Related papers: P2M: A Fast Solver for Querying Distance from Poin…
Approximate near-neighbors search (\textsc{ANNS}) is a long-studied problem in computational geometry. %that has received considerable attention by researchers in the community. In this paper, we revisit the problem and propose the first…
Despite continuous investments in data technologies, the latency of querying data still poses a significant challenge. Modern analytic solutions require near real-time responsiveness both to make them interactive and to support automated…
The closest point method (Ruuth and Merriman, J. Comput. Phys. 227(3):1943-1961, [2008]) is an embedding method developed to solve a variety of partial differential equations (PDEs) on smooth surfaces, using a closest point representation…
Approximating PDEs on surfaces by the diffuse interface approach allows us to use standard numerical tools to solve these problems. This makes it an attractive numerical approach. We extend this approach to vector-valued surface PDEs and…
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,…
The nearest neighbor problem is defined as follows: Given a set $P$ of $n$ points in some metric space $(X,D)$, build a data structure that, given any point $q$, returns a point in $P$ that is closest to $q$ (its "nearest neighbor" in $P$).…
We present a simple and effective framework, named Point2Seq, for 3D object detection from point clouds. In contrast to previous methods that normally {predict attributes of 3D objects all at once}, we expressively model the…
Efficient Maximum Inner Product Search (MIPS) is an important task that has a wide applicability in recommendation systems and classification with a large number of classes. Solutions based on locality-sensitive hashing (LSH) as well as…
Pixel2Mesh (P2M) is a classical approach for reconstructing 3D shapes from a single color image through coarse-to-fine mesh deformation. Although P2M is capable of generating plausible global shapes, its Graph Convolution Network (GCN)…
As we push the boundaries of performance in various vision tasks, the models grow in size correspondingly. To keep up with this growth, we need very aggressive pruning techniques for efficient inference and deployment on edge devices.…
A standard way to approximate the distance between any two vertices $p$ and $q$ on a mesh is to compute, in the associated graph, a shortest path from $p$ to $q$ that goes through one of $k$ sources, which are well-chosen vertices.…
Obtaining high-quality particle distributions for stable and accurate particle-based simulations poses significant challenges, especially for complex geometries. We introduce a preprocessing technique for 2D and 3D geometries, optimized for…
In a classical covering problem, we are given a set of requests that we need to satisfy (fully or partially), by buying a subset of items at minimum cost. For example, in the k-MST problem we want to find the cheapest tree spanning at least…
Meshes are commonly used as 3D maps since they encode the topology of the scene while being lightweight. Unfortunately, 3D meshes are mathematically difficult to handle directly because of their combinatorial and discrete nature. Therefore,…
A method for detecting and approximating fault lines or surfaces, respectively, or decision curves in two and three dimensions with guaranteed accuracy is presented. Reformulated as a classification problem, our method starts from a set of…
Analyzing and identifying the shortcomings of current subdivision methods for finding intersections of rays with fibers defined by the surface of a circular contour swept along a B\'ezier curve, we present a new algorithm that improves…
The emergence of massive graph data sets requires fast mining algorithms. Centrality measures to identify important vertices belong to the most popular analysis methods in graph mining. A measure that is gaining attention is forest…
We propose an extension of tree-based space-partitioning indexing structures for data with low intrinsic dimensionality embedded in a high dimensional space. We call this extension an Angle Tree. Our extension can be applied to both…
We present Fast Approximate Minimum Spanning Tree (FAMST), a novel algorithm that addresses the computational challenges of constructing Minimum Spanning Trees (MSTs) for large-scale and high-dimensional datasets. FAMST utilizes a…
A common approach to compute distances on continuous surfaces is by considering a discretized polygonal mesh approximating the surface and estimating distances on the polygon. We show that exact geodesic distances restricted to the polygon…