格网上移动点的范围报告
Range Reporting for Moving Points on a Grid
摘要：
在本文中，我们描述了一种新的数据结构，支持正交范围报告查询的一组点，沿着线性轨迹上的$U\times U$网格。点位于$U\times U$网格上的假设使我们能够与标准动力学模型相比显着减少查询时间。我们的数据结构在$O(\sqrt{\log U/\log \log U}+k)$时间内回答查询，其中$k$表示答案中的点数。以上改进了在无限精度动力学模型中有效的$Ω(\log n)$下限。本文中使用的方法也可能是独立的利益。
英文摘要：
In this paper we describe a new data structure that supports orthogonal range reporting queries on a set of points that move along linear trajectories on a $U\times U$ grid. The assumption that points lie on a $U\times U$ grid enables us to significantly decrease the query time in comparison to the standard kinetic model. Our data structure answers queries in $O(\sqrt{\log U/\log \log U}+k)$ time, where $k$ denotes the number of points in the answer. The above improves over the $Ω(\log n)$ lower bound that is valid in the infinite-precision kinetic model. The methods used in this paper could be also of independent interest.
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。
