Related papers: MadVoro: Parallel Construction of Voronoi Diagrams…
We present a parallel hierarchical solver for general sparse linear systems on distributed-memory machines. For large-scale problems, this fully algebraic algorithm is faster and more memory-efficient than sparse direct solvers because it…
Achieving accurate and robust global situational awareness of a complex time-evolving field from a limited number of sensors has been a longstanding challenge. This reconstruction problem is especially difficult when sensors are sparsely…
Given a set of sites in a simple polygon, a geodesic Voronoi diagram of the sites partitions the polygon into regions based on distances to sites under the geodesic metric. We present algorithms for computing the geodesic nearest-point,…
This paper considers parallel Gr\"obner bases algorithms on distributed memory parallel computers with multi-core compute nodes. We summarize three different Gr\"obner bases implementations: shared memory parallel, pure distributed memory…
While deep learning excels in natural image and language processing, its application to high-dimensional data faces computational challenges due to the dimensionality curse. Current large-scale data tools focus on business-oriented…
Given two point sets in the plane, we study the minimization of the bottleneck distance between a point set B and an equally-sized subset of a point set A under translations. We relate this problem to a Voronoi-type diagram and derive…
The goal of learning to hash (L2H) is to derive data-dependent hash functions from a given data distribution in order to map data from the input space to a binary coding space. Despite the success of L2H, two observations have cast doubt on…
Unstructured Voronoi mesh simulations offer many advantages for simulating self-gravitating gas dynamics on galactic scales. Adaptive mesh refinement (AMR) can be a powerful tool for simulating the details of star cluster formation and gas…
Computing the Delaunay triangulation (DT) of a given point set in $\mathbb{R}^D$ is one of the fundamental operations in computational geometry. Recently, Funke and Sanders (2017) presented a divide-and-conquer DT algorithm that merges two…
Big graphs (networks) arising in numerous application areas pose significant challenges for graph analysts as these graphs grow to billions of nodes and edges and are prohibitively large to fit in the main memory. Finding the number of…
Nowadays, big data of digital media (including images, videos and 3D graphical models) are frequently modeled as low-dimensional manifold meshes embedded in a high-dimensional feature space. In this paper, we summarized our recent work on…
We present a parallel compositing algorithm for Volumetric Depth Images (VDIs) of large three-dimensional volume data. Large distributed volume data are routinely produced in both numerical simulations and experiments, yet it remains…
Voronoi coverage control is a particular problem of importance in the area of multi-robot systems, which considers a network of multiple autonomous robots, tasked with optimally covering a large area. This is a common task for fleets of…
Overdecomposition has emerged as a powerful and sometimes essential technique in parallel programming. Many application domains or frameworks, including those based on adaptive mesh refinements, or tree codes use it. Charm++ is a parallel…
We present a parallel distributed-memory algorithm for large deformation diffeomorphic registration of volumetric images that produces large isochoric deformations (locally volume preserving). Image registration is a key technology in…
Distributed shared memory (DSM) allows to implement and deploy applications onto distributed architectures using the convenient shared memory programming model in which a set of tasks are able to allocate and access data despite their…
The accurate, reliable and efficient numerical approximation of multi-physics processes in heterogeneous porous media with varying media coefficients that include fluid flow and structure interactions is of fundamental importance in energy,…
Neural operators have been applied in various scientific fields, such as solving parametric partial differential equations, dynamical systems with control, and inverse problems. However, challenges arise when dealing with input functions…
The Voronoi tessellation is a natural way of space segmentation, which has many applications in various fields of science and technology, as well as in social sciences and visual art. The varieties of the Voronoi tessellation methods are…
In this paper, we develop constructive algorithms for generating quasi-uniform point sets and sequences over arbitrary two-dimensional triangular domains. Our proposed method, called the \emph{Voronoi-guided greedy packing} algorithm,…