Conservative Count-Min, an improved version of Count-Min sketch [Cormode, Muthukrishnan 2005], is an online-maintained hashing-based data structure summarizing element frequency information without storing elements themselves. Although several works attempted to analyze the error that can be made by Count-Min, the behavior of this data structure remains poorly understood. In [Fusy, Kucherov 2022], we demonstrated that under the uniform distribution of input elements, the error of conservative Count-Min follows two distinct regimes depending on its load factor. In this work, we provide a series of experimental results providing new insights into the behavior of conservative Count-Min. Our contributions can be seen as twofold. On one hand, we provide a detailed experimental analysis of the behavior of Count-Min sketch in different regimes and under several representative probability distributions of input elements. On the other hand, we demonstrate improvements that can be made by assigning a variable number of hash functions to different elements. This includes, in particular, reduced space of the data structure while still supporting a small error.

翻译：保守型Count-Min（Count-Min草图的改进版本，[Cormode, Muthukrishnan 2005]）是一种基于哈希的在线维护数据结构，用于在不存储元素本身的情况下汇总元素频率信息。尽管已有若干工作尝试分析Count-Min可能产生的误差，但其数据结构的实际行为仍未能被充分理解。在[Fusy, Kucherov 2022]中，我们证明了在输入元素均匀分布的条件下，保守型Count-Min的误差会依据其负载因子呈现两种截然不同的状态。本研究提供了一系列实验成果，为理解保守型Count-Min的行为提供了新视角。我们的贡献可归纳为两方面：其一，对Count-min草图在不同状态及多种代表性输入元素概率分布下的行为进行了详细的实验分析；其二，展示了通过为不同元素分配可变数量的哈希函数所能实现的改进，其中特别包括在保持小误差的同时减少数据结构所需存储空间。