Related papers: Parallel Galton Watson Process

random_tree() is a linear time and space C++ implementation able to create trees of up to a billion nodes for genetic programming and genetic improvement experiments. A 3.60GHz CPU can generate more than 18 million random nodes for GP…

We propose a parallel algorithm for local, on the fly, model checking of a fragment of CTL that is well-suited for modern, multi-core architectures. This model-checking algorithm takes bene t from a parallel state space construction…

Machine learning models have achieved remarkable success in various real-world applications such as data science, computer vision, and natural language processing. However, model training in machine learning requires large-scale data sets…

We give a unified treatment of the limit, as the size tends to infinity, of simply generated random trees, including both the well-known result in the standard case of critical Galton--Watson trees and similar but less well-known results in…

The effective use of parallel computing resources to speed up algorithms in current multi-core parallel architectures remains a difficult challenge, with ease of programming playing a key role in the eventual success of various parallel…

We present parallel algorithms for wavelet tree construction with polylogarithmic depth, improving upon the linear depth of the recent parallel algorithms by Fuentes-Sepulveda et al. We experimentally show on a 40-core machine with two-way…

Dynamic tree data structures maintain a forest while supporting insertion and deletion of edges and a broad set of queries in $O(\log n)$ time per operation. Such data structures are at the core of many modern algorithms. Recent work has…

Generative adversarial networks (GANs) are widely used to learn generative models. GANs consist of two networks, a generator and a discriminator, that apply adversarial learning to optimize their parameters. This article presents a…

An extremely common bottleneck encountered in statistical learning algorithms is inversion of huge covariance matrices, examples being in evaluating Gaussian likelihoods for a large number of data points. We propose general parallel…

Using (a,b)-trees as an example, we show how to perform a parallel split with logarithmic latency and parallel join, bulk updates, intersection, union (or merge), and (symmetric) set difference with logarithmic latency and with information…

Take a continuous-time Galton-Watson tree. If the system survives until a large time $T$, then choose $k$ particles uniformly from those alive. What does the ancestral tree drawn out by these $k$ particles look like? Some special cases are…

The construction of Mapper has emerged in the last decade as a powerful and effective topological data analysis tool that approximates and generalizes other topological summaries, such as the Reeb graph, the contour tree, split, and joint…

The wavelet tree has become a very useful data structure to efficiently represent and query large volumes of data in many different domains, from bioinformatics to geographic information systems. One problem with wavelet trees is their…

Recently Avis and Jordan have demonstrated the efficiency of a simple technique called budgeting for the parallelization of a number of tree search algorithms. The idea is to limit the amount of work that a processor performs before it…

Transformer models have achieved state-of-the-art performance on various domains of applications and gradually becomes the foundations of the advanced large deep learning (DL) models. However, how to train these models over multiple GPUs…

Distinguishing between continuous and first-order phase transitions is a major challenge in random discrete systems. We study the topic for events with recursive structure on Galton-Watson trees. For example, let $\mathcal{T}_1$ be the…

Energy efficiency of training and inferencing with large neural network models is a critical challenge facing the future of sustainable large-scale machine learning workloads. This paper introduces an alternative strategy, called phantom…

It is common practice to use large computational resources to train neural networks, as is known from many examples, such as reinforcement learning applications. However, while massively parallel computing is often used for training models,…

Random networks are widely used for modeling and analyzing complex processes. Many mathematical models have been proposed to capture diverse real-world networks. One of the most important aspects of these models is degree distribution.…

This paper investigates the execution of tree-shaped task graphs using multiple processors. Each edge of such a tree represents some large data. A task can only be executed if all input and output data fit into memory, and a data can only…