Trevor Steil

Keita Iwabuchi, Trevor Steil, Benjamin W. Priest et al.

Neighbor graphs capture relationships among data points and are widely used in data analytics and AI workloads. Many studies have explored approximate construction methods for single-node systems, including GPUs. However, extending this to distributed systems for larger data and further acceleration remains challenging due to irregular computation patterns. We present SOLANET, a GPU-accelerated distributed neighbor graph construction toolkit. SOLANET first constructs local graphs on each GPU after data partitioning and then refines them via approximate nearest neighbor (ANN) searches over remote graphs pulled from other GPUs using MPI one-sided operations. SOLANET also provides a lock-free single-GPU neighbor graph construction algorithm for AMD GPUs. Our single-GPU implementation outperforms a state-of-the-art GPU-based approximate neighbor graph construction implementation across multiple datasets on a single MI300A APU. Furthermore, SOLANET demonstrates 11X speedup from 32 to 512 APUs for 1 billion data points and 6.9x speedup from 64 to 512 APUs for 2 billion points.

Nate Veldt, Thomas Stanley, Benjamin W. Priest et al.

Finding a minimum spanning tree (MST) for $n$ points in an arbitrary metric space is a fundamental primitive for hierarchical clustering and many other ML tasks, but this takes $Ω(n^2)$ time to even approximate. We introduce a framework for metric MSTs that first (1) finds a forest of disconnected components using practical heuristics, and then (2) finds a small weight set of edges to connect disjoint components of the forest into a spanning tree. We prove that optimally solving the second step still takes $Ω(n^2)$ time, but we provide a subquadratic 2.62-approximation algorithm. In the spirit of learning-augmented algorithms, we then show that if the forest found in step (1) overlaps with an optimal MST, we can approximate the original MST problem in subquadratic time, where the approximation factor depends on a measure of overlap. In practice, we find nearly optimal spanning trees for a wide range of metrics, while being orders of magnitude faster than exact algorithms.

Nate Veldt, Thomas Stanley, Benjamin W. Priest et al.

We present improved learning-augmented algorithms for finding an approximate minimum spanning tree (MST) for points in an arbitrary metric space. Our work follows a recent framework called metric forest completion (MFC), where the learned input is a forest that must be given additional edges to form a full spanning tree. Veldt et al. (2025) showed that optimally completing the forest takes $Ω(n^2)$ time, but designed a 2.62-approximation for MFC with subquadratic complexity. The same method is a $(2γ+ 1)$-approximation for the original MST problem, where $γ\geq 1$ is a quality parameter for the initial forest. We introduce a generalized method that interpolates between this prior algorithm and an optimal $Ω(n^2)$-time MFC algorithm. Our approach considers only edges incident to a growing number of strategically chosen ``representative'' points. One corollary of our analysis is to improve the approximation factor of the previous algorithm from 2.62 for MFC and $(2γ+1)$ for metric MST to 2 and $2γ$ respectively. We prove this is tight for worst-case instances, but we still obtain better instance-specific approximations using our generalized method. We complement our theoretical results with a thorough experimental evaluation.