Related papers: Optimal Fully Dynamic $k$-Centers Clustering

We study the problem of $k$-means clustering in the space of straight-line segments in $\mathbb{R}^{2}$ under the Hausdorff distance. For this problem, we give a $(1+\epsilon)$-approximation algorithm that, for an input of $n$ segments, for…

Given a trajectory $T$ and a distance $\Delta$, we wish to find a set $C$ of curves of complexity at most $\ell$, such that we can cover $T$ with subcurves that each are within Fr\'echet distance $\Delta$ to at least one curve in $C$. We…

The Johnson-Lindenstrauss (JL) Lemma introduced the concept of dimension reduction via a random linear map, which has become a fundamental technique in many computational settings. For a set of $n$ points in $\mathbb{R}^d$ and any fixed…

The learning of mixture models can be viewed as a clustering problem. Indeed, given data samples independently generated from a mixture of distributions, we often would like to find the {\it correct target clustering} of the samples…

We present a scalable algorithm for the individually fair ($p$, $k$)-clustering problem introduced by Jung et al. and Mahabadi et al. Given $n$ points $P$ in a metric space, let $\delta(x)$ for $x\in P$ be the radius of the smallest ball…

We introduce the {\it diffusion $K$-means} clustering method on Riemannian submanifolds, which maximizes the within-cluster connectedness based on the diffusion distance. The diffusion $K$-means constructs a random walk on the similarity…

Given a set of points, clustering consists of finding a partition of a point set into $k$ clusters such that the center to which a point is assigned is as close as possible. Most commonly, centers are points themselves, which leads to the…

We study the cluster recovery problem in the semi-supervised active clustering framework. Given a finite set of input points, and an oracle revealing whether any two points lie in the same cluster, our goal is to recover all clusters…

Motivated by the fact that distances between data points in many real-world clustering instances are often based on heuristic measures, Bilu and Linial~\cite{BL} proposed analyzing objective based clustering problems under the assumption…

Kernel-based clustering algorithms have the ability to capture the non-linear structure in real world data. Among various kernel-based clustering algorithms, kernel k-means has gained popularity due to its simple iterative nature and ease…

We consider the problem of explainable $k$-medians and $k$-means introduced by Dasgupta, Frost, Moshkovitz, and Rashtchian~(ICML 2020). In this problem, our goal is to find a threshold decision tree that partitions data into $k$ clusters…

We study Euclidean $k$-Means under the Massively Parallel Computation (MPC) model, focusing on the \emph{fully-scalable} setting. Our main result is a fully-scalable $O((\log n/\log\log n)^2)$-approximation in $O(1)$ rounds. Previously,…

We study the classical metric $k$-median clustering problem over a set of input rankings (i.e., permutations), which has myriad applications, from social-choice theory to web search and databases. A folklore algorithm provides a…

Capacitated fair-range $k$-clustering generalizes classical $k$-clustering by incorporating both capacity constraints and demographic fairness. In this setting, each facility has a capacity limit and may belong to one or more demographic…

In fully dynamic graphs, we know how to maintain a 2-approximation of maximum matching extremely fast, that is, in polylogarithmic update time or better. In a sharp contrast and despite extensive studies, all known algorithms that maintain…

A maximal matching can be maintained in fully dynamic (supporting both addition and deletion of edges) $n$-vertex graphs using a trivial deterministic algorithm with a worst-case update time of O(n). No deterministic algorithm that…

In a geometric $k$-clustering problem the goal is to partition a set of points in $\mathbb{R}^d$ into $k$ subsets such that a certain cost function of the clustering is minimized. We present data structures for orthogonal range-clustering…

We present deterministic algorithms for maintaining a $(3/2 + \epsilon)$ and $(2 + \epsilon)$-approximate maximum matching in a fully dynamic graph with worst-case update times $\hat{O}(\sqrt{n})$ and $\tilde{O}(1)$ respectively. The…

Clustering is an effective technique in data mining to generate groups that are the matter of interest. Among various clustering approaches, the family of k-means algorithms and min-cut algorithms gain most popularity due to their…

We present an efficient algorithm for the min-max correlation clustering problem. The input is a complete graph where edges are labeled as either positive $(+)$ or negative $(-)$, and the objective is to find a clustering that minimizes the…