这里有多少用户已经停留了很久？高效解决长期聚合访问的方案
How many users have been here for a long time? Efficient solutions for counting long aggregated visits
AI总结：
本文提出高效解决方案，用于计算在特定区域中长期停留的用户数量，结合精确和近似数据结构及几何优化方法。
摘要：
本文解决了计数长期聚合访问问题，其定义如下。我们给定n个用户和m个区域，每个用户花费一些时间访问某些区域。对于参数k和一个由r个区域组成的查询，任务是计算那些在查询区域中总访问时间至少为k的distinct用户数量。这个问题由大规模移动数据集分析中出现的查询所驱动。我们提出了几种精确和近似的数据结构，用于支持计数长期聚合访问，以及条件性和无条件性下界。首先，我们描述了一个具有空间-时间权衡的数据结构，以及基于采样和草图技术的高效近似解决方案。然后，我们研究了在几何设置中该问题，其中区域是R^d中的点，查询是超矩形，并推导出在这些结构化空间中实现改进性能的精确数据结构。
英文摘要：
This paper addresses the Counting Long Aggregated Visits problem, which is defined as follows. We are given $n$ users and $m$ regions, where each user spends some time visiting some regions. For a parameter $k$ and a query consisting of a subset of $r$ regions, the task is to count the number of distinct users whose aggregate time spent visiting the query regions is at least $k$. This problem is motivated by queries arising in the analysis of large-scale mobility datasets. We present several exact and approximate data structures for supporting counting long aggregated visits, as well as conditional and unconditional lower bounds. First, we describe an exact data structure that exhibits a space-time tradeoff, as well as efficient approximate solutions based on sampling and sketching techniques. We then study the problem in geometric settings where regions are points in $\mathbb{R}^d$ and queries are hyperrectangles, and derive exact data structures that achieve improved performance in these structured spaces.
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。
