O.k. let's PAUSE for a second and appreciate that. Same number of nodes. Same number of nodes for each customer. Same number of customers. Just by using MATH, we've reduced the blast radius to 1 customer! That's INSANE.
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O.k,. bonus MATH content!! I want to convince you that that rough approximation from earlier is correct, because with more insight we can make smarter decisions.pic.twitter.com/rsgJrYQu63
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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.
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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
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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
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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
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Now let's expand the choose operator into its factorials ...pic.twitter.com/f0L2ZBGZYw
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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
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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!
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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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Hey Ankit, the thread from
@colmmacc is compiled now. You can read it here:https://threader.app/thread/1034492056968736768 …
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