Interval-aware Approximate Nearest Neighbor (ANN) search arises in applications where each object is associated with a numeric value or interval, and queries must satisfy both vector-similarity and interval constraints. Existing methods are typically tailored to a single query semantics, such as interval-filtered ANN search, and therefore require multiple specialized indexes to support diverse workloads, leading to substantial indexing and memory overhead. To address this limitation, we propose the Unified Interval-aware Relative Neighborhood Graph (URNG), a unified graph framework for interval-aware ANN search. URNG preserves the monotonic searchability of relative-neighborhood-graph based ANN indexes while additionally ensuring structural heredity over query-induced subgraphs, enabling a single index to support multiple interval-aware query semantics. Building on this framework, we develop UG, a practical graph index that efficiently approximates URNG through unified interval-aware pruning and iterative repair, together with a query algorithm for interval-aware ANN search. Extensive experiments on 5 datasets show that UG consistently achieves a strong accuracy-efficiency trade-off across diverse interval-aware workloads while maintaining competitive index construction cost and memory usage.

翻译：区间感知近似最近邻（ANN）搜索出现在每个对象关联数值或区间的应用中，且查询需同时满足向量相似性和区间约束。现有方法通常针对单一查询语义设计（如区间过滤ANN搜索），因此需要多个专用索引来支持多样化工作负载，导致索引构建和内存开销显著。为解决此限制，我们提出统一区间感知相对邻域图（URNG），一种用于区间感知ANN搜索的统一图框架。URNG在保留基于相对邻域图的ANN索引单调可搜索性的同时，额外确保查询诱导子图上的结构继承性，从而使得单一索引能够支持多种区间感知查询语义。基于此框架，我们开发了UG，一种通过统一区间感知剪枝和迭代修复高效近似URNG的实用图索引，以及用于区间感知ANN搜索的查询算法。在5个数据集上的大量实验表明，UG在多样化区间感知工作负载下始终实现强精度-效率权衡，同时保持有竞争力的索引构建成本和内存使用。