The is an awesome data structure for estimating the frequencies of different elements in a data stream. Intuitively, it works by picking a variety of hash functions, hashing each element with those hash functions, and incrementing the frequencies of various slots in various tables. To estimate the frequency of an element, the Count-Min sketch applies the hash functions to those elements and takes the minimum value out of all the slots that are see more to. The mentions that the data structure requires ハッシュテーブルスロット independent hash functions in ハッシュテーブルスロット to get the necessary guarantees on its expected performance. However, looking over the structure, I don't see why pairwise independence is necessary. Intuitively, I would think that all that would be required would be that the hash function besince universal hash functions are hash ハッシュテーブルスロット with low probabilities of collisions. The analysis of the collision probabilities in the Count-Min Sketch looks remarkably similar to the analysis of collision probabilities in a chained hash table which only requires a family of universal hash functions, not pairwise independent hash functionsand I can't spot the difference in the analyses. Why is it necessary for the hash functions in the Count-Min Sketch to be pairwise independent? Pairwise independence, while stronger, is the usual method to construct a universal hash family. Also pairwise independence is contrasted in the paper with the 4-wise ハッシュテーブルスロット required by previous methods, such as the AMS sketch. Can you ハッシュテーブルスロット on why this is sufficient? Is this property implied by universal hashing? It doesn't quite specify. I assumed the former, but if we ハッシュテーブルスロット the latter, then I agree the statement follows trivially. So your answer is certainly correct. This has really been bugging me, and it's good to hear that I'm not missing something. Probability isn't my strong suit.