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Optimality of Frequency Moment Estimation
Under the auspices of the Computational Complexity Foundation (CCF) Estimating the second frequency moment of a stream up to $(1\pm\varepsilon)$ multiplicative error requires at most $O(\log n / \varepsilon^2)$ bits of space, due to a seminal result of Alon, Matias, and Szegedy. It is also known that at least $\Omega(\log n + 1/\varepsilon^{2})$ space is needed.
TR24-175 | 4th November 2024 13:05 Optimality of Frequency Moment Estimation Abstract: Estimating the second frequency moment of a stream up to $(1\pm\varepsilon)$ multiplicative error requires at most $O(\log n / \varepsilon^2)$ bits of space, due to a seminal result of Alon, Matias, and Szegedy. For smaller values of $\varepsilon$ we also introduce a revised algorithm that improves the classic AMS bound and matches our lower bound.Our lower bound holds also for the more general problem of $p$-th frequency moment estimation for the range of $p\in (1,2]$, giving a tight bound in the only remaining range to settle the optimal space complexity of estimating frequency moments.
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