Parallel BGL Scalable R-MAT generator

# Scalable R-MAT generator

     template<typename ProcessGroup, typename Distribution,
              typename RandomGenerator, typename Graph>
     class scalable_rmat_iterator
     {
     public:
       typedef std::input_iterator_tag iterator_category;
       typedef std::pair<vertices_size_type, vertices_size_type> value_type;
       typedef const value_type& reference;
       typedef const value_type* pointer;
       typedef void difference_type;

       scalable_rmat_iterator();
       scalable_rmat_iterator(ProcessGroup pg, Distribution distrib,
                              RandomGenerator& gen, vertices_size_type n,
                              edges_size_type m, double a, double b, double c,
                              double d, bool permute_vertices = true);

       // Iterator operations
       reference operator*() const;
       pointer operator->() const;
       scalable_rmat_iterator& operator++();
       scalable_rmat_iterator operator++(int);
       bool operator==(const scalable_rmat_iterator& other) const;
       bool operator!=(const scalable_rmat_iterator& other) const;
    };

This class template implements a generator for R-MAT graphs [CZF04], suitable for initializing an adjacency_list or other graph structure with iterator-based initialization. An R-MAT graph has a scale-free distribution w.r.t. vertex degree and is implemented using Recursive-MATrix partitioning.

# Where Defined

<`boost/graph/rmat_graph_generator.hpp`>

# Constructors

    scalable_rmat_iterator();

Constructs a past-the-end iterator.

    scalable_rmat_iterator(ProcessGroup pg, Distribution distrib,
                           RandomGenerator& gen, vertices_size_type n,
                           edges_size_type m, double a, double b, double c,
                           double d, bool permute_vertices = true);

Constructs an R-MAT generator iterator that creates a graph with `n` vertices and `m` edges. Inside the `scalable_rmat_iterator` processes communicate using `pg` to generate their local edges as defined by `distrib`. `a`, `b`, `c`, and `d` represent the probability that a generated edge is placed of each of the 4 quadrants of the partitioned adjacency matrix. Probabilities are drawn from the random number generator `gen`. Vertex indices are permuted to eliminate locality when `permute_vertices` is true.

# Example

    #include <boost/graph/distributed/mpi_process_group.hpp>
    #include <boost/graph/compressed_sparse_row_graph.hpp>
    #include <boost/graph/rmat_graph_generator.hpp>
    #include <boost/random/linear_congruential.hpp>

    using boost::graph::distributed::mpi_process_group;

    typedef compressed_sparse_row_graph<directedS, no_property, no_property, no_property,
                                        distributedS<mpi_process_group> > Graph;
    typedef boost::scalable_rmat_iterator<boost::minstd_rand, Graph> RMATGen;

    int main()
    {
      boost::minstd_rand gen;
      mpi_process_group pg;

      int N = 100;

      boost::parallel::variant_distribution<ProcessGroup> distrib
        = boost::parallel::block(pg, N);

      // Create graph with 100 nodes and 400 edges
      Graph g(RMATGen(pg, distrib, gen, N, 400, 0.57, 0.19, 0.19, 0.05),
              RMATGen(), N, pg, distrib);
      return 0;
    }

# Bibliography

[CZF04] | D Chakrabarti, Y Zhan, and C Faloutsos. R-MAT: A Recursive Model for Graph Mining. In Proceedings of 4th International Conference on Data Mining, pages 442--446, 2004.

Copyright (C) 2009 The Trustees of Indiana University.

Authors: Nick Edmonds, Brian Barrett, and Andrew Lumsdaine