Question

I’m currently working on a project that enumerates the k-best solutions of a dynamic program using a directed hypergraph framework. My current implementation (in Python) works well, but is fairly slow. The algorithm performs a number of tight loops and a fair bit of recursion. I really think that I could realize significant speed improvements using a C++ implementation. However, after a fair bit of searching, I was unable to find any libraries that provide hypergraph implementations in C++ (specifically directed hypergraphs — but I was unable to find even libraries for undirected hypergraphs). Does anyone know of such a library? It seems there was a GSoC proposal to bring hypergraph support to boost a few years ago, but it looks like it didn’t really pan out.

Answer 1

I don’t know of a library, but you could roll your own.

After messing around with the code for three days, I finally got a hypermap to compile without warnings on MSVC10 and GCC(http://ideone.com/oj46o).
Declarations:

#include <map>
#include <functional>
#include <memory>

template<class V, class E=int, class PV = std::less<V>, class PE=std::less<E>, class A=std::allocator<V> >
// V is data type of vertex
// E is identifier of Edge
// PV is node sorting predicate
// PE is edge sorting predicate
// A is allocator
class hypergraph {

#if _MSC_VER <= 1600
    typedef A sub_allocator;
#else
    typedef std::scoped_allocator_adaptor<A> sub_allocator;
#endif

public:
    class vertex;
    class edge;
    typedef std::map<V, vertex, PV, sub_allocator> vertexset;
    typedef std::map<E, edge, PE, sub_allocator> edgeset;
    typedef typename vertexset::iterator vertexiter;
    typedef typename edgeset::iterator edgeiter;
    typedef typename vertexset::const_iterator cvertexiter;
    typedef typename edgeset::const_iterator cedgeiter;

    typedef std::reference_wrapper<const V> rwv;
    typedef std::reference_wrapper<const E> rwe;
    typedef std::reference_wrapper<vertex> rwvertex;
    typedef std::reference_wrapper<edge> rwedge;
    typedef std::map<rwv, rwvertex, PV, sub_allocator> ivertexset;
    typedef std::map<rwe, rwedge, PE, sub_allocator> iedgeset;
    typedef typename ivertexset::iterator ivertexiter;
    typedef typename iedgeset::iterator iedgeiter;
    typedef typename ivertexset::const_iterator civertexiter;
    typedef typename iedgeset::const_iterator ciedgeiter;

    class vertex { 
        friend class hypergraph<V,E,PV,PE,A>;
        iedgeset edges_;
        vertex(const PE&, const sub_allocator&);/* so users can'V make their own vertices*/
    public:
        vertex(vertex&&);
        vertex& operator=(vertex&&);
        iedgeset& edges();
        const iedgeset& edges() const;
    };
    class edge { 
        friend class hypergraph<V,E,PV,PE,A>;
        ivertexset vertices_;
        ivertexiter head_;
        edge(const PV&, const sub_allocator&); /* so users can'V make their own edges*/
    public: 
        edge(edge&&);
        edge& operator=(edge&&);
        void set_head(const V& v);
        const V* get_head() const;
        ivertexset& vertices();
        const ivertexset& vertices() const;
    };

    hypergraph(const PV& vertexpred=PV(), const PE& edgepred=PE(), const A& alloc=A());

    std::pair<vertexiter,bool> add_vertex(V v=V());
    std::pair<edgeiter,bool> add_edge(E e=E());
    vertexiter erase_vertex(const vertexiter& iter);
    vertexiter erase_vertex(const V& rhs);
    edgeiter erase_edge(const edgeiter& iter);
    edgeiter erase_edge(const E& rhs);

    void connect(const E& e, const V& v);
    void connect(const edgeiter& ei, const vertexiter& vi);
    void disconnect(const E& e, const V& v);
    void disconnect(const edgeiter& ei, const vertexiter& vi);

    vertexset& vertices();
    const vertexset& vertices() const;
    edgeset& edges();
    const edgeset& edges() const;

    A get_allocator() const;
protected:
    hypergraph(const hypergraph& rhs);
    hypergraph& operator=(const hypergraph& rhs);
    PV pv_;
    PE pe_;
    A a_;
    vertexset vertices_;
    edgeset edges_;
};

namespace std {
    template<class E, class T, class R>
    std::basic_ostream<E,T>& operator<<(std::basic_ostream<E,T>& s, const std::reference_wrapper<R>& r);

    template<class E, class T, class R>
    std::basic_istream<E,T>& operator>>(std::basic_istream<E,T>& s, std::reference_wrapper<R>& r);      
}

Definitions:

#include <algorithm>
#include <cassert>

template<class V, class E, class PV, class PE, class A>
inline hypergraph<V,E,PV,PE,A>::vertex::vertex(const PE& pred, const typename hypergraph<V,E,PV,PE,A>::sub_allocator& alloc) 
    : edges_(pred, alloc)
{}

template<class V, class E, class PV, class PE, class A>
inline hypergraph<V,E,PV,PE,A>::vertex::vertex(typename hypergraph<V,E,PV,PE,A>::vertex&& rhs)
    :  edges_(std::move(rhs.edges_))
{}

template<class V, class E, class PV, class PE, class A>
inline typename hypergraph<V,E,PV,PE,A>::vertex& hypergraph<V,E,PV,PE,A>::vertex::operator=(typename hypergraph<V,E,PV,PE,A>::vertex&& rhs)
{
    edges_ = std::move(rhs);
    return *this;
}

template<class V, class E, class PV, class PE, class A>
inline typename hypergraph<V,E,PV,PE,A>::iedgeset& hypergraph<V,E,PV,PE,A>::vertex::edges()
{return edges_;}

template<class V, class E, class PV, class PE, class A>
inline const typename hypergraph<V,E,PV,PE,A>::iedgeset& hypergraph<V,E,PV,PE,A>::vertex::edges() const
{return edges_;}

template<class V, class E, class PV, class PE, class A>
inline hypergraph<V,E,PV,PE,A>::edge::edge(const PV& pred, const typename hypergraph<V,E,PV,PE,A>::sub_allocator& alloc) 
    : vertices_(pred, alloc)
    , head_(vertices_.end())
{}

template<class V, class E, class PV, class PE, class A>
inline hypergraph<V,E,PV,PE,A>::edge::edge(edge&& rhs)
    : vertices_(rhs.vertices_)
    , head_(rhs.head_!=rhs.vertices_.end() ? vertices_.find(rhs.head_->first) : vertices_.end())
{}

template<class V, class E, class PV, class PE, class A>
inline typename hypergraph<V,E,PV,PE,A>::edge& hypergraph<V,E,PV,PE,A>::edge::operator=(typename hypergraph<V,E,PV,PE,A>::edge&& rhs)
{
    vertices_ = std::move(rhs);
    if (rhs.head_ != rhs.vertices_.end())
        head_ = vertices_.find(rhs.head_->first);
    else
        head_ = vertices_.end();
    return *this;
}

template<class V, class E, class PV, class PE, class A>
inline void hypergraph<V,E,PV,PE,A>::edge::set_head(const V& v)
{
    ivertexiter iter = vertices_.find(std::ref(v));
    assert(iter != vertices_.end());
    head_ = iter;
}

template<class V, class E, class PV, class PE, class A>
inline const V* hypergraph<V,E,PV,PE,A>::edge::get_head() const
{return (head_ != vertices_.end() ? &head_->first.get() : NULL);}

template<class V, class E, class PV, class PE, class A>
inline const typename hypergraph<V,E,PV,PE,A>::ivertexset& hypergraph<V,E,PV,PE,A>::edge::vertices() const
{ return vertices_; }

template<class V, class E, class PV, class PE, class A>
inline typename hypergraph<V,E,PV,PE,A>::ivertexset& hypergraph<V,E,PV,PE,A>::edge::vertices()
{ return vertices_; }

template<class V, class E, class PV, class PE, class A>
inline hypergraph<V,E,PV,PE,A>::hypergraph(const PV& vertexpred, const PE& edgepred, const A& alloc)
    :pv_(vertexpred)
    ,pe_(edgepred)
    ,a_(alloc)
    ,vertices_(vertexpred, a_)
    ,edges_(edgepred, a_)
{}

template<class V, class E, class PV, class PE, class A>
inline std::pair<typename hypergraph<V,E,PV,PE,A>::vertexiter, bool> hypergraph<V,E,PV,PE,A>::add_vertex(V v)
{ return vertices_.insert(std::pair<V, vertex>(std::move(v),vertex(pe_, a_))); }

template<class V, class E, class PV, class PE, class A>
inline std::pair<typename hypergraph<V,E,PV,PE,A>::edgeiter, bool> hypergraph<V,E,PV,PE,A>::add_edge(E e)
{ return edges_.insert(std::pair<E,edge>(std::move(e), edge(pv_, a_))); }

template<class V, class E, class PV, class PE, class A>
inline typename hypergraph<V,E,PV,PE,A>::vertexiter hypergraph<V,E,PV,PE,A>::erase_vertex(const typename hypergraph<V,E,PV,PE,A>::vertexiter& iter)
{ 
    for(auto i = iter->edges().begin(); i != iter->edges().end(); ++i)
        i->erase(*iter);
    return vertices_.erase(iter); 
}

template<class V, class E, class PV, class PE, class A>
inline typename hypergraph<V,E,PV,PE,A>::vertexiter hypergraph<V,E,PV,PE,A>::erase_vertex(const V& rhs)
{
    vertexiter vi = vertices_.find(rhs);
    assert(vi != vertices_.end());
    vertex& v = vi->second;
    for(auto i = v.edges().begin(); i != v.edges().end(); ++i)
        i->second.get().vertices_.erase(std::ref(vi->first));
    return vertices_.erase(vi); 
}

template<class V, class E, class PV, class PE, class A>
inline typename hypergraph<V,E,PV,PE,A>::edgeiter hypergraph<V,E,PV,PE,A>::erase_edge(const typename hypergraph<V,E,PV,PE,A>::edgeiter& iter)
{ 
    for(auto i = iter->vertices().begin(); i != iter->vertices().end(); ++i)
        i->edges_.erase(*iter);
    return edges_.erase(iter); 
}

template<class V, class E, class PV, class PE, class A>
inline typename hypergraph<V,E,PV,PE,A>::edgeiter hypergraph<V,E,PV,PE,A>::erase_edge(const E& rhs)
{ 
    edgeiter ei = edges_.find(rhs);
    assert(ei != edges_.end());
    edge& e = ei->second;
    for(auto i = e.vertices().begin(); i != e.vertices().end(); ++i)
        i->second.get().edges_.erase(std::ref(ei->first));
    return edges_.erase(ei); 
}

template<class V, class E, class PV, class PE, class A>
inline void hypergraph<V,E,PV,PE,A>::connect(const E& e, const V& v)
{
    vertexiter vi = vertices_.find(v);
    edgeiter ei = edges_.find(e);
    assert(vi != vertices_.end());
    assert(ei != edges_.end());
    vi->second.edges_.insert(typename iedgeset::value_type(std::ref(ei->first), std::ref(ei->second)));
    auto n = ei->second.vertices_.insert(typename ivertexset::value_type(std::ref(vi->first), std::ref(vi->second)));
    if (ei->second.vertices_.size()==1)
        ei->second.head_ = n.first;
}

template<class V, class E, class PV, class PE, class A>
inline void hypergraph<V,E,PV,PE,A>::connect(const typename hypergraph<V,E,PV,PE,A>::edgeiter& ei, const typename hypergraph<V,E,PV,PE,A>::vertexiter& vi)
{
    assert(std::distance(vertices_.begin(), vi)>=0); //actually asserts that the iterator belongs to this container
    assert(std::distance(edges_.begin(), ei)>=0); //actually asserts that the iterator belongs to this container
    vi->edges_.insert(typename iedgeset::value_type(std::ref(ei->first), std::ref(ei->second)));
    auto n = ei->vertices_.insert(typename ivertexset::value_type(std::ref(vi->first), std::ref(vi->second)));
    if (ei->second.verticies_.size()==1)
        ei->second.head_ = n.first;
}

template<class V, class E, class PV, class PE, class A>
inline void hypergraph<V,E,PV,PE,A>::disconnect(const E& e, const V& v)
{
    edgeiter ei = edges_.find(e);
    vertexiter vi = vertices_.find(v);
    assert(ei != edges.end());
    assert(vi != vertices_.end());
    if (ei->head_.first == v) {
        if (ei->head_ != ei->vertices.begin())
            ei->head = ei->vertices.begin();
        else 
            ei->head = ei->vertices.end();
    }
    ei->vertices_.erase(std::ref(vi->first));
    vi->edges_.erase(std::ref(ei->first));
}

template<class V, class E, class PV, class PE, class A>
inline void hypergraph<V,E,PV,PE,A>::disconnect(const typename hypergraph<V,E,PV,PE,A>::edgeiter& ei, const typename hypergraph<V,E,PV,PE,A>::vertexiter& vi)
{
    assert(std::distance(edges_.begin(), ei)>=0); //actually asserts that the iterator belongs to this container
    assert(std::distance(vertices_.begin(), vi)>=0); //actually asserts that the iterator belongs to this container
    if (ei->head_.first == vi->first) {
        if (ei->head_ != ei->vertices.begin())
            ei->head = ei->vertices.begin();
        else 
            ei->head = ei->vertices.end();
    }
    ei->vertices_.erase(std::ref(vi->first));
    vi->edges_.erase(std::ref(ei->first));
}

template<class V, class E, class PV, class PE, class A>
inline typename hypergraph<V,E,PV,PE,A>::vertexset& hypergraph<V,E,PV,PE,A>::vertices()
{ return vertices_;}

template<class V, class E, class PV, class PE, class A>
inline const typename hypergraph<V,E,PV,PE,A>::vertexset& hypergraph<V,E,PV,PE,A>::vertices() const
{ return vertices_;}

template<class V, class E, class PV, class PE, class A>
inline typename hypergraph<V,E,PV,PE,A>::edgeset& hypergraph<V,E,PV,PE,A>::edges()
{ return edges_;}

template<class V, class E, class PV, class PE, class A>
inline const typename hypergraph<V,E,PV,PE,A>::edgeset& hypergraph<V,E,PV,PE,A>::edges() const
{ return edges_;}

template<class V, class E, class PV, class PE, class A>
inline A hypergraph<V,E,PV,PE,A>::get_allocator() const
{ return a_;}

namespace std {

    template<class E, class T, class R>
    std::basic_ostream<E,T>& operator<<(std::basic_ostream<E,T>& s, const std::reference_wrapper<R>& r) 
    {return s << r.get();}

    template<class E, class T, class R>
    std::basic_istream<E,T>& operator>>(std::basic_istream<E,T>& s, std::reference_wrapper<R>& r) 
    {return s >> r.get();}

}

Note that this is not thoroughly tested, but it compiles and ran through my mini-suite without errors. (As shown in the IDEOne link). The Vertex types and the Edge identifiers can be any types you want, I tested with int verteces and string edge identifiers.