一个可选择的松散堆
A Selectable Sloppy Heap
摘要：
研究了选择问题，即计算给定元素的$n$的$i$阶统计量的问题.在这里，我们提供了一个名为\emph{selectable sloppy heap}的数据结构，它处理一个动态版本，根据请求：（i）~一个新元素被插入或（ii）~一个指定的分位数组的元素从数据结构中删除。每个操作都在（理想！）常数时间-因此与$n$（存储在数据结构中的元素数）无关-假设分位数组的数量是固定的。这是第一个在常数时间内同时容纳插入和删除的结果。因此，我们的数据结构优于Chazelle的软堆数据结构（它只为固定的出错率$0<\varepsilon \leq 1/2$提供恒定的摊销复杂度）在应用程序中，如动态百分位数维护。该设计演示了如何减慢某个计算可以加快数据结构。
英文摘要：
We study the selection problem, namely that of computing the $i$th order statistic of $n$ given elements. Here we offer a data structure called \emph{selectable sloppy heap} handling a dynamic version in which upon request: (i)~a new element is inserted or (ii)~an element of a prescribed quantile group is deleted from the data structure. Each operation is executed in (ideal!) constant time---and is thus independent of $n$ (the number of elements stored in the data structure)---provided that the number of quantile groups is fixed. This is the first result of this kind accommodating both insertion and deletion in constant time. As such, our data structure outperforms the soft heap data structure of Chazelle (which only offers constant amortized complexity for a fixed error rate $0<\varepsilon \leq 1/2$) in applications such as dynamic percentile maintenance. The design demonstrates how slowing down a certain computation can speed up the data structure.
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。
