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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
Live Exploration with Mobile Robots in a Dynamic Ring, Re...
Subhrangsu Mandal, Anisur Rahaman Molla, William K. Moses · 2020-01-14 · via cs.DS updates on arXiv.org

The graph exploration problem requires a group of mobile robots, initially placed arbitrarily on the nodes of a graph, to work collaboratively to explore the graph such that each node is eventually visited by at least one robot. One important requirement of exploration is the {\em termination} condition, i.e., the robots must know that exploration is completed. The problem of live exploration of a dynamic ring using mobile robots was recently introduced in [Di Luna et al., ICDCS 2016]. In it, they proposed multiple algorithms to solve exploration in fully synchronous and semi-synchronous settings with various guarantees when $2$ robots were involved. They also provided guarantees that with certain assumptions, exploration of the ring using two robots was impossible. An important question left open was how the presence of $3$ robots would affect the results. In this paper, we try to settle this question in a fully synchronous setting and also show how to extend our results to a semi-synchronous setting. In particular, we present algorithms for exploration with explicit termination using $3$ robots in conjunction with either (i) unique IDs of the robots and edge crossing detection capability (i.e., two robots moving in opposite directions through an edge in the same round can detect each other), or (ii) access to randomness. The time complexity of our deterministic algorithm is asymptotically optimal. We also provide complementary impossibility results showing that there does not exist any explicit termination algorithm for $2$ robots. The theoretical analysis and comprehensive simulations of our algorithm show the effectiveness and efficiency of the algorithm in dynamic rings. We also present an algorithm to achieve exploration with partial termination using $3$ robots in the semi-synchronous setting.