Let's add one more class of algorithm without which the world as we know it wouldn't function: indexing algorithms for databases, such as B-tree indexes:
Imagine how long a keyword search of the web would take if there was no indexing! Or even finding the bank account associated with your ATM card among your bank's tens of millions of accounts.
I'm sure the HN community can think of other crucially important algorithms that should be added to this list...
Sure. Based on the broad definitions of that posting, the Kalman filter (radar systems), Marzullo's algorithm (internet time keeping), and CRC-32 (every ethernet packet) are also crucially important to the modern world.
There are so many crucially important algorithms that any listing of the top 10 will leave out hundreds if not thousands of equally crucial algorithms.
You are mixing up B-tree and reverse index. B-tree is significant when you have slow media like disk. Most index serving currently happens from memory and B-tree is not used there.
These type of "top 10" lists are usually meaningless. You can argue string search, binary search, hash tables, heaps, BFS/DFS, Monte Carlo methods, compression algorithms etc etc are important enough that modern world won't exist without it.
https://en.wikipedia.org/wiki/B-tree
Imagine how long a keyword search of the web would take if there was no indexing! Or even finding the bank account associated with your ATM card among your bank's tens of millions of accounts.
I'm sure the HN community can think of other crucially important algorithms that should be added to this list...