A Power Law in Logarithm's Clothing: On the Scalability of Graph-Based Vector Search
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 itself. While the dataset size $N$ is small relative to the data's intrinsic dimensionality, searc...
| Authors | Sajad Faghfoor Maghrebi, Navid Eslami, Niv Dayan |
|---|---|
| Primary category | cs.DB |
| Published | 2 September 2026 |
| Last updated at source | 2 September 2026 |
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