Unified Dominance Graph Tames Expensive Interval Predicates in ANNS

Existing range-filtering ANNS treats interval endpoints as independent scalar filters, forcing search to compute a Cartesian product of two constraints. That overhead kills latency in real-world workloads where every query must check object lifespans, price windows, or temporal validity. Enter the Unified Dominance Graph (UDG), a new paper on arXiv that rethinks the indexing primitive from the ground up.

The Two-Endpoint Trap

Interval predicates like containment or overlap rely on two coupled constraints: a start and an end. Separate them into independent filters and you pay intersection overhead that grows with the number of candidate neighbors. Specialized containment methods exist, but each requires its own index structure. UDG completely sidesteps that fragmentation by mapping both object and query endpoints into a normalized two-dimensional dominance space. Every supported interval predicate (containment, overlap, etc.) now reuses the same construction and search algorithms after a simple semantic mapping.

Compressing Proximity Graphs into One Structure

A single UDG instance is tied to exactly one predicate, but it compresses what would have been multiple query-state-specific proximity graphs into one compact index. To prevent search from failing under restrictive interval filters, the authors add validity-preserving patch edges that provide alternative routing choices when few objects remain valid. The result: a graph that stays navigable exactly when it needs to.

Measured Payoff

Extensive evaluations on standard benchmarks and real-world datasets show UDG delivering stable query performance across containment, overlap, and other interval relations. It significantly outperforms existing hybrid search baselines while keeping indexing overhead low. The paper doesn't publish raw QPS or recall numbers in the abstract, but the architecture is sound enough that any engineer who has wrestled with temporal or range-filtering ANNS will see the improvement immediately.

UDG turns a messy multi-structure problem into a clean geometric one. If your pipeline touches RAG over time-stamped documents or financial data with price intervals, this paper gives you a concrete indexing strategy that works out of the box for any two-boundary predicate.

Source: Unified Dominance Graph for Interval-Predicate Approximate Nearest Neighbor Search
Domain: arxiv.org