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

TL;DR

RP-Tuning presents a practical, post-hoc pruning routine to adjust DiskANN's $\alpha$-reachable graphs without rebuilding, enabling rapid exploration of accuracy-latency-size trade-offs. Grounded in the $\alpha$-reachability framework, it proves worst-case guarantees for unsorted and sorted RobustPrune under general and Euclidean metrics, with Euclidean metrics offering improved bounds. Empirically, RP-Tuning accelerates DiskANN tuning up to $43\times$ on four public datasets and yields superior recall-per-QPS frontiers compared with rebuilds, validating both theory and practice. This approach enables index distillation across configurations tailored to diverse hardware and latency requirements while preserving high-quality navigation structure.

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 $α$, 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 $α$ 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 $α$ parameter without reconstructing the full index. Within the $α$-reachability framework of prior theoretical works (Indyk and Xu, 2023; Gollapudi et al., 2025), we prove that pruning an initially $α$-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.

Figures (5)

• Figure 1: The setting that achieves the optimal objective in the optimization problem in \ref{['lem:reduceunsorted']}.
• Figure 2: The settings that achieve optimal objectives in the optimization problem in \ref{['lem:reducesorted']} for (a) general metric spaces and (b) Euclidean metrics.
• Figure 3: Recall-QPS trade-off frontiers achieved by a base DiskANN graph of $\alpha_1 = 1.2$ then pruned graphs from the base graph via $\textsc{RP-Tuning}\xspace$ with $\alpha_2 = 1.1, 1.05, 1.01$, and the same base DiskANN graph of $\alpha = 1.2$ along with rebuilt DiskANN graphs of $\alpha = 1.1, 1.05, 1.01$.
• Figure 4: Recall-QPS trade-off frontiers achieved by a base DiskANN graph of $\alpha_1 = 1.2$ (blue curves with circles) and pruned graphs (curves with squares) from the base graph of $\alpha_2 = 1.1, 1.05, 1.01$. Average degrees (Deg) of individual graphs are also included.
• Figure 5: Compare Recall-QPS performance of pruned (solid curves) and rebuilt (dashed curves) DiskANN indices. Pruned and rebuilt indices of the same $\alpha$ value share a color. Average degrees (Deg) of individual graphs are also included.

Theorems & Definitions (13)

• Definition 2.1: $\alpha$-reachable and $\alpha$-reachability
• Lemma 2.2: Lemma 3.2 and 3.3 in indyk2023worstcaseperformancepopularapproximate
• Theorem 2.3: Theorem 1.1 in gollapudi2025sort
• Theorem 3.1: Unsorted Reachability
• Theorem 3.2: Sorted Reachability
• Lemma 3.3: Lemma 3.3 in indyk2023worstcaseperformancepopularapproximate
• Lemma 3.3
• Lemma 3.4
• proof
• Lemma 3.4