Theoretical and Empirical Analysis of Adaptive Entry Point Selection for Graph-based Approximate Nearest Neighbor Search

We present a theoretical and empirical analysis of the adaptive entry point selection for graph-based approximate nearest neighbor search (ANNS). We introduce novel concepts: $b\textit{-monotonic path}$ and $B\textit{-MSNET}$, which better capture an actual graph in practical algorithms than existing concepts like MSNET. We prove that adaptive entry point selection offers better performance upper bound than the fixed central entry point under more general conditions than previous work. Empirically, we validate the method's effectiveness in accuracy, speed, and memory usage across various datasets, especially in challenging scenarios with out-of-distribution data and hard instances. Our comprehensive study provides deeper insights into optimizing entry points for graph-based ANNS for real-world high-dimensional data applications.

General and Practical Tuning Method for Off-the-Shelf Graph-Based Index: SISAP Indexing Challenge Report by Team UTokyo

Despite the efficacy of graph-based algorithms for Approximate Nearest Neighbor (ANN) searches, the optimal tuning of such systems remains unclear. This study introduces a method to tune the performance of off-the-shelf graph-based indexes, focusing on the dimension of vectors, database size, and entry points of graph traversal. We utilize a black-box optimization algorithm to perform integrated tuning to meet the required levels of recall and Queries Per Second (QPS). We applied our approach to Task A of the SISAP 2023 Indexing Challenge and got second place in the 10M and 30M tracks. It improves performance substantially compared to brute force methods. This research offers a universally applicable tuning method for graph-based indexes, extending beyond the specific conditions of the competition to broader uses.