流中不同元素：一种（教材）适用的算法
数据结构与算法
2023-05-25 v2 数据库
摘要
给定元素流 ，其中每个 ，不同元素问题是估计 中不同元素的数量。过去四十年间，不同元素问题一直是理论和实证研究的对象，并由此产生了空间最优的算法。然而，所有当前最先进的算法都超出了本科教材的范围，因为它们依赖于两两独立和通用哈希函数等概念。我们提出了一种简单、直观、基于采样的空间高效算法，其描述和证明可供具备基础概率论知识的本科生理解。
引用
@article{arxiv.2301.10191,
title = {Distinct Elements in Streams: An Algorithm for the (Text) Book},
author = {Sourav Chakraborty and N. V. Vinodchandran and Kuldeep S. Meel},
journal= {arXiv preprint arXiv:2301.10191},
year = {2023}
}
备注
The version of the paper, as published in ESA-22, contained an error in the proof of Claim 4. The current revised version fixes the error as well as several other errors pointed by Donald E. Knuth. The main theorem and algorithm remain unchanged. The authors decided to forgo the old convention of alphabetical ordering of authors in favor of a randomized ordering, denoted by \textcircled{r}