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cs.DS updates on arXiv.org

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
Forward-backward Contention Resolution Schemes for Fair R...
Will Ma, Calum MacRury, Cliff Stein · 2025-02-14 · via cs.DS updates on arXiv.org

We use contention resolution schemes (CRS) to derive algorithms for the fair rationing of a single resource when agents have stochastic demands. We aim to provide ex-ante guarantees on the level of service provided to each agent, who may measure service in different ways (Type-I, II, or III), calling for CRS under different feasibility constraints (rank-1 matroid or knapsack). We are particularly interested in two-order CRS where the agents are equally likely to arrive in a known forward order or its reverse, which is motivated by online rationing at food banks. In particular, we derive a two-order CRS for rank-1 matroids with guarantee $1/(1+e^{-1/2})\approx 0.622$, which we prove is tight. This improves upon the $1/2$ guarantee that is best-possible under a single order (Alaei, SIAM J. Comput. 2014), while achieving separation with the $1-1/e\approx 0.632$ guarantee that is possible for random-order CRS (Lee and Singla, ESA 2018). Because CRS guarantees imply prophet inequalities, this also beats the two-order prophet inequality with ratio $(\sqrt{5}-1)/2\approx 0.618$ from (Arsenis, SODA 2021), which was tight for single-threshold policies. Rank-1 matroids suffice to provide guarantees under Type-II or III service, but Type-I service requires knapsack. Accordingly, we derive a two-order CRS for knapsack with guarantee $1/3$, improving upon the $1/(3+e^{-2})\approx 0.319$ guarantee that is best-possible under a single order (Jiang et al., SODA 2022). To our knowledge, $1/3$ provides the best-known guarantee for knapsack CRS even in the offline setting. Finally, we provide an upper bound of $1/(2+e^{-1})\approx 0.422$ for two-order knapsack CRS, strictly smaller than the upper bound of $(1-e^{-2})/2\approx0.432$ for random-order knapsack CRS.