一个尴尬并行且最优空间的基数估计算法
An embarrassingly parallel optimal-space cardinality estimation algorithm
AI总结：
本文提出了一种支持合并操作的最优空间基数估计流式算法，在保持最优空间复杂度的同时实现了并行处理，并降低了实现复杂度与伪随机对象需求。
摘要：
2020年，Blasiok（ACM Trans. Algorithms 16(2) 3:1-3:28）为基数估计问题构建了最优空间流式算法，其空间复杂度为 $\mathcal O(\varepsilon^{-2} \ln(δ^{-1}) + \ln n)$，其中 $\varepsilon$、$δ$ 和 $n$ 分别表示相对精度、失败概率和全域大小。然而，他的方案要求流被顺序处理。另一方面，存在支持合并操作的算法；它们可用于分布式环境，允许并行处理流的各个部分，与大规模分布式应用高度相关。遗憾的是，最著名的此类算法的空间复杂度超过 $Ω(\ln(δ^{-1}) (\varepsilon^{-2} \ln \ln n + \ln n))$。本研究提出了一种新算法，改进了Blasiok的方案，在保持其空间复杂度的同时，支持此类合并操作，从而为顺序和并行应用提供了该问题的最优解。此外，新算法在算法层面也优于Blasiok的方案（即使在顺序环境下），降低了实现复杂度并需要更少的独立伪随机对象。
英文摘要：
In 2020 Blasiok (ACM Trans. Algorithms 16(2) 3:1-3:28) constructed an optimal space streaming algorithm for the cardinality estimation problem with the space complexity of $\mathcal O(\varepsilon^{-2} \ln(δ^{-1}) + \ln n)$ where $\varepsilon$, $δ$ and $n$ denote the relative accuracy, failure probability and universe size, respectively. However, his solution requires the stream to be processed sequentially. On the other hand, there are algorithms that admit a merge operation; they can be used in a distributed setting, allowing parallel processing of sections of the stream, and are highly relevant for large-scale distributed applications. The best-known such algorithm, unfortunately, has a space complexity exceeding $Ω(\ln(δ^{-1}) (\varepsilon^{-2} \ln \ln n + \ln n))$. This work presents a new algorithm that improves on the solution by Blasiok, preserving its space complexity, but with the benefit that it admits such a merge operation, thus providing an optimal solution for the problem for both sequential and parallel applications. Orthogonally, the new algorithm also improves algorithmically on Blasiok's solution (even in the sequential setting) by reducing its implementation complexity and requiring fewer distinct pseudo-random objects.
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