Range-filtering approximate nearest neighbor search (RFANNS) is a fundamental operation in modern vector databases. Given a query vector $q$ and a numerical range predicate, RFANNS returns the $k$-approximate nearest neighbors ($k$-ANN) of the query $q$ among the objects whose attributes satisfy the range predicate. However, existing RFANNS methods are not well suited to high-throughput GPU execution. CPU indexes offer limited parallel scalability, generic GPU filtering is highly selectivity-dependent, and GPU indexes built from locally optimized subgraphs can incur long search trajectories and redundant distance computations. To address these limitations, we present FROG, a GPU-oriented RFANNS index that replaces multiple locally optimal substructure building with a globally aware, vertex-centric design. It organizes diverse expansion neighbor candidates for each vertex in a GPU-friendly structure and rapidly identifies the expansion neighbors used for computation at query time. Moreover, GPU-oriented algorithms and implementations are developed for both index construction and query processing. Experiments on six datasets show that FROG improves mixed-selectivity query throughput by 14.7--37.7$\times$ over 44-core CPU baselines and 4.5--7.6$\times$ over the strongest GPU baseline. It also accelerates index construction by 2.4--14.8$\times$ over the GPU baseline.

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