一个求k-遗憾极小集的全动态算法
A Fully Dynamic Algorithm for k-Regret Minimizing Sets
摘要：
从一个大的数据库中选择一个小的代表集是重要的，在许多应用中，如多标准决策，网络搜索和推荐。$k$ -遗憾最小化集（$k$ -RMS）问题最近被提出用于代表元组发现。具体地，对于具有多个数值属性的元组的大型数据库$P$，$k$-RMS问题返回$P$的大小- $r$子集$Q$，使得对于任何可能的排名函数，$Q$中排名最高的元组的得分不比$P$中$k$ \textsuperscript{th}排名元组的得分差多少.虽然$k$ -RMS问题已经在文献中得到了广泛的研究，现有的方法是针对静态设置而设计的，并且当数据库更新时不能有效地维护结果。为了解决这个问题，我们提出了第一个全动态算法的$k$ -RMS问题，可以有效地提供最新的结果w.r.t.~数据库中的任何插入和删除都有可证明的保证。在几个真实世界和合成数据集上的实验结果表明，我们的算法比现有的$k$ -RMS算法快四个数量级，同时返回几乎相同质量的结果。
英文摘要：
Selecting a small set of representatives from a large database is important in many applications such as multi-criteria decision making, web search, and recommendation. The $k$-regret minimizing set ($k$-RMS) problem was recently proposed for representative tuple discovery. Specifically, for a large database $P$ of tuples with multiple numerical attributes, the $k$-RMS problem returns a size-$r$ subset $Q$ of $P$ such that, for any possible ranking function, the score of the top-ranked tuple in $Q$ is not much worse than the score of the $k$\textsuperscript{th}-ranked tuple in $P$. Although the $k$-RMS problem has been extensively studied in the literature, existing methods are designed for the static setting and cannot maintain the result efficiently when the database is updated. To address this issue, we propose the first fully-dynamic algorithm for the $k$-RMS problem that can efficiently provide the up-to-date result w.r.t.~any insertion and deletion in the database with a provable guarantee. Experimental results on several real-world and synthetic datasets demonstrate that our algorithm runs up to four orders of magnitude faster than existing $k$-RMS algorithms while returning results of nearly equal quality.
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。
