Related papers: Improved Incremental Randomized Delaunay Triangula…
Detecting multiple structural breaks in high-dimensional data remains a challenge, particularly when changes occur in higher-order moments or within complex manifold structures. In this paper, we propose REAMP (Resonance-Enhanced Analysis…
We present an algorithm for boundary approximation in locally-linked sensor networks that communicate with a remote monitoring station. Delaunay triangulations and Voronoi diagrams are used to generate a sensor communication network and…
Consider the Delaunay triangulation T of a set P of points in the plane as a Euclidean graph, in which the weight of every edge is its length. It has long been conjectured that the dilation in T of any pair p, p \in P, which is the ratio of…
Retrieval data structures are data structures that answer key-value queries without paying the space overhead of explicitly storing keys. The problem can be formulated in four settings (static, value-dynamic, incremental, or dynamic), each…
We study the problem of finding a triangulation T of a planar point set S such as to minimize the expected distance between two points x and y chosen uniformly at random from S. By distance we mean the length of the shortest path between x…
We investigate ways in which an algorithm can improve its expected performance by fine-tuning itself automatically with respect to an unknown input distribution D. We assume here that D is of product type. More precisely, suppose that we…
We start by considering the problem of estimating intrinsic distances on a smooth submanifold. We show that minimax optimality can be obtained via a reconstruction of the surface, and discuss the use of a particular mesh construction -- the…
Recently proposed neural network architectures like PointNet [QSMG16] and PointNet++ [QYSG17] have made it possible to apply Deep Learning to 3D point sets. The feature representations of shapes learned by these two networks enabled…
Recent advances in deep learning have improved 3D point cloud registration but increased graphics processing unit (GPU) memory usage, often requiring preliminary sampling that reduces accuracy. We propose an overlapping region sampling…
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…
The Delaunay-Rips filtration is a lighter and faster alternative to the well-known Rips filtration for low-dimensional Euclidean point clouds. Despite these advantages, it has seldom been studied. In this paper, we aim to bridge this gap by…
Parsimony, including sparsity and low rank, has been shown to successfully model data in numerous machine learning and signal processing tasks. Traditionally, such modeling approaches rely on an iterative algorithm that minimizes an…
Let $G$ be a (possibly disconnected) planar subdivision and let $D$ be a probability measure over $\R^2$. The current paper shows how to preprocess $(G,D)$ into an O(n) size data structure that can answer planar point location queries over…
Random dimensionality reduction is a versatile tool for speeding up algorithms for high-dimensional problems. We study its application to two clustering problems: the facility location problem, and the single-linkage hierarchical clustering…
In this work we introduce a triangular Delaunay mesh generator that can be trained using reinforcement learning to maximize a given mesh quality metric. Our mesh generator consists of a graph neural network that distributes and modifies…
Several classic problems in graph processing and computational geometry are solved via incremental algorithms, which split computation into a series of small tasks acting on shared state, which gets updated progressively. While the…
UAV trajectory planning is often done in a two-step approach, where a low-dimensional path is refined to a dynamic trajectory. The resulting trajectories are only locally optimal, however. On the other hand, direct planning in…
In this paper, we analyze the complexity of natural parallelizations of Delaunay refinement methods for mesh generation. The parallelizations employ a simple strategy: at each iteration, they choose a set of ``independent'' points to insert…
Machine learning (ML) is probably the first and foremost used technique to deal with the size and complexity of the new generation of data. In this paper, we analyze one of the means to increase the performances of ML algorithms which is…
Consider a weighted graph G where vertices are points in the plane and edges are line segments. The weight of each edge is the Euclidean distance between its two endpoints. A routing algorithm on G has a competitive ratio of c if the length…