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$\newcommand{\norm}[1]{\left\lVert#1\right\rVert}$ Denote the support of $f$ by $f_1\le f_2\le...\le f_s$. Given a frequency sequence $f$, denote by $E_{f,a}$ the random variable $\hat{f}_a$ where the stream frequencies are given by $f$ (the evaluation depends on the inner randomness of the sketch and the input stream). The probability that the hash of one ...


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I think this is a reasonable approach. To make it more solid, I suggest replacing Murmur3 with a cryptographic hash, such as SHA256. Then we get a kind of guarantee: it is believed to be intractable to find a collision for the hash function. In other words, for all engineering purposes, we expect you will never in your lifetime encounter a pair of inputs ...


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