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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
Efficient Deterministic Leader Election for Programmable ...
2021-06-02 · via cs.DS updates on arXiv.org

It was suggested that a programmable matter system (composed of multiple computationally weak mobile particles) should remain connected at all times since otherwise, reconnection is difficult and may be impossible. At the same time, it was not clear that allowing the system to disconnect carried a significant advantage in terms of time complexity. We demonstrate for a fundamental task, that of leader election, an algorithm where the system disconnects and then reconnects automatically in a non-trivial way (particles can move far away from their former neighbors and later reconnect to others). Moreover, the runtime of the temporarily disconnecting deterministic leader election algorithm is linear in the diameter. Hence, the disconnecting -- reconnecting algorithm is as fast as previous randomized algorithms. When comparing to previous deterministic algorithms, we note that some of the previous work assumed weaker schedulers. Still, the runtime of all the previous deterministic algorithms that did not assume special shapes of the particle system (shapes with no holes) was at least quadratic in $n$, where $n$ is the number of particles in the system. (Moreover, the new algorithm is even faster in some parameters than the deterministic algorithms that did assume special initial shapes.) Since leader election is an important module in algorithms for various other tasks, the presented algorithm can be useful for speeding up other algorithms under the assumption of a strong scheduler. This leaves open the question: "can a deterministic algorithm be as fast as the randomized ones also under weaker schedulers?"