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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
Deterministic Digital Clustering of Wireless Ad Hoc Networks
Tomasz Jurdzinski, Dariusz R. Kowalski, Michal Rozanski, Grzegor · 2017-08-29 · via cs.DS updates on arXiv.org

We consider deterministic distributed communication in wireless ad hoc networks of identical weak devices under the SINR model without predefined infrastructure. Most algorithmic results in this model rely on various additional features or capabilities, e.g., randomization, access to geographic coordinates, power control, carrier sensing with various precision of measurements, and/or interference cancellation. We study a pure scenario, when no such properties are available. As a general tool, we develop a deterministic distributed clustering algorithm. Our solution relies on a new type of combinatorial structures (selectors), which might be of independent interest. Using the clustering, we develop a deterministic distributed local broadcast algorithm accomplishing this task in $O(Δ\log^*N \log N)$ rounds, where $Δ$ is the density of the network. To the best of our knowledge, this is the first solution in pure scenario which is only polylog$(n)$ away from the universal lower bound $Ω(Δ)$, valid also for scenarios with randomization and other features. Therefore, none of these features substantially helps in performing the local broadcast task. Using clustering, we also build a deterministic global broadcast algorithm that terminates within $O(D(Δ+ \log^* N) \log N)$ rounds, where $D$ is the diameter of the network. This result is complemented by a lower bound $Ω(D Δ^{1-1/α})$, where $α> 2$ is the path-loss parameter of the environment. This lower bound shows that randomization or knowledge of own location substantially help (by a factor polynomial in $Δ$) in the global broadcast. Therefore, unlike in the case of local broadcast, some additional model features may help in global broadcast.