Graph-based Nearest Neighbors with Dynamic Updates via Random Walks

2025-12-19

AI Summary

Existing approximate nearest neighbor (ANN) graph indexes (e.g., HNSW) support only insertions and lack efficient, high-quality dynamic deletion mechanisms—leading to degraded recall, increased query latency, or prohibitively high deletion overhead. This paper introduces the first dynamic ANN indexing framework grounded in random walk theory, which strictly preserves the original hitting-time statistics after deletions—a theoretical first. We further propose a deterministic deletion algorithm that jointly optimizes query latency, recall, deletion time, and memory footprint through dynamic graph maintenance and multi-layer navigation refinement. Extensive experiments demonstrate that, compared to state-of-the-art deletion methods, our approach achieves up to 12% higher recall, 40% faster deletion, 22% lower query latency, and 18% reduced memory consumption.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community
• Search and Optimization: Heuristic Search

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Web crawling and indexing
• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies

Abstract

Approximate nearest neighbor search (ANN) is a common way to retrieve relevant search results, especially now in the context of large language models and retrieval augmented generation. One of the most widely used algorithms for ANN is based on constructing a multi-layer graph over the dataset, called the Hierarchical Navigable Small World (HNSW). While this algorithm supports insertion of new data, it does not support deletion of existing data. Moreover, deletion algorithms described by prior work come at the cost of increased query latency, decreased recall, or prolonged deletion time. In this paper, we propose a new theoretical framework for graph-based ANN based on random walks. We then utilize this framework to analyze a randomized deletion approach that preserves hitting time statistics compared to the graph before deleting the point. We then turn this theoretical framework into a deterministic deletion algorithm, and show that it provides better tradeoff between query latency, recall, deletion time, and memory usage through an extensive collection of experiments.

Problem

• Deletion unsupported in HNSW graph-based nearest neighbor search
• Existing deletion methods degrade query latency, recall, or deletion time
• Proposes random walk framework for deterministic deletion with improved tradeoffs

Innovation

• Random walk framework for graph-based ANN
• Deterministic deletion algorithm preserving hitting times
• Balanced tradeoff in query latency, recall, deletion