COL-Trees: Efficient Hierarchical Object Search in Road Networks

2026-01-28

AI Summary

This work addresses the inefficiency of existing multi-agent nearest neighbor (AkNN) and farthest neighbor (kFN) query methods on road networks, which rely on Euclidean distance heuristics that poorly capture graph-structured properties. To overcome this limitation, the authors propose COL-Tree, a novel hierarchical data structure that introduces, for the first time, a landmark-based compact hierarchy into object search on road networks. By integrating landmark embedding with graph compression techniques, COL-Tree enables more accurate heuristic estimation and supports diverse spatial queries through an efficient hierarchical traversal algorithm. Extensive experiments on both real-world and synthetic datasets demonstrate that the proposed approach achieves up to four orders of magnitude improvement in query performance over state-of-the-art methods, with low preprocessing overhead, thereby offering significant theoretical innovation and practical utility.

Technology Category

• Search and Optimization: Heuristic Search
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Data Mining & Knowledge Management: Intelligent Query Processing

Application Category

• Graph Algorithms and Modeling for the Web: Querying, indexing, and retrieval in Web-related graphs
• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines
• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies

Abstract

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.

Problem

• hierarchical object search
• road networks
• aggregate k nearest neighbor
• k farthest neighbor
• location-based services

Innovation

• COL-Tree
• landmark-based heuristic
• hierarchical graph traversal
• road network search
• aggregate kNN