TedPride,
Per our /msg conversation, here is a version of my implementation that uses a binary search:

sub Long_Inc_Sub {
    my @list = @_;
    my (@pile, @seq);
    for my $num (@list) {
        if (@pile) {
            if ($num < $pile[-1][-1][VAL]) {
                my ($beg, $end) = (0, $#pile);
                while ($beg <= $end) {
                    my $mid = int(($beg + $end) / 2);
                    if ($num < $pile[$mid][-1][VAL]) {
                        $end = $mid - 1;
                    }
                    else {
                        $beg = $mid + 1;
                    }
                }
                my $prev = $beg ? $#{$pile[$beg - 1]} : undef;
                push @{$pile[$beg]}, [$num, $prev];
            }
            else {
                push @pile, [[$num, $#{$pile[-1]}]];
            }
        }
        else {
            push @pile, [[$num, undef]];
        }
    }
    my ($prev, $len) = ($#{$pile[-1]}, scalar @pile);   
    while ($len--) {
        $seq[$len] = $pile[$len][$prev][VAL];
        $prev = $pile[$len][$prev][PREV];
    }
    return @seq;
}
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It does not currently handle exact matches since there should not be any duplicates in the list (1..N). I did leave this open as a question to ponder and it should be fairly trivial to adapt if you decide it is safe to do so ;-)