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.