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/, $);
            $pr->addarc($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