Prune, Don't Rebuild: Efficiently Tuning $\alpha$-Reachable Graphs for Nearest Neighbor Search

TL;DR

This paper introduces RP-Tuning, a post-hoc method to efficiently adjust the reachability parameter in graph-based nearest neighbor search algorithms, avoiding costly index rebuilds and maintaining theoretical guarantees.

Contribution

RP-Tuning provides a scalable, post-hoc approach to tune the reachability parameter in DiskANN, preserving theoretical guarantees and significantly reducing tuning time.

Findings

RP-Tuning accelerates DiskANN tuning by up to 43 times.

RP-Tuning maintains worst-case reachability guarantees in general metrics.

Empirical results show negligible overhead in tuning process.

Abstract

Vector similarity search is an essential primitive in modern AI and ML applications. Most vector databases adopt graph-based approximate nearest neighbor (ANN) search algorithms, such as DiskANN (Subramanya et al., 2019), which have demonstrated state-of-the-art empirical performance. DiskANN's graph construction is governed by a reachability parameter $\alpha$, which gives a trade-off between construction time, query time, and accuracy. However, adaptively tuning this trade-off typically requires rebuilding the index for different $\alpha$ values, which is prohibitive at scale. In this work, we propose RP-Tuning, an efficient post-hoc routine, based on DiskANN's pruning step, to adjust the $\alpha$ parameter without reconstructing the full index. Within the $\alpha$-reachability framework of prior theoretical works (Indyk and Xu, 2023; Gollapudi et al., 2025), we prove that pruning an initially $\alpha$-reachable graph with RP-Tuning preserves worst-case reachability guarantees in general metrics and improved guarantees in Euclidean metrics. Empirically, we show that RP-Tuning accelerates DiskANN tuning on four public datasets by up to $43\times$ with negligible overhead.