Boost Graph Library: Converting Existing Graphs to BGL

# How to Convert Existing Graphs to BGL

Though the main goal of BGL is to aid the development of new applications and graph algorithms, there are quite a few existing codes that could benefit from using BGL algorithms. One way to use the BGL algorithms with existing graph data structures is to copy data from the older graph format into a BGL graph which could then be used in the BGL algorithms. The problem with this approach is that it can be expensive to make this copy. Another approach is to wrap the existing graph data structure with a BGL interface.

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;
      }

Copyright © 2000-2001 | Jeremy Siek, Indiana University (jsiek@osl.iu.edu) Lie-Quan Lee, Indiana University (llee@cs.indiana.edu) Andrew Lumsdaine, Indiana University (lums@osl.iu.edu)