Graph-based Nearest Neighbors with Dynamic Updates via Random Walks

TL;DR

This paper introduces a new graph-based ANN framework using random walks, enabling efficient data deletion with minimal impact on search quality, addressing limitations of existing methods.

Contribution

It proposes a novel theoretical framework for graph-based ANN with randomized and deterministic deletion algorithms that improve tradeoffs in query latency, recall, and deletion time.

Findings

Deterministic deletion algorithm preserves hitting time statistics.

Proposed methods outperform existing approaches in experiments.

Enhanced balance between query speed, accuracy, and deletion efficiency.

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.