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PAC Learning with Bandit Feedback: Sharp Sample Complexity in the Realizable Setting Algorithms with Polynomially-Improved Approximation Factors for the $2 \rightarrow q$ Norm, and Applications A computational phase transition for learning-to-sample from Ising models Covering vertices by sequential stars Fermi-Dirac machines as quantizations of neurons A Comprehensive Evaluation of Vertex Elimination Algorithms for Algorithmic Differentiation A Tight Bound on Localization of Electrical Flows Optimal Dimension-Free Sampling for Regularized Classification Reducing the Randomness in Partition Oracles for Bounded Degree Minor-Free Graphs Beyond the Half-Approximation: Fair and Efficient Online Class Matching Efficient Uniform Sampling of Surjections via their Profiles Tractable Maximization of Budgeted Phylogenetic Diversity on Networks Utilizing Node Scanwidth Fairness in Aggregation: Optimal Top-$k$ and Improved Full Ranking Learning-Augmented Online Scheduling with Parsimonious Preemption Entropy Equivalence Testing Lumberjack: Better Differentially Private Random Forests through Heavy Hitter Detection in Trees The Secretary Problem with a Stochastic Precursor Polynomial-Time Robust Multiclass Linear Classification under Gaussian Marginals Efficient Banzhaf-Based Data Valuation for $k$-Nearest Neighbors Classification Block-Sphere Vector Quantization An Approximation Algorithm for Graph Label Selection Iterative Chow Filtering for Learning with Distribution Shift Complexity of Non-Log-Concave Sampling in Fisher Information Stochastic Matching via Local Sparsification Finite Sample Bounds for Learning with Score Matching What is Learnable in Valiant's Theory of the Learnable? Provable Quantization with Randomized Hadamard Transform Min-Max Optimization Requires Exponentially Many Queries Fast and Compact Graph Cuts for the Boykov-Kolmogorov Algorithm A proximal gradient algorithm for composite log-concave sampling
Optimized Customizable Route Planning in Large Road Netwo...
Muhammad Farhan, Henning Koehler · 2026-04-12 · via cs.DS updates on arXiv.org

Modern route planners such as Google Maps and Apple Maps serve millions of users worldwide, optmizing routes in large-scale road networks where fast responses are required under diverse cost metrics including travel time, fuel consumption, and toll costs. Classical algorithms like Dijkstra or A$^*$ are too slow at this scale, and while index-based techniques achieve fast queries, they are often tied to fixed metrics, making them unsuitable for dynamic conditions or user-specific metrics. Customizable approaches address this limitation by separating metric-independent preprocessing and metric-dependent customization, but they remain limited by slower query performance. Notably, Customizable Tree Labeling (CTL) was recently introduced as a promising framework that combines tree labelings with shortcut graphs. The shortcut graph enables efficient customization to different cost metrics, while tree labeling, supported by path arrays, provides fast query answering. Although CTL enables optimizing routes under different cost metrics, it still faces challenges in storing and reconstructing path information efficiently, which hinders its scalability for answering millions of queries. In this article, we build on the Customizable Tree Labeling framework to introduce new optimizations for the storage and reconstruction of path information. We develop several algorithmic variants that differ in the information retained within shortcut graphs and path arrays, offering a spectrum of trade-offs between memory usage and query performance. To further enhance scalability, we propose a batch processing strategy that shares path information across queries to eliminate redundant computation. Empirically, we have evaluated the performance of our algorithms on 13 real-world road networks. The results show that they significantly outperform state-of-the-art methods.