Recent GPU generations include special-purpose ray tracing (RT) cores for graphics applications. While RT cores are primarily used for rendering, recent works show they can be leveraged for general-purpose tasks, including similarity searches. However, existing approaches do not support datasets exceeding three dimensions. In this work, we propose RT-HiSS, the first exact GPU RT-core-based similarity search algorithm for high-dimensional datasets. GPU similarity search often scales poorly for large datasets with substantial search distances. To address this, RT-HiSS uses RT cores for fast index construction and searches, followed by candidate refinement on CUDA cores. We introduce a two-pass approach to estimate an upper bound on result size, enabling efficient batching under GPU memory constraints with near-perfect load balancing. Additionally, we examine shared memory tiling and compressed result masks to improve GPU resource utilization. RT-HiSS yields speedups up to 8.37$\times$ over competitive state-of-the-art GPU algorithms and up to 2,368.26$\times$ relative to the brute-force algorithm across six real-world datasets.

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