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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 Parallel Algorithms for k-Center Clustering
Jessica McClintock, Anthony Wirth · 2016-04-12 · via cs.DS updates on arXiv.org

The k-center problem is one of several classic NP-hard clustering questions. For contemporary massive data sets, RAM-based algorithms become impractical. And although there exist good sequential algorithms for k-center, they are not easily parallelizable. In this paper, we design and implement parallel approximation algorithms for this problem. We observe that Gonzalez's greedy algorithm can be efficiently parallelized in several MapReduce rounds; in practice, we find that two rounds are sufficient, leading to a 4-approximation. We contrast this with an existing parallel algorithm for k-center that runs in a constant number of rounds, and offers a 10-approximation. In depth runtime analysis reveals that this scheme is often slow, and that its sampling procedure only runs if k is sufficiently small, relative to the input size. To trade off runtime for approximation guarantee, we parameterize this sampling algorithm, and find in our experiments that the algorithm is not only faster, but sometimes more effective. Yet the parallel version of Gonzalez is about 100 times faster than both its sequential version and the parallel sampling algorithm, barely compromising solution quality.