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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
Spatial Locality and Granularity Change in Caching
Nathan Beckmann, Phillip B Gibbons, Charles McGuffey · 2022-05-29 · via cs.DS updates on arXiv.org

Caches exploit temporal and spatial locality to allow a small memory to provide fast access to data stored in large, slow memory. The temporal aspect of locality is extremely well studied and understood, but the spatial aspect much less so. We seek to gain an increased understanding of spatial locality by defining and studying the Granularity-Change Caching Problem. This problem modifies the traditional caching setup by grouping data items into blocks, such that a cache can choose any subset of a block to load for the same cost as loading any individual item in the block. We show that modeling such spatial locality significantly changes the caching problem. This begins with a proof that Granularity-Change Caching is NP-Complete in the offline setting, even when all items have unit size and all blocks have unit load cost. In the online setting, we show a lower bound for competitive ratios of deterministic policies that is significantly worse than traditional caching. Moreover, we present a deterministic replacement policy called Item-Block Layered Partitioning and show that it obtains a competitive ratio close to that lower bound. Moreover, our bounds reveal a new issue arising in the Granularity-Change Caching Problem where the choice of offline cache size affects the competitiveness of different online algorithms relative to one another. To deal with this issue, we extend a prior (temporal) locality model to account for spatial locality, and provide a general lower bound in addition to an upper bound for Item-Block Layered Partitioning.