Related papers: The Parallel Complexity of Growth Models
Clustering multi-dimensional points is a fundamental task in many fields, and density-based clustering supports many applications as it can discover clusters of arbitrary shapes. This paper addresses the problem of Density-Peaks Clustering…
Differential evolution (DE) is an effective global evolutionary optimization algorithm using to solve global optimization problems mainly in a continuous domain. In this field, researchers pay more attention to improving the capability of…
Diffusion models are powerful generative models but suffer from slow sampling, often taking 1000 sequential denoising steps for one sample. As a result, considerable efforts have been directed toward reducing the number of denoising steps,…
In both high-performance computing (HPC) environments and the public cloud, the duration of time to retrieve or save your results is simultaneously unpredictable and important to your over all resource budget. It is generally accepted…
The advent of high performance computing (HPC) and graphics processing units (GPU), present an enormous computation resource for Large data transactions (big data) that require parallel processing for robust and prompt data analysis. While…
Most generative models for clustering implicitly assume that the number of data points in each cluster grows linearly with the total number of data points. Finite mixture models, Dirichlet process mixture models, and Pitman--Yor process…
We introduce perhaps the simplest models of graph evolution with choice that demonstrate discontinuous percolation transitions and can be analyzed via mathematical evolution equations. These models are local, in the sense that at each step…
In this paper, we design an algorithm to accelerate the diffusion process on the $SO(3)$ manifold. The inherently sequential nature of diffusion models necessitates substantial time for denoising perturbed data. To overcome this limitation,…
The sheer sizes of modern datasets are forcing data-structure designers to consider seriously both parallel construction and compactness. To achieve those goals we need to design a parallel algorithm with good scalability and with low…
We consider the asymptotic shape of clusters in the Eden model on a d-dimensional hypercubical lattice. We discuss two improvements for the well-known upper bound to the growth velocity in different directions by that of the independent…
Random graphs (or networks) have gained a significant increase of interest due to its popularity in modeling and simulating many complex real-world systems. Degree sequence is one of the most important aspects of these systems. Random…
This paper studies growth, percolation, and correlations in disordered fiber networks. We start by introducing a 2D continuum deposition model with effective fiber-fiber interactions represented by a parameter $p$ which controls the degree…
Sorting is one of the fundamental problems in computer science. Playing a role in many processes, it has a lower complexity bound imposed by $\mathcal{O}(n\log{n})$ when executing on a sequential machine. This limit can be brought down to…
This paper presents our work on developing parallel computational methods for two-phase flow on modern parallel computers, where techniques for linear solvers and nonlinear methods are studied and the standard and inexact Newton methods are…
Recently, diffusion models have achieved significant advances in vision, text, and robotics. However, they still face slow generation speeds due to sequential denoising processes. To address this, a parallel sampling method based on Picard…
Sequential computation is well understood but does not scale well with current technology. Within the next decade, systems will contain large numbers of processors with potentially thousands of processors per chip. Despite this, many…
Gaussian processes (GP) are Bayesian non-parametric models that are widely used for probabilistic regression. Unfortunately, it cannot scale well with large data nor perform real-time predictions due to its cubic time cost in the data size.…
Gaussian processes (GP) are Bayesian non-parametric models that are widely used for probabilistic regression. Unfortunately, it cannot scale well with large data nor perform real-time predictions due to its cubic time cost in the data size.…
Metastability is a common obstacle to performing long molecular dynamics simulations. Many numerical methods have been proposed to overcome it. One method is parallel replica dynamics, which relies on the rapid convergence of the underlying…
Clustering is a fundamental tool for analyzing large data sets. A rich body of work has been devoted to designing data-stream algorithms for the relevant optimization problems such as $k$-center, $k$-median, and $k$-means. Such algorithms…