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Found 10 papers, 2 papers with code
An Analysis of $D^α$ seeding for $k$-means
For any $\alpha>2$, we show that $D^\alpha$ seeding guarantees in expectation an approximation factor of $$ O_\alpha \left((g_\alpha)^{2/\alpha}\cdot \left(\frac{\sigma_{\mathrm{max}}}{\sigma_{\mathrm{min}}}\right)^{2-4/\alpha}\cdot (\min\{\ell,\log k\})^{2/\alpha}\right)$$ with respect to the standard $k$-means cost of any underlying clustering; where $g_\alpha$ is a parameter capturing the concentration of the points in each cluster, $\sigma_{\mathrm{max}}$ and $\sigma_{\mathrm{min}}$ are the maximum and minimum standard deviation of the clusters around their means, and $\ell$ is the number of distinct mixing weights in the underlying clustering (after rounding them to the nearest power of $2$).
Parallel and Efficient Hierarchical k-Median Clustering
In this paper we introduce a new parallel algorithm for the Euclidean hierarchical $k$-median problem that, when using machines with memory $s$ (for $s\in \Omega(\log^2 (n+\Delta+d))$), outputs a hierarchical clustering such that for every fixed value of $k$ the cost of the solution is at most an $O(\min\{d, \log n\} \log \Delta)$ factor larger in expectation than that of an optimal solution.
Nearly-Tight and Oblivious Algorithms for Explainable Clustering
We give an algorithm that outputs an explainable clustering that loses at most a factor of $O(\log^2 k)$ compared to an optimal (not necessarily explainable) clustering for the $k$-medians objective, and a factor of $O(k \log^2 k)$ for the $k$-means objective.
Semi-Streaming Algorithms for Submodular Matroid Intersection
Their approach is based on the versatile local ratio technique and also applies to generalizations such as weighted hypergraph matchings.
Data Structures and Algorithms
Fast and Accurate $k$-means++ via Rejection Sampling
$k$-means++ \cite{arthur2007k} is a widely used clustering algorithm that is easy to implement, has nice theoretical guarantees and strong empirical performance.
The Primal-Dual method for Learning Augmented Algorithms
The extension of classical online algorithms when provided with predictions is a new and active research area.
Learning Augmented Energy Minimization via Speed Scaling
As power management has become a primary concern in modern data centers, computing resources are being scaled dynamically to minimize energy consumption.
Beyond $1/2$-Approximation for Submodular Maximization on Massive Data Streams
It is the first low-memory, single-pass algorithm that improves the factor $0. 5$, under the natural assumption that elements arrive in a random order.
Beyond 1/2-Approximation for Submodular Maximization on Massive Data Streams
It is the first low-memory, singlepass algorithm that improves the factor 0. 5, under the natural assumption that elements arrive in a random order.
Linear Relaxations for Finding Diverse Elements in Metric Spaces
We first study the approximation quality of the algorithm by comparing with the LP objective.
