is the same as dataG[0] but with other labels.

equal(dataG[0], dataG[3],my_callback)=1

---

工作样本：

Live On Coliru

#include <boost/graph/adjacency_list.hpp>
#include <boost/graph/vf2_sub_graph_iso.hpp>
#include <boost/graph/mcgregor_common_subgraphs.hpp>
#include <boost/algorithm/string/split.hpp>
#include <boost/algorithm/string/classification.hpp>
#include <boost/config.hpp>
#include <boost/graph/isomorphism.hpp>
#include <boost/graph/graph_utility.hpp>

#include <fstream>
#include <iostream>
#include <vector>

// for mmap:
#include <sys/mman.h>
#include <sys/stat.h>
#include <fcntl.h>

using namespace std;
using namespace boost;

//==========STRUCTURES==========
// vertex
struct VertexProperties {
    int id;
    int label;
    VertexProperties(unsigned i = 0, unsigned l = 0) : id(i), label(l) {}
};

// edge
struct EdgeProperties {
    unsigned label;
    EdgeProperties(unsigned l = 0) : label(l) {}
};

// Graph
struct GraphProperties {
    unsigned id;
    unsigned label;
    GraphProperties(unsigned i = 0, unsigned l = 0) : id(i), label(l) {}
};

// adjency list
typedef boost::adjacency_list<boost::vecS, boost::vecS, boost::undirectedS, VertexProperties, EdgeProperties,
                              GraphProperties> Graph;

// descriptors

typedef boost::graph_traits<Graph>::vertex_descriptor vertex_t;
typedef std::pair<boost::graph_traits<Graph>::edge_descriptor, bool> edge_t;
// iterators
typedef graph_traits<Graph>::vertex_iterator vertex_iter;
typedef graph_traits<Graph>::edge_iterator edge_iter;
typedef std::pair<edge_iter, edge_iter> edge_pair;

//*********global variables*************

vector<Graph> dataG;

//=================callback used fro subgraph_iso=================================================================
// Default print_callback
template <typename Graph1, typename Graph2>
struct my_callback {

    my_callback(const Graph1 &graph1, const Graph2 &graph2) : graph1_(graph1), graph2_(graph2) {}

    template <typename CorrespondenceMap1To2, typename CorrespondenceMap2To1>
    bool operator()(CorrespondenceMap1To2 f, CorrespondenceMap2To1) const {
        // vf2_graph_iso
        return true;
    }

    template <typename CorrespondenceMap1To2, typename CorrespondenceMap2To1, typename X>
    bool operator()(CorrespondenceMap1To2 f, CorrespondenceMap2To1, X) const {
        // mcgregor_common_subgraphs
        return true;
    }

  private:
    const Graph1 &graph1_;
    const Graph2 &graph2_;
};

//==========handle_error==========
void handle_error(const char *msg) {
    perror(msg);
    exit(255);
}

//============READ ALL THE FILE AND RETURN A STRING===================
const char *readfromfile(const char *fname, size_t &length) {
    int fd = open(fname, O_RDONLY);
    if (fd == -1)
        handle_error("open");

    // obtain file size
    struct stat sb;
    if (fstat(fd, &sb) == -1)
        handle_error("fstat");

    length = sb.st_size;

    const char *addr = static_cast<const char *>(mmap(NULL, length, PROT_READ, MAP_PRIVATE, fd, 0u));
    if (addr == MAP_FAILED)
        handle_error("mmap");

    // TODO close fd at some point in time, call munmap(...)
    return addr;
}
//==========SPLIT THE STRING BY NEWLINE (\n) ==========
vector<string> splitstringtolines(string const &str) {

    std::vector<string> split_vector;
    split(split_vector, str, is_any_of("\n"));

    return split_vector;
}

//============Get a string starting from pos============
string getpos(int const &pos, string const &yy) {
    size_t i = pos;
    string str;
    for (; ((yy[i] != ' ') && (i < yy.length())); i++) {
        str += yy[i];
    }
    return str;
}
//==================read string vector and return graphs vector===================
std::vector<Graph> creategraphs(std::vector<string> const &fichlines) {

    for (string yy : fichlines) {
        switch (yy[0]) {
        case 't': {
            string str2 = getpos(4, yy);
            unsigned gid = atoi(str2.c_str());
            dataG.emplace_back(GraphProperties(gid, gid));

        } break;
        case 'v': {
            assert(!dataG.empty()); // assert will terminate the program  if its argument turns out to be false
            // cout<<yy<<endl;
            int vId, vLabel;
            string vvv = getpos(2, yy);
            vId = atoi(vvv.c_str());
            string vvvv = getpos((int)vvv.length() + 3, yy);
            // cout<<vvvv<<endl;
            vLabel = atoi(vvvv.c_str());
            boost::add_vertex(VertexProperties(vId, vLabel), dataG.back());
        }

        break;

        case 'e': {                 // cout<<yy<<endl;
            assert(!dataG.empty()); // assert will terminate the program  if its argument turns out to be false

            int fromId, toId, eLabel;
            string eee = getpos(2, yy);
            // cout<<eee<<endl;
            fromId = atoi(eee.c_str());
            string eee2 = getpos((int)eee.length() + 3, yy);
            // cout<<eee2<<endl;
            toId = atoi(eee2.c_str());
            int c = (int)eee.length() + (int)eee2.length() + 4;
            //    cout<<c<<endl;
            string eee3 = getpos(c, yy);
            //  cout<<eee3<<endl;
            eLabel = atoi(eee3.c_str());
            for (size_t i = 0; i < num_vertices(dataG.back()); ++i) // size_t vertice number in the graph
            {
                if (dataG.back()[i].id == fromId)
                    fromId = i;
                else if (dataG.back()[i].id == toId)
                    toId = i;
            }

            boost::add_edge(fromId, toId, EdgeProperties(eLabel), dataG.back());

        } break;
        }
    }

    return dataG;
}

//==============================M A I N   P R O G R A M =======================================
int main() {

    size_t length;

    std::vector<Graph> dataG = creategraphs(splitstringtolines(readfromfile("3test.txt", length)));

    cout << "***PS***\n dataG[0] is a subgraph of dataG[1]\n dataG[2] is the same as dataG[0]\n dataG[3] is the same "
            "as dataG[0] but with other labels.\n" << endl;

    my_callback<Graph, Graph> my_callback(dataG[0], dataG[3]);
    cout << "equal(dataG[0], dataG[3],my_callback)=" << vf2_graph_iso(dataG[0], dataG[3], my_callback) << endl;
    mcgregor_common_subgraphs(dataG[0], dataG[3], true, my_callback);
}