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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 Adaptive Multi-Round Allocation with Stochastic Arrivals The tractability landscape of diffusion alignment: regularization, rewards, and computational primitives Mistake-Bounded Language Generation Positional LSH: Binary Block Matrix Approximation for Attention with Linear Biases Learning-Augmented Scalable Linear Assignment Problem Optimization via Neural Dual Warm-Starts A Note on Non-Negative $L_1$-Approximating Polynomials Curvature Beyond Positivity: Greedy Guarantees for Arbitrary Submodular Functions Convex Optimization with Nested Evolving Feasible Sets On the Complexity of the Matching Problem of Regular Expressions with Backreferences Simple KNN-Based Outlier Detection Achieves Robust Clustering Online Allocation with Unknown Shared Supply Equivalence of Coarse and Fine-Grained Models for Learning with Distribution Shift Accelerated Relax-and-Round for Concave Coverage Problems Contrastive Identification and Generation in the Limit Quantizing With Randomized Hadamard Transforms: Efficient Heuristic Now Proven Nearly Optimal Attention Coresets On Computing Total Variation Distance Between Mixtures of Product Distributions Exact and Approximate Algorithms for Polytree Learning Provable Accuracy Collapse in Embedding-Based Representations under Dimensionality Mismatch New Bounds for Kernel Sums via Fast Spherical Embeddings Unlearning Offline Stochastic Multi-Armed Bandits Matroid Algorithms Under Size-Sensitive Independence Oracles On the Learning Curves of Revenue Maximization Asymptotically Robust Learning-Augmented Algorithms for Preemptive FIFO Buffer Management Flashback: A Reversible Bilateral Run-Peeling Decomposition of Strings Incremental Strongly Connected Components with Predictions Characterizing Admissible Objective Functions for Hierarchical Clustering Well-Conditioned Oblivious Perturbations in Linear Space Mathematical Foundations for Peer-to-Peer Lattice Computation Graph Neural Network-Informed Predictive Flows for Faster Ford-Fulkerson and PAC-Learnability A weighted angle distance on strings Towards Universal Convergence of Backward Error in Linear System Solvers Constant-Factor Approximations for Doubly Constrained Fair k-Center, k-Median and k-Means Tight Bounds for Learning Polyhedra with a Margin Efficiency of Proportional Mechanisms in Online Auto-Bidding Advertising Skyline-First Traversal as a Control Mechanism for Multi-Criteria Graph Search Constant-Factor Approximation for the Uniform Decision Tree Limited Perfect Monotonical Surrogates constructed using low-cost recursive linkage discovery with guaranteed output Query Lower Bounds for Diffusion Sampling Early Pruning for Public Transport Routing Adapting Dijkstra for Buffers and Unlimited Transfers Exploiting Low-Rank Structure in Max-K-Cut Problems Partial Optimality in the Preordering Problem High-accuracy log-concave sampling with stochastic queries Learning to Approximate Uniform Facility Location via Graph Neural Networks Linear Regression with Unknown Truncation Beyond Gaussian Features Adaptive Power Iteration Method for Differentially Private PCA Finite and Corruption-Robust Regret Bounds in Online Inverse Linear Optimization under M-Convex Action Sets Learning Mixture Models via Efficient High-dimensional Sparse Fourier Transforms Variance Computation for Weighted Model Counting with Knowledge Compilation Approach Deterministic Coreset for Lp Subspace Online Algorithms for Repeated Optimal Stopping: Balancing Baseline Guarantees and Regret Learned Static Function Data Structures Optimal hypersurface decision trees A Perfectly Truthful Calibration Measure The Geometry of LLM Quantization: GPTQ as Babai's Nearest Plane Algorithm Best Agent Identification for General Game Playing A Faster Generalized Two-Stage Approximate Top-K Fast and Simple Densest Subgraph with Predictions Smoothed Analysis of Learning from Positive Samples Ineffectiveness for Search and Undecidability of PCSP Meta-Problems Sample-Efficient Optimization over Generative Priors via Coarse Learnability Efficient distributional regression trees learning algorithms for calibrated non-parametric probabilistic forecasts Testing Noise Assumptions of Learning Algorithms Testing Support Size More Efficiently Than Learning Histograms Sharper Bounds for Chebyshev Moment Matching, with Applications Expander Hierarchies for Normalized Cuts on Graphs Multilayer Correlation Clustering Efficient Parameter Estimation of Truncated Boolean Product Distributions Faster Hamiltonian Monte Carlo by Learning Leapfrog Scale: a self-calibrated randomized solution
Group Evacuation on a Line by Agents with Different Communication Abilities
Jurek Czyzowicz, Ryan Killick, Evangelos Kranakis, Danny Krizanc · 2021-09-27 · via cs.DS updates on arXiv.org

We consider evacuation of a group of $n \geq 2$ autonomous mobile agents (or robots) from an unknown exit on an infinite line. The agents are initially placed at the origin of the line and can move with any speed up to the maximum speed $1$ in any direction they wish and they all can communicate when they are co-located. However, the agents have different wireless communication abilities: while some are fully wireless and can send and receive messages at any distance, a subset of the agents are senders, they can only transmit messages wirelessly, and the rest are receivers, they can only receive messages wirelessly. The agents start at the same time and their communication abilities are known to each other from the start. Starting at the origin of the line, the goal of the agents is to collectively find a target/exit at an unknown location on the line while minimizing the evacuation time, defined as the time when the last agent reaches the target. We investigate the impact of such a mixed communication model on evacuation time on an infinite line for a group of cooperating agents. In particular, we provide evacuation algorithms and analyze the resulting competitive ratio ($CR$) of the evacuation time for such a group of agents. If the group has two agents of two different types, we give an optimal evacuation algorithm with competitive ratio $CR=3+2 \sqrt{2}$. If there is a single sender or fully wireless agent, and multiple receivers we prove that $CR \in [2+\sqrt{5},5]$, and if there are multiple senders and a single receiver or fully wireless agent, we show that $CR \in [3,5.681319]$. Any group consisting of only senders or only receivers requires competitive ratio 9, and any other combination of agents has competitive ratio 3.