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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
Run-Length Encoding in a Finite Universe
N. Jesper Larsson · 2019-09-15 · via cs.DS updates on arXiv.org

Text compression schemes and compact data structures usually combine sophisticated probability models with basic coding methods whose average codeword length closely match the entropy of known distributions. In the frequent case where basic coding represents run-lengths of outcomes that have probability $p$, i.e. the geometric distribution $\Pr(i)=p^i(1-p)$, a \emph{Golomb code} is an optimal instantaneous code, which has the additional advantage that codewords can be computed using only an integer parameter calculated from $p$, without need for a large or sophisticated data structure. Golomb coding does not, however, gracefully handle the case where run-lengths are bounded by a known integer~$n$. In this case, codewords allocated for the case $i>n$ are wasted. While negligible for large $n$, this makes Golomb coding unattractive in situations where $n$ is recurrently small, e.g., when representing many short lists of integers drawn from limited ranges, or when the range of $n$ is narrowed down by a recursive algorithm. We address the problem of choosing a code for this case, considering efficiency from both information-theoretic and computational perspectives, and arrive at a simple code that allows computing a codeword using only $O(1)$ simple computer operations and $O(1)$ machine words. We demonstrate experimentally that the resulting representation length is very close (equal in a majority of tested cases) to the optimal Huffman code, to the extent that the expected difference is practically negligible. We describe efficient branch-free implementation of encoding and decoding.