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A Power Law in Logarithm's Clothing: On the Scalability of Graph-Based Vector Search

arXiv · AI, language, vision and robotics · article · Sep 2, 2026 · UTC

Most vector databases rely on graph-based indexes, notably HNSW and Vamana, for approximate nearest neighbor search. With embedding models widely adopted, the datasets these databases store grow rapidly. At a fixed accuracy, how does search cost scale with dataset size? The prevailing answer is poly-logarithmic growth. Yet the claim is proven only under special conditions and asserted without proof for the indexes used in practice. It is also largely untested: standard benchmarks measure cost at one dataset size, not across sizes. We put the claim to the test. The answer depends on the scale i

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