Related papers: Computing Tropical Prevarieties in Parallel
Already for bivariate tropical polynomials, factorization is an NP-Complete problem. In this paper, we give an efficient algorithm for factorization and rational factorization of a rich class of tropical polynomials in $n$ variables.…
A performance prediction method for massively parallel computation is proposed. The method is based on performance modeling and Bayesian inference to predict elapsed time T as a function of the number of used nodes P (T=T(P)). The focus is…
Tree codes that approximate groups of distant particles with multipole expansions are the standard way to accelerate the computation of self-gravity on particles. While momentum-conserving fast multipole methods exist, parallelisation is…
We introduce tropical complexes, as an enrichment of the dual complex of a degeneration with additional data from non-transverse intersection numbers. We define cycles, divisors, and linear equivalence on tropical complexes, analogous both…
We introduce an algorithm that samples a set of loop momenta distributed as a given Feynman integrand. The algorithm uses the tropical sampling method and can be applied to evaluate phase-space-type integrals efficiently. We provide an…
In this paper we combine the Parareal parallel-in-time method together with spatial parallelization and investigate this space-time parallel scheme by means of solving the three-dimensional incompressible Navier-Stokes equations.…
We derive a parallel sampling algorithm for computational inverse problems that present an unknown linear forcing term and a vector of nonlinear parameters to be recovered. It is assumed that the data is noisy and that the linear part of…
Approximation via sampling is a widespread technique whenever exact solutions are too expensive. In this paper, we present techniques for an efficient parallelization of adaptive (a. k. a. progressive) sampling algorithms on multi-threaded…
Hardware double precision is often insufficient to solve large scientific problems accurately. Computing in higher precision defined by software causes significant computational overhead. The application of parallel algorithms compensates…
Many important computational problems require utilization of high performance computing (HPC) systems that consist of multi-level structures combining higher and higher numbers of devices with various characteristics. Utilizing full power…
We present an adaptive methodology for the solution of (linear and) non-linear time dependent problems that is especially tailored for massively parallel computations. The basic concept is to solve for large blocks of space-time unknowns…
The problem of solving tropical linear systems, a natural problem of tropical mathematics, has already proven to be very interesting from the algorithmic point of view: it is known to be in $NP\cap coNP$ but no polynomial time algorithm is…
We present the Glasgow Parallel Reduction Machine (GPRM), a novel, flexible framework for parallel task-composition based many-core programming. We allow the programmer to structure programs into task code, written as C++ classes, and…
Multi-threaded programs have traditionally fallen into one of two domains: cooperative and competitive. These two domains have traditionally remained mostly disjoint, with cooperative threading used for increasing throughput in…
We present ParaDRAM, a high-performance Parallel Delayed-Rejection Adaptive Metropolis Markov Chain Monte Carlo software for optimization, sampling, and integration of mathematical objective functions encountered in scientific inference.…
We examine the problem of optimizing classification tree evaluation for on-line and real-time applications by using GPUs. Looking at trees with continuous attributes often used in image segmentation, we first put the existing algorithms for…
We present a computational framework for piecewise constant functions (PCFs) and use this for several types of computations that are useful in statistics, e.g., averages, similarity matrices, and so on. We give a linear-time,…
We propose an algebraic geometric framework to study the expressivity of linear activation neural networks. A particular quantity of neural networks that has been actively studied is the number of linear regions, which gives a…
Many academic disciplines - including information systems, computer science, and operations management - face scheduling problems as important decision making tasks. Since many scheduling problems are NP-hard in the strong sense, there is a…
The efficient solution of moderately large-scale linear systems arising from the KKT conditions in optimal control problems (OCPs) is a critical challenge in robotics. With the stagnation of Moore's law, there is growing interest in…