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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
Notes on Bit-reversal Broadcast Scheduling
Marcin Kik · 2012-01-17 · via cs.DS updates on arXiv.org

This report contains revision and extension of some results about RBO [arXiv:1108.5095]. RBO is a simple and efficient broadcast scheduling of $n = 2^k$ uniform frames for battery powered radio receivers. Each frame contains a key from some arbitrary linearly ordered universe. The broadcast cycle -- a sequence of frames sorted by the keys and permuted by $k$-bit reversal -- is transmitted in a round robin fashion by the broadcaster. At arbitrary time during the transmission, the receiver may start a simple protocol that reports to him all the frames with the keys that are contained in a specified interval of the key values $[K', K"]$. RBO receives at most $2 k + 1$ other frames' keys before receiving the first key from $[K', K"]$ or noticing that there are no such keys in the broadcast cycle. As a simple corollary, $4 k + 2$ is upper bound the number of keys outside $[K', K"]$ that will ever be received. In unreliable network the expected number of efforts to receive such frames is bounded by $(8 k + 4) / p + 2 (1 - p) / p^2$, where $p$ is probability of successful reception, and the reception rate of the requested frames is $p$ -- the highest possible. The receiver's protocol state consists of the values $k$, $K'$ and $K"$, one wake-up timer and two other $k$-bit variables. Its only nontrivial computation -- the computation of the next wake-up time slot -- can be performed in $O (k)$ simple operations, such as arithmetic/bit-wise operations on $k$-bit numbers, using only constant number of $k$-bit variables.