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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
Reducing Shortcut and Hopset Constructions to Shallow Graphs
Bernhard Haeupler, Yonggang Jiang, Thatchaphol Saranurak · 2025-08-28 · via cs.DS updates on arXiv.org

We introduce a blackbox framework that simplifies all known parallel algorithms with near-linear work for single-source reachability and shortest paths in directed graphs. Specifically, existing reachability algorithms rely on constructing shortcuts; our blackbox allows these algorithms that construct shortcuts with hopbound $h$ to assume the input graph $G$ is ``shallow'', meaning if vertex $s$ can reach vertex $t$, it can do so in approximately $h$ hops. This assumption significantly simplifies shortcut construction [Fin18, JLS19], resulting in simpler parallel reachability algorithms. Furthermore, our blackbox extends naturally to simplify parallel algorithms for constructing hopsets and, consequently, for computing shortest paths [CFR20 , CF23 , RHM+23 ].