An Empirical Survey and Benchmark of Learned Distance Indexes for Road Networks

The calculation of shortest-path distances in road networks is a core operation in navigation systems, location-based services, and spatial analytics. Although classical algorithms, e.g., Dijkstra’s algorithm, provide exact answers, their latency is prohibitive for modern real-time, large-scale deployments. Over the past two decades, numerous distance indexes have been proposed to speed up query processing for shortest distance queries. More recently, with the advancement in machine learning (ML), researchers have designed and proposed ML-based distance indexes to answer approximate shortest path and distance queries efficiently. However, a comprehensive and systematic evaluation of these ML-based approaches is lacking. This paper presents the first empirical survey of ML-based distance indexes on road networks, evaluating them along four key dimensions: Training time, query latency, storage, and accuracy. Using seven real-world road networks and workload-driven query datasets derived from trajectory data, we benchmark ten representative ML techniques and compare them against strong classical non-ML baselines, highlighting key insights and practical trade-offs. We release a unified open-source codebase to support reproducibility and future research on learned distance indexes.

💡 Research Summary

The paper presents the first comprehensive empirical survey and benchmark of machine‑learning‑based distance indexes for road networks. Shortest‑path distance queries are a fundamental operation in navigation, route planning, traffic monitoring, and location‑based services, yet classical exact algorithms such as Dijkstra or all‑pairs distance oracles are too slow or storage‑intensive for modern real‑time, large‑scale deployments. Over the past two decades, a rich body of classical distance indexes (graph hierarchies, separators, landmarks, hub labeling) has been proposed, achieving microsecond‑level query latency at the cost of substantial preprocessing time and memory. More recently, researchers have introduced learned distance indexes that approximate the distance function using neural networks, graph neural networks (GNNs), or tree‑based models, thereby compressing the O(n²) distance matrix into O(n·d) embeddings and enabling constant‑time inference on modern hardware accelerators.

The authors formalize the problem as learning a function ˆd(u,v) ≈ d(u,v) from a training set of node‑pair distances. They introduce a unified encoder‑decoder abstraction: the encoder maps each vertex to a d‑dimensional embedding (via lookup tables, pre‑trained graph embeddings, or GNN message passing), and the decoder combines two embeddings using a fusion operator (concatenation, average, sum, difference, Hadamard product) and a lightweight scoring model (norm‑based or small feed‑forward network). This abstraction neatly captures both non‑ML landmark methods and a variety of ML approaches.

Ten representative ML techniques are surveyed, spanning four categories: (1) Landmark‑based non‑ML (serves as a baseline within the abstraction); (2) GeoDNN, a simple feed‑forward network that consumes raw latitude/longitude coordinates; (3) DistanceNN and EmbedNN, which freeze unsupervised graph embeddings (Node2Vec, LINE, Poincaré) as encoders and train a small decoder; (4) GNN‑based models that learn embeddings end‑to‑end by propagating messages over the road graph. For each method the authors discuss scalability to large graphs, handling of dynamic updates, and computational trade‑offs. The majority of parameters reside in the encoder’s embedding matrix, while decoders remain lightweight.

The experimental evaluation uses seven real‑world road networks (e.g., California, Germany, major Korean cities) and workload‑driven query sets derived from trajectory logs, rather than synthetic random pairs. Four strong classical baselines are included: three approximate indexes (landmarks, hub labeling, contraction hierarchies) and one exact state‑of‑the‑art index. The benchmark measures training time, index construction time, storage overhead, average and tail query latency, mean absolute error (MAE), and relative error.

Key findings: • Learned indexes achieve 5‑10× storage reduction compared with classical approximate indexes while cutting average query latency by 2‑3×, but incur relative errors ranging from 5 % to 12 % depending on the model. • GNN‑based models deliver the highest accuracy (MAE < 5 %) but require substantial GPU memory and longer training times. • Landmark‑based non‑ML indexes remain the fastest (sub‑microsecond queries) and simplest to implement, yet they lack efficient update mechanisms; any edge insertion or weight change forces a full recomputation of landmark distances. • GeoDNN is the lightest model (only coordinate features) and answers queries in O(1) time, but its error is higher because it cannot capture the non‑linear topology of road graphs. • Fusion operators matter: average and Hadamard product consistently outperform simple concatenation, especially when embedding dimensions are modest. • Updating a learned index is most practical when the encoder is a static lookup table (e.g., landmark distances) and only the decoder is retrained; full‑graph retraining is costly for dynamic road networks.

The authors derive several practical insights: road networks have low average degree and large diameters, which makes low‑dimensional embeddings surprisingly effective; hardware accelerators dramatically reduce training cost but inference can be performed efficiently on CPUs with a lightweight decoder; a hybrid approach that combines a static, easily updatable encoder (e.g., landmark distances) with a learned decoder offers a good balance of accuracy, latency, and update friendliness. The paper also releases an open‑source benchmarking framework that standardizes data preprocessing, model training, and evaluation, facilitating reproducibility and future extensions.

In conclusion, learned distance indexes show strong promise for reducing storage and latency in road‑network distance queries, but their adoption must consider accuracy requirements, update frequency, and hardware resources. Future work is suggested on dynamic update mechanisms, incorporation of multimodal features (traffic conditions, time‑of‑day), and large‑scale deployment studies.