On the I/O Complexity of the k-Nearest Neighbors Problem
Summary: Shows Ω(k) I/O lower bounds for static external-memory k-NN under an indivisibility assumption: polynomial-space schemes need Ω(k) block reads in high‑dim Hamming, and for L_∞ the bound holds for 1<c<3. Introduces a relaxed λ-set workload and a deterministic dimension-reduction to extend bounds to d=O(k log(n/k)), and proves tightness at c=3 via an O(k n)-space index achieving ⌈k/B⌉ I/Os. (summarized by gpt-5-mini on Feb 09 2026)
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Authors
- 1. Mayank Goswami
- 2. Riko Jacob
- 3. Rasmus Pagh
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| Rank | Cited Paper | Year | Venue | Pagerank |
|---|---|---|---|---|
| 34 | Similarity Search in High Dimensions via Hashing | 1999 | VLDB | 0.00076637636 |
| 242 | Generalized Search Trees for Database Systems (Extended Abstract) | 1995 | VLDB | 0.00031110894 |
| 1,183 | A Cost Model For Nearest Neighbor Search in High-Dimensional Data Space | 1997 | PODS | 0.00013455596 |
| 1,488 | On the Analysis of Indexing Schemes | 1997 | PODS | 0.00011699446 |
| 2,203 | Independent Range Sampling | 2014 | PODS | 9.2981095e-05 |
| 3,833 | Output-optimal Parallel Algorithms for Similarity Joins | 2017 | PODS | 6.7173578e-05 |
| 8,763 | Smooth Tradeoffs between Insert and Query Complexity in Nearest Neighbor Search | 2015 | PODS | 4.456315e-05 |
| 8,767 | Dynamic Indexability and Lower Bounds for Dynamic One-Dimensional Range Query Indexes | 2009 | PODS | 4.456315e-05 |
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