# Graph-based Nearest Neighbor Search: From Practice to Theory

arXiv: https://arxiv.org/abs/1907.00845 · HTML: https://mlsanity.com/paper/1907.00845/

## Key facts

- Cited by 19 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Jul 2019.

## Built on by (most cited first, 19 of 19)

- [SPANN: Highly-efficient Billion-scale Approximate Nearest Neighbor Search](https://mlsanity.com/paper/2111.08566/) (2021)
- [Worst-case Performance of Popular Approximate Nearest Neighbor Search Implementations: Guarantees and Limitations](https://mlsanity.com/paper/2310.19126/) (2023)
- [RoarGraph: A Projected Bipartite Graph for Efficient Cross-Modal Approximate Nearest Neighbor Search](https://mlsanity.com/paper/2408.08933/) (2024)
- [Approximate Nearest Neighbor Search with Window Filters](https://mlsanity.com/paper/2402.00943/) (2024)
- [A Theoretical Analysis Of Nearest Neighbor Search On Approximate Near Neighbor Graph](https://mlsanity.com/paper/2303.06210/) (2023)
- [Survival Kernets: Scalable and Interpretable Deep Kernel Survival Analysis with an Accuracy Guarantee](https://mlsanity.com/paper/2206.10477/) (2022)
- [Navigable Proximity Graph-Driven Native Hybrid Queries with Structured and Unstructured Constraints](https://mlsanity.com/paper/2203.13601/) (2022)
- [Navigable Graphs for High-Dimensional Nearest Neighbor Search: Constructions and Limits](https://mlsanity.com/paper/2405.18680/) (2024)
- [PECANN: Parallel Efficient Clustering with Graph-Based Approximate Nearest Neighbor Search](https://mlsanity.com/paper/2312.03940/) (2023)
- [Probabilistic Routing for Graph-Based Approximate Nearest Neighbor Search](https://mlsanity.com/paper/2402.11354/) (2024)
- [Approximate Nearest Neighbour Search on Dynamic Datasets: An Investigation](https://mlsanity.com/paper/2404.19284/) (2024)
- [ELEMENT: Episodic and Lifelong Exploration via Maximum Entropy](https://mlsanity.com/paper/2412.03800/) (2024)
- [ARM 4-BIT PQ: SIMD-based Acceleration for Approximate Nearest Neighbor Search on ARM](https://mlsanity.com/paper/2203.02505/) (2022)
- [Theoretical and Empirical Analysis of Adaptive Entry Point Selection for Graph-based Approximate Nearest Neighbor Search](https://mlsanity.com/paper/2402.04713/) (2024)
- [Distance Adaptive Beam Search for Provably Accurate Graph-Based Nearest Neighbor Search](https://mlsanity.com/paper/2505.15636/) (2025)
- [Graph-based Nearest Neighbors with Dynamic Updates via Random Walks](https://mlsanity.com/paper/2512.18060/) (2025)
- [FGIM: a Fast Graph-based Indexes Merging Framework for Approximate Nearest Neighbor Search](https://mlsanity.com/paper/2603.21710/) (2026)
- [MERIT: Efficient In-Place Deletion for Dynamic Graph-Based Approximate Nearest Neighbor Indexes](https://mlsanity.com/paper/2607.29173/) (2026)
- [A Power Law in Logarithm's Clothing: On the Scalability of Graph-Based Vector Search](https://mlsanity.com/paper/2609.02143/) (2026)

## Abstract (arXiv)

Graph-based approaches are empirically shown to be very successful for the nearest neighbor search (NNS). However, there has been very little research on their theoretical guarantees. We fill this gap and rigorously analyze the performance of graph-based NNS algorithms, specifically focusing on the low-dimensional (d << log n) regime. In addition to the basic greedy algorithm on nearest neighbor graphs, we also analyze the most successful heuristics commonly used in practice: speeding up via adding shortcut edges and improving accuracy via maintaining a dynamic list of candidates. We believe that our theoretical insights supported by experimental analysis are an important step towards understanding the limits and benefits of graph-based NNS algorithms.