package Graph::Clique;
use 5.008;
use strict;
use warnings;
use re 'eval';
use base qw(Exporter);
our @EXPORT = qw(getcliques);
our @EXPORT_OK = qw(_internalfunctions);
our %EXPORT_TAGS = (all => \@EXPORT,
test => \@EXPORT_OK,
);
our $VERSION = '0.02';
# Below is stub documentation for your module. You'd better edit it!
=head1 NAME
Graph::Clique - Return all k-cliques in a graph
=head1 SYNOPSIS
use Graph::Clique;
#Edges in the form of LoL (numerical values required)
my @edges = (
[1,2], [1,3], [1,4], [1,5],
[2,3], [2,4],
[3,4],
[5,6], [5,7], [5,9],
[6,9],
[7,8],
[8,9],
);
my $k = shift || 3;
my @cliques = getcliques($k,\@edges);
print join("\n", @cliques), "\n";
#Output:
#1 2 3
#1 2 4
#1 3 4
#2 3 4
#5 6 9
=head1 DESCRIPTION
This module extends Greg Bacon's implementation on clique reduction with regular expression.
Originally can be found at: L
The function take clique size (k) and vertices (list of lists) and return all the vertices
that form the clique.
K-clique problem is known to be NP-complete, so it is advisable to limit the number
of edges according to your predefined threshold, rather than exhaustively searching them.
=head1 ACKNOWLEDGEMENT
Greg Bacon who started all this, Mike Rosulek
and Roy Johnson for his advice on ways to return all k-cliques.
Finally all guys in Perlmonks.org, and beginners.perl who has helped
me in many ways.
=head1 SEE ALSO
L
=head1 AUTHOR
Edward Wijaya,
=head1 COPYRIGHT AND LICENSE
Copyright 2004 by Edward Wijaya
This library is free software; you can redistribute it and/or modify
it under the same terms as Perl itself.
=cut
# Preloaded methods go here.
sub getcliques {
my ($k,$edges) = @_;
my @cliques = ();
my @vertices = ();
@vertices = edges2vertices(@{$edges});
my $string = (join ',' => @vertices) . ';'
. (join ',' => map "$_->[0]-$_->[1]", @{$edges});
my $regex = '^ .*\b '
. join(' , .*\b ' => ('(\d+)') x $k)
. '\b .* ;'
. "\n";
for (my $i = 1; $i < $k; $i++) {
for (my $j = $i+1; $j <= $k; $j++) {
$regex .= '(?= .* \b ' . "\\$i-\\$j" . ' \b)' . "\n";
}
}
# Backtrack to regain all the identified k-cliques (Credit Mike Mikero)
$regex .= '(?{ push (@cliques, join(" ", map $$_, 1..$k) ) })(?!)';
$string =~ /$regex/x;
return sort @cliques;
}
#----Subroutines -------------------
sub edges2vertices {
my @edges = @_;
my %hTemp;
my @vertices;
my @aTemp = map{@{$_}} @edges;
@hTemp{@aTemp} = ();
@vertices = sort keys %hTemp;
return @vertices;
}
sub edges2vertices_slow {
#AoA to uniq array;
my @edges = @_;
my @vertices;
my @uniqv;
for my $i ( 0 .. $#edges ) {
for my $j ( 0 .. $#{$edges[$i]} ) {
push @vertices, $edges[$i][$j];
}
}
@uniqv = sort keys %{{map {$_,1} @vertices}};
return @uniqv;
}
1;
__END__