打破二次障碍：面向自适应查询的鲁棒基数草图
Breaking the Quadratic Barrier: Robust Cardinality Sketches for Adaptive Queries
AI总结：
本文通过设计细粒度鲁棒估计器，将基数草图的二次失效障碍从总查询数转移到共享同一元素的查询数，从而支持指数级自适应查询，并扩展了鲁棒算法设计工具。
摘要：
基数草图是一种紧凑数据结构，能够在多个查询中高效估计不同元素的数量，同时最小化存储、通信和计算成本。然而，近期研究表明，这些草图在自适应选择的查询下可能会失效，大约在 \ ilde{O}(k^2) 次查询后就会崩溃，其中 k 是草图大小。在本工作中，我们通过设计具有细粒度保证的鲁棒估计器来克服这一二次障碍。具体而言，我们的构造能够处理指数数量的自适应查询，前提是每个元素最多参与 \ ilde{O}(k^2) 次查询。这有效地将二次障碍从查询总数转移到共享同一元素的查询数量上，而后者可能显著更小。除基数草图之外，我们的方法还扩展了鲁棒算法设计的工具箱。
英文摘要：
Cardinality sketches are compact data structures that efficiently estimate the number of distinct elements across multiple queries while minimizing storage, communication, and computational costs. However, recent research has shown that these sketches can fail under {\em adaptively chosen queries}, breaking down after approximately $\tilde{O}(k^2)$ queries, where $k$ is the sketch size. In this work, we overcome this \emph{quadratic barrier} by designing robust estimators with fine-grained guarantees. Specifically, our constructions can handle an {\em exponential number of adaptive queries}, provided that each element participates in at most $\tilde{O}(k^2)$ queries. This effectively shifts the quadratic barrier from the total number of queries to the number of queries {\em sharing the same element}, which can be significantly smaller. Beyond cardinality sketches, our approach expands the toolkit for robust algorithm design.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
