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

Key points

• 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.1
• This paper presents a set of GPU parallelization strategies, implemented in CUDA, that make Gabriel graph construction practical at scale.1
• We evaluate these strategies on the acceleration of a Gabriel-graph-based large-margin classifier (NN-clas) and on a novel Gabriel-graph clustering algorithm that identifies connected components on a residual graph and performs GPU-parallel Union-Find with hierarchical edge-based merging.1

Sources (1)

• [1]GPU-Accelerated Construction of the Gabriel Graph: Parallelization Strategies and Applications to Large-Margin Classification and Graph-Based Clustering
  arXiv (AI, ML, NLP, CV, robotics, multi-agent) · Oct 20, 06:03 PM

  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.

Extractive summary: sentences quoted from the sources.