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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
Design Patterns in Beeping Algorithms: Examples, Emulatio...
Arnaud Casteigts, Yves Métivier, John Michael Robson, Akka Zemma · 2016-07-11 · via cs.DS updates on arXiv.org

We consider networks of processes which interact with beeps. In the basic model defined by Cornejo and Kuhn (2010), processes can choose in each round either to beep or to listen. Those who beep are unable to detect simultaneous beeps. Those who listen can only distinguish between silence and the presence of at least one beep. We refer to this model as $BL$ (beep or listen). Stronger models exist where the nodes can detect collision while they are beeping ($B_{cd}L$), listening ($BL_{cd}$), or both ($B_{cd}L_{cd}$). Beeping models are weak in essence and even simple tasks are difficult or unfeasible within. We present a set of generic building blocks (design patterns) which seem to occur frequently in the design of beeping algorithms. They include multi-slot phases: the fact of dividing the main loop into a number of specialised slots; exclusive beeps: having a single node beep at a time in a neighbourhood (within one or two hops); adaptive probability: increasing or decreasing the probability of beeping to produce more exclusive beeps; internal (resp. peripheral) collision detection: for detecting collision while beeping (resp. listening). Based on these patterns, we provide algorithms for a number of basic problems, including colouring, 2-hop colouring, degree computation, 2-hop MIS, and collision detection (in $BL$). The patterns make it possible to formulate these algorithms in a rather concise and elegant way. Their analyses are more technical; one of them improves significantly upon that of the best known MIS algorithm by Jeavons et al. (2016). Finally, inspired by a technique from Afek et al. (2013), our last contribution is to show that any Las Vegas algorithm relying on collision detection can be transposed into a Monte Carlo algorithm without collision detection at the cost of a logarithmic slowdown, which we prove is optimal.