Related papers: Formal study of plane Delaunay triangulation

Motivated by recent work on Delaunay triangulations of hyperbolic surfaces, we consider the minimal number of vertices of such triangulations. First, we will show that every hyperbolic surface of genus $g$ has a simplicial Delaunay…

Diagonalization of a large matrix is the computational bottleneck in many applications such as electronic structure calculations. We show that a speedup of over 30% can be achieved by exploiting 32-bit floating point operations, while…

We prove that the theory of the Farey graph is pseudofinite by constructing a sequence of finite structures that satisfy increasingly large subsets of its first-order axiomatization. This graph is an important object in the study of curve…

We propose an algorithm to create a 3-colorable Delaunay Triangulation. The input of the problem we are trying to solve is a set X of n twodimensional points. The output is a 3-colorable two-dimensional Delaunay triangulation T for X U Y ,…

This paper develops a clustering algorithm for formations in team sports, with a focus on football games. Our method first clusters formations into several average formations: `442,' `4141,' `433,' `541,' and `343.' Then, each average…

Many applications require robustness, or ideally invariance, of neural networks to certain transformations of input data. Most commonly, this requirement is addressed by training data augmentation, using adversarial training, or defining…

Extracting planes from a 3D scene is useful for downstream tasks in robotics and augmented reality. In this paper we tackle the problem of estimating the planar surfaces in a scene from posed images. Our first finding is that a surprisingly…

A novel and detailed convergence analysis is presented for a greedy algorithm that was previously introduced for operator reconstruction problems in the field of quantum mechanics. This algorithm is based on an offline/online decomposition…

Reconstructing building wireframe from airborne LiDAR point clouds yields a compact, topology-centric representation that enables structural understanding beyond dense meshes. Yet a key limitation persists: conventional methods have failed…

We introduce an algorithm that conjectures the structure of a permutation class in the form of a disjoint cover of "rules"; similar to generalized grid classes. The cover is usually easily verified by a human and translated into an…

The cutting plane approach to optimal matchings has been discussed by several authors over the past decades (e.g., Padberg and Rao '82, Grotschel and Holland '85, Lovasz and Plummer '86, Trick '87, Fischetti and Lodi '07) and its…

In this paper, we establish two necessary conditions for a joint triangulation of two sets of $n$ points in the plane and conjecture that they are sufficient. We show that these necessary conditions can be tested in $O(n^3)$ time. For the…

In this paper, we propose a novel parameterization method for genus-one and multiply connected genus-zero surfaces, called periodic conformal flattening. The conformal energy minimization technique is utilized to compute the desired…

We present a new framework for creating elegant algorithms for exact uniform sampling of important Catalan structures, such as triangulations of convex polygons, Dyck words, monotonic lattice paths and mountain ranges. Along with sampling,…

In this paper, we introduce plane permutations, i.e. pairs $\mathfrak{p}=(s,\pi)$ where $s$ is an $n$-cycle and $\pi$ is an arbitrary permutation, represented as a two-row array. Accordingly a plane permutation gives rise to three distinct…

This work presents a novel deep-learning-based pipeline for the inverse problem of image deblurring, leveraging augmentation and pre-training with synthetic data. Our results build on our winning submission to the recent Helsinki Deblur…

Thinning is the removal of contour pixels/points of connected components in an image to produce their skeleton with retained connectivity and structural properties. The output requirements of a thinning procedure often vary with…

We challenge the idea that edge insertions are local improvement operations and show that the edge-insertion algorithm must sometimes insert an edge between vertices that are at the farthest combinatorial distance apart, and that this edge…

In this paper, we provide new discrete uniformization theorems for bounded, $m$-connected planar domains. To this end, we consider a planar, bounded, $m$-connected domain $\Omega$ and let $\bord\Omega$ be its boundary. Let $\mathcal{T}$…

We use a phase space analysis to give some classification results for rotational hypersurfaces in $\mathbb{R}^{n+1}$ whose mean curvature is given as a prescribed function of its Gauss map. For the case where the prescribed function is an…