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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
Advice Complexity bounds for Online Delayed F-Node-, H-No...
Niklas Berndt, Henri Lotze · 2023-03-30 · via cs.DS updates on arXiv.org

Let F be a fixed finite obstruction set of graphs and G be a graph revealed in an online fashion, node by node. The online Delayed F-Node-Deletion Problem (F-Edge-Deletion Problem}) is to keep G free of every H in F by deleting nodes (edges) until no induced subgraph isomorphic to any graph in F can be found in G. The task is to keep the number of deletions minimal. Advice complexity is a model in which an online algorithm has access to a binary tape of infinite length, on which an oracle can encode information to increase the performance of the algorithm. We are interested in the minimum number of advice bits that are necessary and sufficient to solve a deletion problem optimally. In this work, we first give essentially tight bounds on the advice complexity of the Delayed F-Node-Deletion Problem and F-Edge-Deletion Problem where F consists of a single, arbitrary graph H. We then show that the gadget used to prove these results can be utilized to give tight bounds in the case of node deletions if F consists of either only disconnected graphs or only connected graphs. Finally, we show that the number of advice bits that is necessary and sufficient to solve the general Delayed F-Node-Deletion Problem is heavily dependent on the obstruction set F. To this end, we provide sets for which this number is either constant, logarithmic or linear in the optimal number of deletions.