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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
Hypergraph dualization with FPT-delay parameterized by th...
Valentin Bartier, Oscar Defrain, Fionn Mc Inerney · 2023-05-12 · via cs.DS updates on arXiv.org

At STOC 2002, Eiter, Gottlob, and Makino presented a technique called ordered generation that yields an $n^{O(d)}$-delay algorithm listing all minimal transversals of an $n$-vertex hypergraph of degeneracy $d$. Recently at IWOCA 2019, Conte, Kanté, Marino, and Uno asked whether this XP-delay algorithm parameterized by $d$ could be made FPT-delay for a weaker notion of degeneracy, or even parameterized by the maximum degree $Δ$, i.e., whether it can be turned into an algorithm with delay $f(Δ)\cdot n^{O(1)}$ for some computable function $f$. Moreover, and as a first step toward answering that question, they note that they could not achieve these time bounds even for the particular case of minimal dominating sets enumeration. In this paper, using ordered generation, we show that an FPT-delay algorithm can be devised for minimal transversals enumeration parameterized by the degeneracy and dimension, giving a positive and more general answer to the latter question.