发表机构
Peking University; Massachusetts Institute of Technology; Tsinghua University（北京大学; 麻省理工学院; 清华大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出XYZ-Sketch，实现集合调和任务中接近最小通信空间与O(1)时间更新的同时优化，并在规范模型下证明其渐近最优性，实验验证了其性能。
AI 中文摘要
集合调和（Set reconciliation）是一项在许多领域中的基础任务，其中两方各自持有大量元素集合，旨在识别它们的集合差异。该问题有两个重要指标：时间（计算成本）和空间（通信成本）。以往的大多数工作侧重于优化其中一个指标，而牺牲另一个。我们提出了XYZ-Sketch，证明了可以同时实现接近最小的空间和$O(1)$时间更新。具体来说，对于足够大的$d$，XYZ-Sketch仅需通信$(1+\varepsilon)d$个元素即可调和集合，同时实现$O(1)$插入时间和$O(d\log V)$解码时间。这里，$d$和$V$分别表示两个集合之间差异的大小和全集大小。我们进一步为该问题建立了一个广泛的固定支持规范模型，表明在一个开放的极值猜想下，XYZ-Sketch在该模型内是渐近最优的。实验验证了XYZ-Sketch的预测近最优性能。源代码可在该https URL获取。
英文摘要
Set reconciliation, where two parties each holding a large set of elements aim to identify their set difference, is a fundamental task in many areas. There are two important metrics in this problem: time (computation cost) and space (communication cost). Most previous work focuses on optimizing one metric at the expense of the other. We present XYZ-Sketch, proving that it is possible to achieve near-minimal space and $O(1)$ time updates simultaneously. Specifically, for sufficiently large $d$, XYZ-Sketch reconciles sets with only $(1+\varepsilon)d$ elements for communication, while achieving $O(1)$ insertion time and $O(d\log V)$ decoding time. Here, $d$ and $V$ denote the size of the difference between two sets and the universe size, respectively. We further establish a broad fixed-support canonical model for the problem, showing that, under an open extremality conjecture, XYZ-Sketch is asymptotically optimal within this model. Experiments validate the predicted near-optimal performance of XYZ-Sketch. The source code is available at https://github.com/djwj233/XYZ-Sketch.
