arXiv subjects

Ben Landrum

Publications and source records attributed to Ben Landrum.

4 recordsLinked to original sources

arXiv2026

Fast Sparse $α$-Navigable Graph Construction with Improved Resource Augmentation

Graph-based nearest neighbor search methods, which run greedy search on a directed graph over the data points, have surged in popularity in recent years. A common goal is to construct a search graph with the $α$-navigability property, which ensures that greedy search returns provably good approximate nearest neighbors and converges in few iterations. Increasing $α\geq 1$ improves accuracy and convergence rate, but requires more edges, which increases both space and search time. This tradeoff has motivated the study of algorithms for constructing a sparsest $α$-navigable graph for a given set of points. For any point set and any distance function, we show how to compute an $α$-navigable graph with at most $O(\log n)$ times as many edges as the sparsest $(1+\varepsilon)α$-navigable graph, in $O(n^ω\log(Δ)/\varepsilon)$ time, where $ω< 2.372$ is the matrix multiplication exponent and $Δ$ is the aspect ratio of the input. This improves on Khanna, Padaki, and Waingarten (SODA 2026), who achieve the same runtime but are only competitive with the sparsest $2(1+\varepsilon)α$-navigable graph. Since sparsity often increases rapidly with $α$ (typically $α\leq 1.1$), their bound can be significantly weaker. Previously, the best algorithm competing with the sparsest $(1+\varepsilon)α$-navigable graph required $\widetilde{O}(n^{2.5})$ time. Our techniques also extend to constructing sparse $τ$-monotonic graphs, another popular target in nearest neighbor search. Finally, we give a fine-grained complexity analysis suggesting that improving the $O(n^ω)$ running time is unlikely, or would require a very different approach. It is based on hardness results for problems related to verifying whether a graph is navigable, a topic of independent interest.

cs.DS↗

arXiv2026

Passing the Baton: High Throughput Distributed Disk-Based Vector Search with BatANN

Vector search underpins modern information-retrieval systems, including retrieval-augmented generation (RAG) pipelines and search engines over unstructured text and images. As datasets scale to billions of vectors, disk-based vector search has emerged as a practical solution. However, looking to the future, we must anticipate datasets too large for any single server and throughput demands that exceed the limits of locally attached SSDs. We present BatANN, a distributed disk-based approximate nearest neighbor (ANN) system that retains the logarithmic search efficiency of a single global graph while achieving near-linear throughput scaling in the number of servers. Our core innovation is that when accessing a neighborhood which is stored on another machine, we send the full state of the query to the other machine to continue executing there for improved locality. On 1B-point datasets at 0.95 recall using 10 servers, BatANN achieves 3.5-5.59x of the scatter-gather baseline and 1.44-2.09x the throughput of DistributedANN, respectively, while maintaining mean latency below 3 ms. Moreover, we get these results on standard TCP. To our knowledge, BatANN is the first open-source distributed disk-based vector search system to operate over a single global graph.

cs.DC↗

arXiv2025

Efficiently Constructing Sparse Navigable Graphs

Graph-based nearest neighbor search methods have seen a surge of popularity in recent years, offering state-of-the-art performance across a wide variety of applications. Central to these methods is the task of constructing a sparse navigable search graph for a given dataset endowed with a distance function. Unfortunately, doing so is computationally expensive, so heuristics are universally used in practice. In this work, we initiate the study of fast algorithms with provable guarantees for search graph construction. For a dataset with $n$ data points, the problem of constructing an optimally sparse navigable graph can be framed as $n$ separate but highly correlated minimum set cover instances. This yields a naive $O(n^3)$ time greedy algorithm that returns a navigable graph whose sparsity is at most $O(\log n)$ higher than optimal. We improve significantly on this baseline, taking advantage of correlation between the set cover instances to leverage techniques from streaming and sublinear-time set cover algorithms. By also introducing problem-specific pre-processing techniques, we obtain an $\tilde{O}(n^2)$ time algorithm for constructing an $O(\log n)$-approximate sparsest navigable graph under any distance function. The runtime of our method is optimal up to logarithmic factors under the Strong Exponential Time Hypothesis via a reduction from Monochromatic Closest Pair. Moreover, we prove that, as with general set cover, obtaining better than an $O(\log n)$-approximation is NP-hard, despite the significant additional structure present in the navigable graph problem. Finally, we show that our approach can also beat cubic time for the closely related and practically important problems of constructing $α$-shortcut reachable and $τ$-monotonic graphs, which are also used for nearest neighbor search. For such graphs, we obtain $\tilde{O}(n^{2.5})$ time or better algorithms.

cs.DS↗

arXiv2024

Results of the Big ANN: NeurIPS'23 competition

The 2023 Big ANN Challenge, held at NeurIPS 2023, focused on advancing the state-of-the-art in indexing data structures and search algorithms for practical variants of Approximate Nearest Neighbor (ANN) search that reflect the growing complexity and diversity of workloads. Unlike prior challenges that emphasized scaling up classical ANN search ~\cite{DBLP:conf/nips/SimhadriWADBBCH21}, this competition addressed filtered search, out-of-distribution data, sparse and streaming variants of ANNS. Participants developed and submitted innovative solutions that were evaluated on new standard datasets with constrained computational resources. The results showcased significant improvements in search accuracy and efficiency over industry-standard baselines, with notable contributions from both academic and industrial teams. This paper summarizes the competition tracks, datasets, evaluation metrics, and the innovative approaches of the top-performing submissions, providing insights into the current advancements and future directions in the field of approximate nearest neighbor search.

cs.IR↗