Parallel BGL Sorted unique R-MAT generator

# Sorted unique R-MAT generator

     template<typename RandomGenerator, typename Graph,
              typename EdgePredicate = keep_all_edges>
     class sorted_unique_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;

       sorted_unique_rmat_iterator();
       sorted_unique_rmat_iterator(RandomGenerator& gen, vertices_size_type n,
                                   edges_size_type m, double a, double b, double c,
                                   double d, bool bidirectional = true,
                                   bool permute_vertices = true,
                                   EdgePredicate ep = keep_all_edges());
       // Iterator operations
       reference operator*() const;
       pointer operator->() const;
       sorted_unique_rmat_iterator& operator++();
       sorted_unique_rmat_iterator operator++(int);
       bool operator==(const sorted_unique_rmat_iterator& other) const;
       bool operator!=(const sorted_unique_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. The output of this generator is sorted for use with a compressed sparse row graph. The edge list produced by this iterator is guaranteed not to contain parallel edges.

# Where Defined

<`boost/graph/rmat_graph_generator.hpp`>

# Constructors

    sorted_unique_rmat_iterator();

Constructs a past-the-end iterator.

    sorted_unique_rmat_iterator(RandomGenerator& gen, vertices_size_type n,
                                edges_size_type m, double a, double b, double c,
                                double d, bool bidirectional = false,
                                bool permute_vertices = true,
                                EdgePredicate ep = keep_all_edges());

Constructs an R-MAT generator iterator that creates a graph with `n` vertices and `m` edges. `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. When `bidirectional` is `true` for every edge s-t, the corresponding anti-edge t-s is added as well, these anti-edges are not counted towards `m`. `ep` allows the user to specify which edges are retained, this is useful in the case where the user wishes to refrain from storing remote edges locally during generation to reduce memory consumption.

# 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 keep_local_edges<boost::parallel::variant_distribution<mpi_process_group>,
                             mpi_process_group::process_id_type> EdgeFilter;
    typedef boost::sorted_unique_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);

      mpi_process_group::process_id_type id = process_id(pg);

      // Create graph with 100 nodes and 400 edges
      Graph g(RMATGen(gen, N, 400, 0.57, 0.19, 0.19, 0.05, true,
                      true, EdgeFilter(distrib, id)),
              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 and Andrew Lumsdaine