COL-Trees: Efficient Hierarchical Object Search in Spatial Networks

arXiv:2601.22183v2 Announce Type: replace Abstract: Many spatial network applications, such as map-based services, rely heavily on efficient methods to search for relevant nearby points-of-interest (POIs). A $k$ Nearest Neighbor ($k$NN) query is one such example that finds the $k$ closest POIs from an agent's location. While most existing techniques for spatial networks 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 (A$k$NN) queries require POIs that are close to multiple agents. $k$ Farthest Neighbors ($k$FN) 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 spatial networks such as road network graphs. 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 A$k$NN, $k$FN, and other queries. Our experiments evaluate performance on real-world and synthetic datasets including multiple types of spatial networks, such as road networks of varying sizes and edge weights, terrain networks, and 2D physics meshes. The results demonstrate that our techniques significantly outperform existing approaches, achieving up to three orders of magnitude improvement. Moreover, this comes at a small pre-processing overhead in both theory and practice.