Computing of high breakdown regression estimators without sorting on graphics processing units

We present an approach to computing high-breakdown regression estimators in parallel on graphics processing units (GPU).We show that sorting the residuals is not necessary, and it can be substituted by calculating the median. We present and compare various methods to calculate the median and order statistics on GPUs. We introduce an alternative method based on the optimization of a convex function, and showits numerical superiority when calculating the order statistics of very large arrays on GPUs.

Parallel bucket sorting on graphics processing units based on convex optimization

We found an interesting relation between convex optimization and sorting problem. We present a parallel algorithm to compute multiple order statistics of the data by minimizing a number of related convex functions. The computed order statistics serve as splitters that group the data into buckets suitable for parallel bitonic sorting. This led us to a parallel bucket sort algorithm, which we implemented for many-core architecture of graphics processing units (GPUs). The proposed sorting method is competitive to the state-of-the-art GPU sorting algorithms and is superior to most of them for long sorting keys.

Emergent effects in massive agent swarms in real-time game environments

 Computational efficiency and hence the scale of agent-based swarm simulations is bound by the nearest neighbour computation for each agent. This article proposes the use of GPU texture memory to implement lookup tables for a spatial partitioning based k-Nearest Neighbours algorithm. These improvements allow simulation of swarms of 220 agents at higher rates than the current best alternative algorithms. This approach is incorporated into an existing framework for simulating steering behaviours allowing for a complete implementation of massive agent swarm simulations, with per agent behaviour preferences, on a Graphics Processing Unit. These simulations have enabled an investigation of the emergent dynamics that occur when massive swarms interact with a choke point in their environment. Various modes of sustained dynamics with temporal and spatial coherence are identified when a critical mass of agents is simulated and some elementary properties are presented. The algorithms presented in this article enable researchers and content designers in games and movies to implement truly massive agent swarms in real time and thus provide a basis for further identification and analysis of the emergent dynamics in these swarms. This will improve not only the scale of swarms used in commercial games and movies but will also improve the reliability of swarm behaviour with respect to content design goals.