Maybe I'm recreating the wheel here, but wouldn't the following work for you?

#!/usr/bin/perl
 
my @data = (
        [ 2, 8 ],
        [ 1, 3 ],
        [ 4, 6 ],
        [ 7, 10 ],
        [ 8, 20 ],
);
 
foreach my $pair (@data)
{
        @{$pair}[1,0] = @{$pair}[1,0]
                if $pair->[0] > $pair->[1];
        $pair->[2] = $pair->[1] - $pair->[0];
}
 
@data = sort { $a->[2] cmp $b->[2] || $a->[0] cmp $b->[0] || $a->[1] c
+mp $b->[1] } @data;
 
my @good;
PAIR:
foreach my $pair (@data)
{
 
        my @check;
        foreach my $i (0 .. $#good)
        {
                my $good = $good[$i];
 
                if (
                        ($good->[0] <= $pair->[0] && $pair->[0] < $goo
+d->[1])
                                ||
                        ($good->[0] < $pair->[1] && $pair->[1] <= $goo
+d->[1])
                                ||
                        ($pair->[0] <= $good->[0] && $good->[0] < $pai
+r->[1])
                                ||
                        ($pair->[0] < $good->[1] && $good->[1] <= $pai
+r->[1])
                ) {
                        push @check, [
                                $good,
                                $i,
                        ];
                }
        }
 
        unless (@check)
        {
                push @good, $pair;
                next PAIR;
        }
 
        my $max = 0;
        $max += $_->[2] for map { $_->[0] } @check;
        next PAIR if $max > $pair->[2];
 
        splice @good, $_, 1 for sort { $b <=> $a } map { $_->[1] } @ch
+eck;
        push @good, $pair;
}
 
@good = sort { $a->[0] cmp $b->[0] || $a->[1] cmp $b->[1] } @good;
 
print "$_->[0] ... $_->[1] ($_->[2])\n" for @good;
my $cover = 0;
$cover += $_->[2] for @good;
print "Total coverage is $cover\n";
[download]

------
We are the carpenters and bricklayers of the Information Age.

The idea is a little like C++ templates, except not quite so brain-meltingly complicated. -- TheDamian, Exegesis 6

Please remember that I'm crufty and crochety. All opinions are purely mine and all code is untested, unless otherwise specified.

---

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