GPU-Accelerated Construction of the Gabriel Graph: Parallelization Strategies and Applications to Large-Margin Classification and Graph-Based Clustering

Diego Sanches Nere dos Santos, Luiz Carlos Bambirra Torres

The Gabriel graph is a proximity graph widely used in computational geometry and geometric machine learning, underlying large-margin classifiers and, as we show in this work, density-aware clustering methods. Its construction, however, has cubic time complexity $O(N^3)$ in the naive formulation, which severely limits its use on datasets beyond a few thousand samples. This paper presents a set of GPU parallelization strategies, implemented in CUDA, that make Gabriel graph construction practical at scale. We introduce (i) an implicit closed-form mapping from a linear thread index to the corresponding vertex pair $(i,j)$, which removes the need for an explicit $O(N^2)$ adjacency structure and lets every thread locate its pair in constant time and constant memory; (ii) a two-pass, bitmask-based, atomically-compacted edge-list construction that produces a dense edge array proportional only to the number of edges actually found; and (iii) a thread-coarsening strategy in which each thread evaluates several candidate pairs, trading launch and scheduling overhead against load balance. We evaluate these strategies on the acceleration of a Gabriel-graph-based large-margin classifier…