The blast radius ends up getting really small. It's roughly proportionate to the factorial of the shard size (small) divided by the factorial of the number of nodes (which is big) ... so it can get really really small.pic.twitter.com/LmaffLA3tR
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Shuffle Sharding is just like a lottery. Think about your nodes like the numbers in a lottery, and each customer gets a ticket with |shardsize| count of numbers. You want to measure the probability that two or tickets match.
First, we have to define some shorthand. N is the number of nodes. S is the shard size. O is the potential overlap between two tickets/customers. https://en.wikipedia.org/wiki/Lottery_mathematics … has good background on how we then come to this equation ...pic.twitter.com/RMPYMIBtx4
Now, let's take the special case of "full overlap". That's the case we care the most about; the problem request eats all of the nodes it can reach. How many other customers are impacted? Since O=S in this case, we end up with ...pic.twitter.com/hIb2VR7RPq
The bracket notation is short for "choose" and since x choose x is 1, and x choose 0 is 1, we can replace everything above the line with 1.pic.twitter.com/X6evtSZMsv
Now let's expand the choose operator into its factorials ...pic.twitter.com/f0L2ZBGZYw
When you were about 10 you probably learned the reciprocal of a reciprocal is just to turn it upside down. That's still true. That gives us our final form ...pic.twitter.com/KfL5vELMxy
In that form it's pretty easy to see that the smaller S is relative to N, that Shuffle Sharding gets dramatically more and more effective! Convinced? I hope so!
That was my whole talk and it took me longer to tweet it than it did to give it on stage! Go figure. Feel free to AMA. And thanks for reading and making it to the end. Now use Shuffle Sharding anywhere that you can!
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