How to Convert Existing Graphs to BGL

The Adaptor pattern [12] typically requires that the adaptee object be contained inside a new class that provides the desired interface. This containment is not required when wrapping a graph for BGL because the BGL graph interface consists solely of free (global) functions. Instead of creating a new graph class, you need to overload all the free functions required by the interface. We call this free function wrapper approach external adaptation.

One of the more commonly used graph classes is the LEDA parameterized GRAPH class [22]. In this section we will show how to create a BGL interface for this class. The first question is which BGL interfaces (or concepts) we should implement. The following concepts are straightforward and easy to implement on top of LEDA: VertexListGraph, BidirectionalGraph, and MutableGraph.

All types associated with a BGL graph class are accessed though the graph_traits class. We can partially specialize this traits class for the LEDA GRAPH class in the following way. The node and edge are the LEDA types for representing vertices and edges. The LEDA GRAPH is for directed graphs, so we choose directed_tag for the directed_category. The LEDA GRAPH does not automatically prevent the insertion of parallel edges, so we choose allow_parallel_edge_tag for the edge_parallel_category. The return type for the LEDA function number_of_nodes() and number_of_edges() is int, so we choose that type for the vertices_size_type and edges_size_type of the graph. The iterator types will be more complicated, so we leave that for later.

namespace boost {
  template <class vtype, class etype>
  struct graph_traits< GRAPH<vtype,etype> > {
    typedef node vertex_descriptor;
    typedef edge edge_descriptor;

    // iterator typedefs...

    typedef directed_tag directed_category;
    typedef allow_parallel_edge_tag edge_parallel_category;
    typedef int vertices_size_type;
    typedef int edges_size_type;
  };
} // namespace boost

First we will write the source() and target() functions of the IncidenceGraph concept, which is part of the VertexListGraph concept. We use the LEDA GRAPH type for the graph parameter, and use graph_traits to specify the edge parameter and the vertex return type. We could also just use the LEDA types node and edge here, but it is better practice to always use graph_traits. If there is a need to change the associated vertex or edge type, you will only need to do it in one place, inside the specialization of graph_traits instead of throughout your code. LEDA provides source() and target() functions, so we merely call them.

namespace boost {
  template <class vtype, class etype>
  typename graph_traits< GRAPH<vtype,etype> >::vertex_descriptor
  source(
    typename graph_traits< GRAPH<vtype,etype> >::edge_descriptor e,
    const GRAPH<vtype,etype>& g)
  {
    return source(e);
  }

  template <class vtype, class etype>
  typename graph_traits< GRAPH<vtype,etype> >::vertex_descriptor
  target(
    typename graph_traits< GRAPH<vtype,etype> >::edge_descriptor e,
    const GRAPH<vtype,etype>& g)
  {
    return target(e);
  }
} // namespace boost

The next function from IncidenceGraph that we need to implement is out_edges(). This function returns a pair of out-edge iterators. Since LEDA does not use STL-style iterators we need to implement some. There is a very handy boost utility for implementing iterators, called iterator_adaptor. Writing a standard conforming iterator classes is actually quite difficult, harder than you may think. With the iterator_adaptor class, you just implement a policy class and the rest is taken care of. The following code is the policy class for our out-edge iterator. In LEDA, the edge object itself is used like an iterator. It has functions Succ_Adj_Edge() and Pred_Adj_Edge() to move to the next and previous (successor and predecessor) edge. One gotcha in using the LEDA edge as an iterator comes up in the dereference() function, which merely returns the edge object. The dereference operator for standard compliant iterators must be a const member function, which is why the edge argument is const. However, the return type should not be const, hence the need for const_cast.

namespace boost {
  struct out_edge_iterator_policies
  {
    static void increment(edge& e)
    { e = Succ_Adj_Edge(e,0); }

    static void decrement(edge& e)
    { e = Pred_Adj_Edge(e,0); }

    template <class Reference>
    static Reference dereference(type<Reference>, const edge& e)
    { return const_cast<Reference>(e); }

    static bool equal(const edge& x, const edge& y)
    { return x == y; }
  };
} // namespace boost

Now we go back to the graph_traits class, and use iterator_adaptor to fill in the out_edge_iterator. We use the iterator type to specify the associated types of the iterator, including iterator category and value type.

  namespace boost {
    template <class vtype, class etype>
    struct graph_traits< GRAPH<vtype,etype> > {
      // ...
      typedef iterator_adaptor<edge,
        out_edge_iterator_policies,
        iterator<std::bidirectional_iterator_tag,edge>
      > out_edge_iterator;
      // ...
    };
  } // namespace boost

With the out_edge_iterator defined in graph_traits we are ready to define the out_edges() function. The following definition looks complicated at first glance, but it is really quite simple. The return type should be a pair of out-edge iterators, so we use std::pair and then graph_traits to access the out-edge iterator types. In the body of the function we construct the out-edge iterators by passing in the first adjacenct edge for the begin iterator, and 0 for the end iterator (which is used in LEDA as the end sentinel). The 0 argument to First_Adj_Edge tells LEDA we want out-edges (and not in-edges).

namespace boost {
  template <class vtype, class etype>
  inline std::pair<
    typename graph_traits< GRAPH<vtype,etype> >::out_edge_iterator,
    typename graph_traits< GRAPH<vtype,etype> >::out_edge_iterator >
  out_edges(
    typename graph_traits< GRAPH<vtype,etype> >::vertex_descriptor u,
    const GRAPH<vtype,etype>& g)
  {
    typedef typename graph_traits< GRAPH<vtype,etype> >
      ::out_edge_iterator Iter;
    return std::make_pair( Iter(First_Adj_Edge(u,0)), Iter(0) );
  }
} // namespace boost

The rest of the iterator types and interface functions are constructed using the same techniques as above. The complete code for the LEDA wrapper interface is in boost/graph/leda_graph.hpp. In the following code we use the BGL concept checks to make sure that we correctly implemented the BGL interface. These checks do not test the run-time behaviour of the implementation; that is tested in test/graph.cpp.

  #include <boost/graph/graph_concepts.hpp>
  #include <boost/graph/leda_graph.hpp>

  int
  main(int,char*[])
  {
    typedef GRAPH<int,int> Graph;
    BOOST_CONCEPT_ASSERT(( VertexListGraphConcept<Graph> ));
    BOOST_CONCEPT_ASSERT(( BidirectionalGraphConcept<Graph> ));
    BOOST_CONCEPT_ASSERT(( MutableGraphConcept<Graph> ));
    return 0;
  }