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arXiv · 2203.15496

Phase transition in count approximation by Count-Min sketch with conservative updates

Éric Fusy·Gregory Kucherov
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Abstract

Count-Min sketch is a hash-based data structure to represent a dynamically changing associative array of counters. Here we analyse the counting version of Count-Min under a stronger update rule known as \textit{conservative update}, assuming the uniform distribution of input keys. We show that the accuracy of conservative update strategy undergoes a phase transition, depending on the number of distinct keys in the input as a fraction of the size of the Count-Min array. We prove that below the threshold, the relative error is asymptotically $o(1)$ (as opposed to the regular Count-Min strategy), whereas above the threshold, the relative error is $Θ(1)$. The threshold corresponds to the peelability threshold of random $k$-uniform hypergraphs. We demonstrate that even for small number of keys, peelability of the underlying hypergraph is a crucial property to ensure the $o(1)$ error. Finally, we provide an experimental evidence that the phase transition does not extend to non-uniform distributions, in particular to the popular Zipf's distribution.

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Éric Fusy, Gregory Kucherov. 2022-07-14. Phase transition in count approximation by Count-Min sketch with conservative updates. https://doi.org/10.1007/978-3-031-30448-4_17

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