A hash is not the right structure for this problem. You should use an array:

my @box;
for (...) {
  my ($NetName, $MinX, $MinY, $MaxX, $MaxY) = ...;
  push @box, [$NetName,
              $MinX, $MinY, $MaxX, $MaxY,
              ($MaxX - $MinX) * ($MaxY - $MinY)];
}
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and you can sort it as:

@box = sort { $a->[5] <=> $b->[5] } @box;
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or if that sort results too slow:

use Sort::Key qw(nkeysort_inplace);

nkeysort_inplace { $_->[5] } @box;
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Then, you have to look for the N largest areas. It can be done recursively: get the biggest rectangle and look for the N-1 largest, non-overlapping areas.

BTW, "the N largest boxes" is not very precise. Which is larger, a set of rectangles with areas (9, 1) or another with (7, 6)?

I suppose you want to maximize the total area:

# untested!

my ($area, @best) = n_largest_boxes(\@box, $n);

sub overlap {
  my ($box1, $box2) = @_;
  return !( $box1->[3] < $box2->[1] or
            $box1->[1] > $box2->[3] or
            $box1->[4] < $box2->[2] or
            $box1->[2] > $box2->[4] )
}

sub n_largest_boxes {
  my ($boxes, $n, $start, @acu) = @_;
  my $max = 0; # area for the biggest set of boxes found
  my @max;     # rectangles on the biggest set
  for ($i = $start || 0;
       $i + $n <= @$boxes and $boxes->[$i][5] * $n > $max;
       $i++) {
    my $box = $boxes->[$i];
    next if grep overlap($_, $box), @acu;
    if ($n > 1) {
      my $max1, @max1 = n_largest_boxes($boxes, $i+1, $n-1,
                                        @acu, $box);
      if ($max1 and $max1 + $box->[5] > $max) {
        $max = $max1 + $box->[5];
        @max = ($box, @max1);
      }
    }
    else {
      return ($box->[5], $box);
    }
  }
  return ($max, @max);
}
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