Ok. Here's a better version. While I haven't benchmarked it, my feeling are that it's a hog, but I bullet proofed several areas. It's less than a hog than my earlier post. I'm posting the new version for an easier compare.

#!/usr/bin/perl 

# string, min_len of pattern, min_num of patterns

use strict;
use warnings;

  my $string = "bookhelloworldhellohellohihellohiworldhihelloworldhihe
+llobookpenbookpenworld";
  get_pattern($string, 2, 2);
  exit;

sub get_pattern {
  my ($string, $min_len, $min_num) = @_;

  my $str_len = length($string);
  my $srch_max = int($str_len/2);
  my %patterns;
# First we find all patterns that are up to 1/2 the length of the stri
+ng
  print "length  : $str_len\n";
  my %tmp_hash;
  foreach my $len ($min_len..$srch_max) {
    my $eol = $str_len - $len;
    foreach my $ind1 (0..$eol) {
      my $pat = substr($string, $ind1, $len);
      unless ( defined($tmp_hash{$pat}) ) {
        $tmp_hash{$pat} = 0;
        $tmp_hash{$pat}++ while ($string =~ /\Q$pat\E/g);
        $patterns{$pat} = $tmp_hash{$pat} if ($tmp_hash{$pat} >= $min_
+num);
      }
    }
  }
  undef %tmp_hash;
  print "Patterns: ", scalar (keys %patterns), "\n";
#  We then go through the patterns by order and remove those
#  that are invalidated by better patterns
#  Longer strings that occur more often are considered better
  my $mod_str = $string;
  foreach my $key (sort { $patterns{$b} * (length($b)-1) <=>
                     $patterns{$a} * (length($a)-1)
                     or  length($b) <=> length($a) }
                     keys %patterns) {
    my $tstr = $mod_str;
# We null out any area with pattern and count
    $patterns{$key} = ($tstr =~ s/\Q$key\E/\000/g);
    if ($patterns{$key} >= $min_num) {
# If it hits threshold we keep
      $mod_str = $tstr;
    }
    else {
# If not we toss pattern
      delete $patterns{$key};
    }
  }
  print "Valid   : ", scalar (keys %patterns), "\n";

# We finally print results
  foreach my $key
        (sort { $patterns{$b} * (length($b)-1) <=>
                $patterns{$a} * (length($a)-1)
              or length($b) <=> length($a)
              or $a cmp $b } keys %patterns) {
    (my $pat = $key) =~ s/\n/\\n/g;
    printf "%3d: (%s)\n", $patterns{$key}, $pat;
  }
}
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