mlsanityData to 7 Oct 2026

Graph-based Nearest Neighbor Search: From Practice to Theory

arXiv 1907.00845 ↗First posted 1 Jul 2019cs.DS math.PRcited by 19

Not on the map. Why?

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.

Key facts. Cited by 19 papers in the map (data through 7 Oct 2026). First posted on arXiv 1 Jul 2019.

Builds on

No reference list yet.

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 1; 2022: 3; 2023: 3; 2024: 7; 2025: 2; 2026: 3.

19 papers.

Sort:

By area:

  1. 2021SPANN: Highly-efficient Billion-scale Approximate Nearest Neighbor Searchcited by 35
  2. 2023Worst-case Performance of Popular Approximate Nearest Neighbor Search Implementations: Guarantees and Limitationscited by 20
  3. 2024RoarGraph: A Projected Bipartite Graph for Efficient Cross-Modal Approximate Nearest Neighbor Searchcited by 12
  4. 2024Approximate Nearest Neighbor Search with Window Filterscited by 11
  5. 2023A Theoretical Analysis Of Nearest Neighbor Search On Approximate Near Neighbor Graphcited by 10
  6. 2022Survival Kernets: Scalable and Interpretable Deep Kernel Survival Analysis with an Accuracy Guaranteecited by 9
  7. 2024Navigable Graphs for High-Dimensional Nearest Neighbor Search: Constructions and Limitscited by 7
  8. 2022Navigable Proximity Graph-Driven Native Hybrid Queries with Structured and Unstructured Constraintscited by 6
  9. 2023PECANN: Parallel Efficient Clustering with Graph-Based Approximate Nearest Neighbor Searchcited by 3
  10. 2024Probabilistic Routing for Graph-Based Approximate Nearest Neighbor Searchcited by 3
  11. 2024Approximate Nearest Neighbour Search on Dynamic Datasets: An Investigationcited by 2
  12. 2024ELEMENT: Episodic and Lifelong Exploration via Maximum Entropycited by 2
7 more
  1. 2022ARM 4-BIT PQ: SIMD-based Acceleration for Approximate Nearest Neighbor Search on ARMcited by 1
  2. 2024Theoretical and Empirical Analysis of Adaptive Entry Point Selection for Graph-based Approximate Nearest Neighbor Searchcited by 1
  3. 2025Distance Adaptive Beam Search for Provably Accurate Graph-Based Nearest Neighbor Searchcited by 0
  4. 2025Graph-based Nearest Neighbors with Dynamic Updates via Random Walkscited by 0
  5. 2026FGIM: a Fast Graph-based Indexes Merging Framework for Approximate Nearest Neighbor Searchcited by 0
  6. 2026MERIT: Efficient In-Place Deletion for Dynamic Graph-Based Approximate Nearest Neighbor Indexescited by 0
  7. 2026A Power Law in Logarithm's Clothing: On the Scalability of Graph-Based Vector Searchcited by 0