Example backup schedule

I have mentioned that I found my old backup volume rotation schedule-generating program from back when I had a large stack of such volumes on a shelf. The two variables of interest are how many backup volumes one has and how many rotations' history one may want to go back. To take a simple example, if I have only five volumes A, B, C, D, E for daily backups but want them to include many months' history then I could generate a schedule of,

CAAAEAAAEAAAEAAADAAAEAAAEAAAEAAADAAAEAAAEAAAEAAADAAAEAAAEAAAEAAA
DBBBABBBABBBABBBEBBBABBBABBBABBBEBBBABBBABBBABBBEBBBABBBABBBABBB
ECCCBCCCBCCCBCCCACCCBCCCBCCCBCCCACCCBCCCBCCCBCCCACCCBCCCBCCCBCCC
ADDDCDDDCDDDCDDDBDDDCDDDCDDDCDDDBDDDCDDDCDDDCDDDBDDDCDDDCDDDCDDD
BEEEDEEEDEEEDEEECEEEDEEEDEEEDEEECEEEDEEEDEEEDEEECEEEDEEEDEEEDEEE

I figured that such an example would help to make the abstract idea clearer. I have no idea how professionals currently achieve such spreads of backup intervals.

Implementation note: This example sequence clearly has a three-fold repetition built in. Let us then say that r=3 and, for our five backup volumes, that v=5. The number of rotations' history offered by my program's generated sequences is at most 2×(r+1)^(v-2), so 128 for this example.

Slow hardlinking

I tried hardlink 0.3 RC2; I read that performance issues on large data sets caused it to be rewritten in C. It reduced the used space on my backup volume from 484GB to 325GB but took nearly 1½ days to do so. Considering that it then took under 4⅓ hours to rsync -aH that 325GB onto an empty volume, I wonder what on Earth hardlink was up to for much of that time, it's not like deduplication requires cryptographic-strength hashing.