Unified Dominance Graph for Interval-Predicate Approximate Nearest Neighbor Search

2026-06-23

AI Summary

This work addresses the challenge of efficiently supporting mixed queries involving interval predicates—such as containment and overlap—in approximate nearest neighbor (ANN) search, a task poorly handled by existing methods due to their reliance on coupled endpoint conditions or lack of a general indexing abstraction. The authors propose the Unified Dominance Graph (UDG), which maps both data objects and query intervals into a normalized two-dimensional dominance space and constructs a graph index annotated with dominance labels. This framework is the first to enable unified ANN search across diverse interval predicates. By leveraging semantic mappings, UDG facilitates index reuse, and it further enhances traversal efficiency under strong filtering through validity-preserving patch edges. Experiments demonstrate that UDG consistently outperforms state-of-the-art approaches across various interval relationships and workloads, achieving low indexing overhead and stable query performance.

Abstract

Approximate Nearest Neighbor Search (ANNS) is a core primitive for unstructured data retrieval. Real-world applications--such as temporal databases, financial data analysis, and retrieval-augmented generation--often require hybrid queries whose valid objects are constrained by continuous interval attributes, such as lifespans or price ranges. We study Interval-Predicate ANNS (IPANNS), where validity is determined by a predicate between an object interval and a query interval. Existing range-filtering ANNS (RFANNS) methods are designed for single-dimensional scalar filters, but interval predicates such as containment and overlap rely on two coupled endpoint constraints. Treating endpoints as independent scalar attributes can incur large intersection overhead, while containment-specific methods lack a generalized indexing abstraction. In this paper, we propose the Unified Dominance Graph (UDG), a graph-indexing framework for the closed two-bound conjunctive fragment of IPANNS. For a chosen interval predicate, UDG maps object and query endpoints into a normalized two-dimensional dominance space and builds a dominance-labeled graph over the transformed coordinates. Containment, overlap, and other supported endpoint-bound predicates therefore reuse the same construction and search algorithms after semantic mapping, while each UDG instance remains tied to its selected predicate. UDG compresses query-state-specific proximity graphs into one compact index. To improve graph search under restrictive interval filters, we add validity-preserving patch edges that provide routing choices when few objects remain valid. Extensive evaluations on standard benchmarks and real-world datasets show that UDG achieves stable query performance across multiple interval relations and workloads, significantly outperforming existing hybrid search baselines while maintaining low indexing overhead.

Problem

• Approximate Nearest Neighbor Search
• Interval Predicate
• Hybrid Query
• Range Filtering
• Graph Indexing

Innovation

• Unified Dominance Graph
• Interval-Predicate ANNS
• dominance space
• graph indexing
• hybrid query