Location-based services rely heavily on efficient methods that search for relevant points-of-interest (POIs) near a given location. A k Nearest Neighbor (kNN) query is one such example that finds the k closest POIs from an agent's location. While most existing techniques focus on retrieving nearby POIs for a single agent, these search heuristics do not translate to many other applications. For example, Aggregate k Nearest Neighbor (AkNN) queries require POIs that are close to multiple agents. k Farthest Neighbor (kFN) queries require POIs that are the antithesis of nearest. Such problems naturally benefit from a hierarchical approach, but existing methods rely on Euclidean-based heuristics, which have diminished effectiveness in graphs such as road networks. We propose a novel data structure, COL-Tree (Compacted Object-Landmark Tree), to address this gap by enabling efficient hierarchical graph traversal using a more accurate landmark-based heuristic. We then present query algorithms that utilize COL-Trees to efficiently answer AkNN, kFN, and other queries. In our experiments on real-world and synthetic datasets, we demonstrate that our techniques significantly outperform existing approaches, achieving up to 4 orders of magnitude improvement. Moreover, this comes at a small pre-processing overhead in both theory and practice.

翻译：基于位置的服务严重依赖于在给定位置附近搜索相关兴趣点（POI）的高效方法。k近邻（kNN）查询即为一例，它从智能体位置查找k个最近的POI。现有技术大多专注于为单个智能体检索附近POI，但这些搜索启发式方法无法适用于许多其他应用场景。例如，聚合k近邻（AkNN）查询需要为多个智能体寻找邻近的POI；k远邻（kFN）查询则需要获取与"最近"相反的POI。此类问题天然适合采用层次化方法解决，但现有方法依赖于基于欧氏距离的启发式规则，其在路网等图结构中的有效性会显著降低。为弥补这一缺陷，我们提出一种新颖的数据结构——COL-Tree（压缩对象地标树），通过采用更精确的基于地标的启发式方法实现高效的层次化图遍历。随后我们提出基于COL-T树的查询算法，可高效应答AkNN、kFN及其他类型查询。在真实数据集与合成数据集上的实验表明，我们的方法显著优于现有技术，最高可实现4个数量级的性能提升，且无论在理论还是实践中都仅需极小的预处理开销。