Fully-Dynamic Coresets

  title={Fully-Dynamic Coresets},
  author={Monika Henzinger and Sagar Kale},
With input sizes becoming massive, coresets -- small yet representative summary of the input -- are relevant more than ever. A weighted set $C_w$ that is a subset of the input is an $\varepsilon$-coreset if the cost of any feasible solution $S$ with respect to $C_w$ is within $[1 {\pm} \varepsilon]$ of the cost of $S$ with respect to the original input. We give a very general technique to compute coresets in the fully-dynamic setting where input points can be added or deleted. Given a static… Expand
2 Citations
Coresets for Clustering with Missing Values
The first coreset for clustering points in R that have multiple missing values (coordinates) is provided, which exhibits a flexible tradeoff between coreset size and accuracy, and generally outperforms the uniformsampling baseline. Expand
Robust Coreset for Continuous-and-Bounded Learning (with Outliers)
This paper proposes a novel robust coreset method for the continuous-and-bounded learning problem (with outliers) which includes a broad range of popular optimization objectives in machine learning, like logistic regression and k-means clustering and can be efficiently maintained in fully-dynamic environment. Expand


New Frameworks for Offline and Streaming Coreset Constructions
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Data streaming algorithms for the k-median problem in high-dimensional dynamic geometric data streams that guarantee only positive weights in the coreset with additional logarithmic factors in the space and time complexities are presented. Expand
On Coresets for k-Median and k-Means Clustering in Metric and Euclidean Spaces and Their Applications
  • K. Chen
  • Mathematics, Computer Science
  • SIAM J. Comput.
  • 2009
These are the first streaming algorithms, for those problems, that have space complexity with polynomial dependency on the dimension, using $O(d^2k^2\varepsilon^{-2}\log^8n)$ space. Expand
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An Improved Approximation for k-Median and Positive Correlation in Budgeted Optimization
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It is shown that a conjecture that there is no truly subcubic (O(n3-ε) time algorithm for this problem can be used to exhibit the underlying polynomial time hardness shared by many dynamic problems. Expand