The n-body problem is the simulation of pair-wise interactions between n objects. This problem appears in many forms, with the classic example being the modeling of gravitational forces between point masses, necessary for cosmological simulations. Many approximation approaches have been devised to reduce the complexity of this problem.

t-SNE is a data visualization method that requires repeatedly solving a variant of the n-body problem. A recent paper (An Efficient Dual-Hierarchy t-SNE Minimization, van de Ruit et. al.) proposes a novel algorithm that outperforms other t-SNE minimization methods on medium-scale datasets. The report proves the viability of a dual-traversal method that uses an embedding tree to emit forces and an independent field tree to collect forces. Because the embedding tree is a Linear-BVH and the field tree is an orthtree built to a fixed depth, the overall algorithm has linear complexity.

This thesis demonstrates how the dual-tree approach can be adapted for gravitational n-body simulations. Following this, it measures the performance against similar implementations of other algorithms and shows that while the adapted Dual Hierarchy approach is faster than Barnes-Hut, it is outperformed by the Fast Multipole Method on realistic large-scale cosmological datasets.