随机四叉树中的部分匹配查询
Partial match queries in random quadtrees
摘要：
我们考虑在多维树（四叉树和k-d树）中恢复与部分指定模式匹配的项目的问题。我们假设传统的模型，其中的数据由独立的和均匀的点在单位正方形。对于该模型，在$n$点上的结构中，已知为了报告与$[0,1]$上的独立且一致的随机查询$ξ$匹配的项目而访问的节点$C_n(ξ)$的数量满足$\Ec{C_n(ξ)}\sim κn^β$，其中$κ$和$β$是显式常数。我们开发了一种方法的基础上的任何固定查询$x\in [0,1]$的成本$C_n(x)$的分析，并给出精确的估计方差和极限分布的成本$C_n(x)$。我们的结果允许描述$[0,1]$中$x$变化时$C_n(x)$成本的极限过程;结果之一是$E{\max_{x\in [0,1]} C_n(x)} \sim γn^β$。
英文摘要：
We consider the problem of recovering items matching a partially specified pattern in multidimensional trees (quad trees and k-d trees). We assume the traditional model where the data consist of independent and uniform points in the unit square. For this model, in a structure on $n$ points, it is known that the number of nodes $C_n(ξ)$ to visit in order to report the items matching an independent and uniformly on $[0,1]$ random query $ξ$ satisfies $\Ec{C_n(ξ)}\sim κn^β$, where $κ$ and $β$ are explicit constants. We develop an approach based on the analysis of the cost $C_n(x)$ of any fixed query $x\in [0,1]$, and give precise estimates for the variance and limit distribution of the cost $C_n(x)$. Our results permit to describe a limit process for the costs $C_n(x)$ as $x$ varies in $[0,1]$; one of the consequences is that $E{\max_{x\in [0,1]} C_n(x)} \sim γn^β$.
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。
