Previous studies on Approximate Near-Neighbors Search (ANNS) among curves are either focused on curves in ${\mathbb{R}}^1$ or under the discrete Fréchet distance. In this paper, we propose the first data structure for curves under the (continuous) Fréchet distance in higher dimensions. Given a set $\mathcal{P}$ of n curves each with number of vertices at most m in ${\mathbb{R}}^d$, and a fixed $\delta >0$, we aim to preprocess $\mathcal{P}$ into a data structure so that for any given query curve Q with k vertices, we can efficiently report all curves in $\mathcal{P}$ whose Fréchet distances to Q are at most δ. In the case that k is given in the preprocessing stage, for any $\epsilon >0$ we propose a deterministic data structure whose space is $n\cdot O(\max \{{\left(\frac{\sqrt{d}}{\epsilon }\right)}^{kd},{\left(\frac{\mathcal{D}\sqrt{d}}{{\epsilon }^2}\right)}^{kd}\left\}\right)$ that can answer $(1+\mathit{\epsilon })\mathit{\delta }$-ANNS queries in $O(kd)$ query time, where $\mathcal{D}$ is the diameter of $\mathcal{P}$. Considering k as part of the query slightly changes the space to $n\cdot O{(1/\epsilon )}^{md}$ with $O(kd)$ query time within an approximation factor of $5+\epsilon$. Moreover, we show that our generic data structure for ANNS can give an alternative treatment of the approximate subtrajectory range searching problem studied by de Berg et al. [1].

以前关于曲线间近似近邻搜索（ANNS）的研究要么集中在曲线中${\mathbb{R}}^{\mathrm{1个}}$或在离散的 Fréchet 距离下。在本文中，我们提出了高维（连续）Fréchet 距离下曲线的第一个数据结构。给定一个集合$\mathcal{P}$n 条曲线，每条曲线的顶点数最多为m${\mathbb{R}}^d$, 和一个固定的$\delta >0$，我们的目标是预处理$\mathcal{P}$进入数据结构，以便对于任何给定的具有k 个顶点的查询曲线Q，我们可以有效地报告所有曲线$\mathcal{P}$到Q的 Fréchet 距离最多为δ。在预处理阶段给定k的情况下，对于任意$\epsilon >0$我们提出了一个确定性的数据结构，其空间是$n\cdot 欧(\mathrm{最大限度}\{{\left(\frac{\sqrt{d}}{\epsilon }\right)}^{kd},{\left(\frac{\mathcal{丁}\sqrt{d}}{{\epsilon }^{\mathrm{2个}}}\right)}^{kd}\left\}\right)$可以回答$(\mathrm{1个}+\mathit{\epsilon })\mathit{\delta }$-ANNS查询$欧(kd)$查询时间，哪里$\mathcal{丁}$是直径$\mathcal{P}$. 将k视为查询的一部分，将空间略微更改为$n\cdot 欧{(\mathrm{1个}/\epsilon )}^{米d}$和$欧(kd)$近似因子内的查询时间$\mathrm{5个}+\epsilon$. 此外，我们表明我们的 ANNS 通用数据结构可以为 de Berg 等人研究的近似子轨迹范围搜索问题提供替代处理。[1]。