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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
Preemptive Online Partitioning of Sequences
Christian Konrad, Tigran Tonoyan · 2017-02-21 · via cs.DS updates on arXiv.org

Online algorithms process their inputs piece by piece, taking irrevocable decisions for each data item. This model is too restrictive for most partitioning problems, since data that is yet to arrive may render it impossible to extend partial partitionings to the entire data set reasonably well. In this work, we show that preemption might be a potential remedy. We consider the problem of partitioning online sequences, where $p-1$ separators need to be inserted into a sequence of integers that arrives online so as to create $p$ contiguous partitions of similar weight. While without preemption no algorithm with non-trivial competitive ratio is possible, if preemption is allowed, i.e., inserted partition separators may be removed but not reinserted again, then we show that constant competitive algorithms can be obtained. Our contributions include: We first give a simple deterministic $2$-competitive preemptive algorithm for arbitrary $p$ and arbitrary sequences. Our main contribution is the design of a highly non-trivial partitioning scheme, which, under some natural conditions and $p$ being a power of two, allows us to improve the competitiveness to $1.68$. We also show that the competitiveness of deterministic (randomized) algorithms is at least $\frac{4}{3}$ (resp. $\frac{6}{5}$). For $p=2$, the problem corresponds to the interesting special case of preemptively guessing the center of a weighted request sequence. While deterministic algorithms fail here, we provide a randomized $1.345$-competitive algorithm for all-ones sequences and prove that this is optimal. For weighted sequences, we give a $1.628$-competitive algorithm and a lower bound of $1.5$.