Stochastic Barnes-Hut Approximation for Fast Summation on the GPU

TL;DR

This paper introduces a stochastic Barnes-Hut approximation method that provides unbiased kernel sum estimates, significantly accelerating GPU computations in graphics applications while maintaining accuracy.

Contribution

It proposes a novel stochastic approach using control variates for unbiased approximation, optimized for GPU, outperforming deterministic Barnes-Hut in speed.

Findings

Achieves up to 9.4x faster computation than deterministic Barnes-Hut

Maintains comparable median error levels in GPU applications

Demonstrates effectiveness in graphics tasks like winding number and distance evaluation

Abstract

We present a novel stochastic version of the Barnes-Hut approximation. Regarding the level-of-detail (LOD) family of approximations as control variates, we construct an unbiased estimator of the kernel sum being approximated. Through several examples in graphics applications such as winding number computation and smooth distance evaluation, we demonstrate that our method is well-suited for GPU computation, capable of outperforming a GPU-optimized implementation of the deterministic Barnes-Hut approximation by achieving equal median error in up to 9.4x less time.