相关论文: Fast, precise and dynamic distance queries

We study approximate-near-neighbor data structures for time series under the continuous Fr\'echet distance. For an attainable approximation factor $c>1$ and a query radius $r$, an approximate-near-neighbor data structure can be used to…

We consider exact distance oracles for directed weighted planar graphs in the presence of failing vertices. Given a source vertex $u$, a target vertex $v$ and a set $X$ of $k$ failed vertices, such an oracle returns the length of a shortest…

We improve the space bound for streaming approximation of Diameter but also of Farthest Neighbor queries, Minimum Enclosing Ball and its Coreset, in high-dimensional Euclidean spaces. In particular, our deterministic streaming algorithms…

We propose a dynamic data structure for the distribution-sensitive point location problem. Suppose that there is a fixed query distribution in $\mathbb{R}^2$, and we are given an oracle that can return in $O(1)$ time the probability of a…

We give a reduction from $(1+\varepsilon)$-approximate Earth Mover's Distance (EMD) to $(1+\varepsilon)$-approximate Closest Pair (CP). As a consequence, we improve the fastest known approximation algorithm for high-dimensional EMD. Here,…

$\renewcommand{\Re}{\mathbb{R}}$We present an efficient $O (n + 1/\varepsilon^{4.5})$-time algorithm for computing a $(1+\varepsilon$)-approximation of the minimum-volume bounding box of $n$ points in $\Re^3$. We also present a simpler…

Given a vertex-labeled graph, each vertex $v$ is attached with a label from a set of labels. The vertex-label query desires the length of the shortest path from the given vertex to the set of vertices with the given label. We show how to…

It is unlikely that the discrete Fr\'echet distance between two curves of length $n$ can be computed in strictly subquadratic time. We thus consider the setting where one of the curves, $P$, is known in advance. In particular, we wish to…

The question of whether quantum spatial search in two dimensions can be made optimal has long been an open problem. We report progress towards its resolution by showing that the oracle complexity for target location can be made optimal, by…

We present an algorithm for approximating the edit distance between two strings of length $n$ in time $n^{1+\varepsilon}$ up to a constant factor, for any $\varepsilon>0$. Our result completes a research direction set forth in the recent…

We design an efficient data structure for computing a suitably defined approximate depth of any query point in the arrangement $\mathcal{A}(S)$ of a collection $S$ of $n$ halfplanes or triangles in the plane or of halfspaces or simplices in…

We study the problem of computing Chamfer distance in the fully dynamic setting, where two set of points $A, B \subset \mathbb{R}^{d}$, each of size up to $n$, dynamically evolve through point insertions or deletions and the goal is to…

Given two distributions $\mathcal{P}$ and $\mathcal{Q}$ over a high-dimensional domain $\{0,1\}^n$, and a parameter $\varepsilon$, the goal of distance estimation is to determine the statistical distance between $\mathcal{P}$ and…

We consider the problem of estimating the partition function $Z(\beta)=\sum_x \exp(-\beta(H(x))$ of a Gibbs distribution with a Hamilton $H(\cdot)$, or more precisely the logarithm of the ratio $q=\ln Z(0)/Z(\beta)$. It has been recently…

For any two point sets $A,B \subset \mathbb{R}^d$ of size up to $n$, the Chamfer distance from $A$ to $B$ is defined as $\text{CH}(A,B)=\sum_{a \in A} \min_{b \in B} d_X(a,b)$, where $d_X$ is the underlying distance measure (e.g., the…

We introduce a new class of objectives for optimal transport computations of datasets in high-dimensional Euclidean spaces. The new objectives are parametrized by $\rho \geq 1$, and provide a metric space $\mathcal{R}_{\rho}(\cdot, \cdot)$…

We revisit a fundamental problem in string matching: given a pattern of length m and a text of length n, both over an alphabet of size $\sigma$, compute the Hamming distance between the pattern and the text at every location. Several…

Let $G$ be an unweighted, undirected graph. An additive $k$-spanner of $G$ is a subgraph $H$ that approximates all distances between pairs of nodes up to an additive error of $+k$, that is, it satisfies $d_H(u,v) \le d_G(u,v)+k$ for all…

We present new data structures for approximately counting the number of points in orthogonal range. There is a deterministic linear space data structure that supports updates in O(1) time and approximates the number of elements in a 1-D…

We present a near-linear time algorithm that approximates the edit distance between two strings within a polylogarithmic factor; specifically, for strings of length n and every fixed epsilon>0, it can compute a (log n)^O(1/epsilon)…