RNSG: A Range-Aware Graph Index for Efficient Range-Filtered Approximate Nearest Neighbor Search

TL;DR

RNSG introduces a range-aware graph index based on RRNG theory, enabling efficient range-filtered approximate nearest neighbor search with lower cost and higher performance.

Contribution

The paper proposes the RNSG index built on RRNG theory, unifying spatial and attribute proximity for efficient RFANN search with theoretical guarantees.

Findings

RNSG outperforms existing methods in query speed and index compactness.

RNSG has lower construction cost than state-of-the-art approaches.

Experiments on real datasets validate RNSG's efficiency and effectiveness.

Abstract

Range-filtered approximate nearest neighbor (RFANN) search is a fundamental operation in modern data systems. Given a set of objects, each with a vector and a numerical attribute, an RFANN query retrieves the nearest neighbors to a query vector among those objects whose numerical attributes fall within the range specified by the query. Existing state-of-the-art methods for RFANN search often require constructing multiple range-specific graph indexes to achieve high query performance, which incurs significant indexing overhead. To address this, we first establish a novel graph indexing theory, the range-aware relative neighborhood graph (RRNG), which jointly considers spatial and attribute proximity. We prove that the RRNG satisfies two crucial properties: (1) monotonic search-ability, which ensures correct nearest neighbor retrieval via beam search; and (2) structural heredity, which guarantees that any range-induced subgraph remains a valid RRNG, thus enabling efficient search with a single graph index. Based on this theoretical foundation, we propose a new graph index called RNSG as a practical solution that efficiently approximates RRNG. We develop fast algorithms for both constructing the RNSG index and processing RFANN queries with it. Extensive experiments on five real-world datasets show that RNSG achieves significantly higher query performance with a more compact index and lower construction cost than existing state-of-the-art methods.