You may want a compromise between the two extremes of caching the frequencies of all the pairs (which for large data sets will use too much RAM) and caching nothing (which for large data sets will use too much CPU). What about caching just a list of which sets each number occurs in?

#!/usr/bin/perl

my @set = map {[split /\s+/]} <DATA>;

# We want for each number a list of which sets it's in:
for (@set) {
  for (@$_) {
    push @{$sets{$_}}, $setnum+0; # +0 numifies undef.
  } $setnum++
}

my ($element, $k) = (1, 3); # or =@ARGV or whatever.
{ my %count;
  # Note that this block could be a loop with different
  # values of $element and $k each time.

  for (@{$sets{$element}}) {
    for (uniq(grep { $_ != $element } @{$set[$_]})) {
      $count{$_}++; }
  }

  my @result = (sort { $count{$b} <=> $count{$a} } keys %count)[0..($k
+-1)];

  print "Results:  ", (join ", ", map {"($element, $_)"} @result), $/;
}

sub uniq {
  my %used;
  return grep { !$used{$_}++ } @_
}

__DATA__
2 4 5 7 8 10
1 2 5 6 7 9
2 6 7 8 9 10
1 3 5 10
1 3 4 5 6 8 9
1 2 4 6
1 2 4 5 7 10
1 3 4 6 7 8 9
[download]

$;=sub{$/};@;=map{my($a,$b)=($_,$;);$;=sub{$a.$b->()}}
split//,".rekcah lreP rehtona tsuJ";$\=$ ;->();print$/
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