my @search_space;
  my $N = 100;
  foreach my $line (<FILE_A>) {
      # fill up @search_space with lines from FILE_B until it has N things
      # of course, this pukes when FILE_B reaches EOF ;)

      push(@search_space, <FILE_B>) while (@search_space < $N);

      # look for $line in @search_space

      my $pos = find(\@search_space, $line);
      if ($pos >= 0) {
          splice(@search_space, 0, $pos);
          # shift off the stuff in @search_space before the match
      } else {
          print "No match for $line";
      }

  }

  sub find {
      my ($arr_ref, $find) = @_;
      $arr_ref->[$_] eq $find and return $_ for (0 .. $#{$arr_ref});
      return -1;
  }

##</code><code>##

  my $N = 100;
  my @file_b;
  tie @file_b, Tie::File, 'path/to/file_b' or die;
  my $last_match = 0;

  for my $line (<FILE_A>) {
      chomp $line;
      my $min = $last_match - $N >= 0 ? $last_match - $N : 0;
      my $max = $last_match + $N <= $#file_b ? $last_match + $N : $#file_b;

      my $pos = find(\@file_b[$min .. $max], $line);
      if ($pos >= 0) {
          $last_match = $min + $pos;
      } else {
          print "No match for $line\n";
      }
  }