NAME
    Algorithm::PageRank::XS - A Fast PageRank implementation

DESCRIPTION
    This module implements a simple PageRank algorithm in C. The goal is to
    quickly get a vector that is closed to the eigenvector of the stochastic
    matrix of a graph.

    Algorithm::PageRank does some pagerank calculations, but it's slow and
    memory intensive. This module was developed to compute pagerank on
    graphs with millions of arcs. This module will not, however, scale up to
    quadrillions of arcs (see the TODO).

SYNOPSYS
        use Algorithm::PageRank::XS;

        my $pr = Algorithm::PageRank::XS->new();

        $pr->graph([
                  'John'  => 'Joey',
                  'John'  => 'James',
                  'Joey'  => 'John',
                  'James' => 'Joey',
                  ]
                  );

        $pr->result();
        # {
        #      'James' => '0.569840431213379',
        #      'Joey'  => '1',
        #      'John'  => '0.754877686500549'
        # }



        #
        #
        # The following simple program takes up arcs and prints the ranks.
        use Algorithm::PageRank::XS;

        my $pr = Algorithm::PageRank::XS->new();

        while (<>) {
            chomp;
            my ($from, to) = split(/\t/, $_);
            $pr->add_arc($from, $to);
        }

        my $r = $pr->results();
        while (my ($name, $rank) = each(%{$r})) {
            print "$name,$rank\n";
        }

METHODS
  new %PARAMS
    Create a new PageRank object. Possible parameters:

    alpha
        This is (1 - how much people can move from one node to another
        unconnected one randomly). Decreasing this number makes convergence
        more likely, but brings us further from the true eigenvector.

    max_tries
        The maximum number of tries until we give up trying to achieve
        convergence.

    convergence
        The maximum number the difference between two subsequent vectors
        must be before we say we are "convergent enough". The convergence
        rate is the rate at which "alpha^t" goes to 0. Thus, if you set
        "alpha" to 0.85, and "convergence" to 0.000001, then you will need
        85 tries.

  add_arc
    Add an arc to the pagerank object before running the computation. The
    actual values don't matter. So you can run:

        $pr->add_arc("Apple", "Orange");

    and you mean that "Apple" links to "Orange".

  graph
    Add a graph, which is just an array of from, to combinations. This is
    equivalent to calling "add_arc" a bunch of times, but may be more
    convenient.

  from_file FILE
    This will load arcs from a file, whose lines contain:

        from,to\n

    It's designed to be fast, and doesn't handle quoting or even commas in
    the from string. This will just allow you to load a bit faster and maybe
    save a few megabytes of ram if you wanted to.

  iterate
    Doesn't do anything, but provided so that you can substitute this module
    in for Algorithm::PageRank.

  result
    Compute the pagerank vector, and return it as a hash.

    Whatever you called the nodes when specifying the arcs will be the keys
    of this hash, where the values will be the vector.

    The result vector is normalized such that the sum is 1 (the L-1 norm).
    You can normalize it any other way you like if you don't like this.

BUGS
    None known.

TODO
    *   Support for "Personalized PageRank" (see
        <http://ilpubs.stanford.edu:8090/596/>)

    *   We may want to support "double" values rather than single floats

    *   We may or may not want to adjust the weighting of individual arcs,
        as you cannot do now.

    *   At present the indexes are "unsigned int", rather than "size_t".
        Thus this will not scale with 64-bit architectures.

    *   It'd be nice to be able to use mmap(2) to efficiently use the hard
        drive to scale to places where memory can't take us.

SPEED
    This module is pretty fast. I ran this on a 1 million node set with 4.5
    million arcs in 57 seconds on my 32-bit 1.8GHz laptop. Let me know if
    you have any performance tips.

    Below are the tables for the current iteration in trials per second and
    arcs per second. Keep in mind that for some of these there are large
    numbers of arcs (".2%" load with "100,000" nodes means "20,000,000"
    arcs!

        +-----------------+-----------------+-----------------+---------------+---------------+
        | test            | XS trials / sec | PL trials / sec | XS arcs / sec | PL arcs / sec |
        +-----------------+-----------------+-----------------+---------------+---------------+
        | 10 nodes @50%   | 4533.207        | 53.741          | 6890.474      | 81.687        | 
        | 10 nodes @100%  | 3822.595        | 46.084          | 13761.342     | 165.901       | 
        | 1000 @10%       | 4.542           | 0.120           | 18109.287     | 2390.898      | 
        | 1000 @50%       | 1.055           | 0.031           | 21082.599     | 15720.595     | 
        | 1000 @100%      | 0.562           | 0.016           | 56121.722     | 16301.088     | 
        | 100000 @.0001%* | 1.348           |                 | 141855.819    |               | 
        | 100000 @.01%*   | 0.217           |                 | 23174.341     |               | 
        | 100000 @.1%*    | 0.034           |                 | 344796.415    |               | 
        | 100000 @.2%*    | 0.017           |                 | 348070.697    |               | 
        +-----------------+-----------------+-----------------+---------------+---------------+

    * For some of these tests I cheated a little bit and used from_file()
    since there were so many arcs.

SEE ALSO
    Algorithm::PageRank

AUTHOR
    Michael Axiak <mike@axiak.net>

COPYRIGHT
    Copyright (C) 2008 by Michael Axiak <mike@axiak.net>

    This package is free software; you can redistribute it and/or modify it
    under the same terms as Perl itself