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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
On computing the (exact) Fréchet distance with a frog
Jacobus Conradi, Ivor van der Hoog, Eva Rotenberg · 2025-12-09 · via cs.DS updates on arXiv.org

The continuous Frechet distance between two polygonal curves is classically computed by exploring their free space diagram. Recently, Har-Peled, Raichel, and Robson [SoCG'25] proposed a radically different approach: instead of directly traversing the continuous free space, they approximate the distance by computing paths in a discrete graph derived from the discrete free space, recursively bisecting edges until the discrete distance converges to the continuous Frechet distance. They implement this so-called frog-based technique and report substantial practical speedups over the state of the art. We revisit the frog-based approach and address three of its limitations. First, the method does not compute the Frechet distance exactly. Second, the recursive bisection procedure only introduces the monotonicity events required to realise the Frechet distance asymptotically, that is, only in the limit. Third, the applied simplification technique is heuristic. Motivated by theoretical considerations, we develop new techniques that guarantee exactness, polynomial-time convergence, and near-optimal lossless simplifications. We provide an open-source C++ implementation of our variant. Our primary contribution is an extensive empirical evaluation. As expected, exact computation introduces overhead and increases the median running time. Yet, our method is often faster in the worst case, the slowest ten percent of instances, or even on average due to its convergence guarantees. More surprisingly, in our experiments, the implementation of Bringmann, Kuennemann, and Nusser [SoCG'19] consistently outperforms all frog-based approaches in practice. This appears to contrast published claims of the efficiency of the frog-based techniques. These results thereby provide nuanced perspective on frogs: highlighting both the theoretical appeal, but also the practical limitations.