相关论文: Approximation Algorithms for Socially Fair Cluster…

A basic problem in spectral clustering is the following. If a solution obtained from the spectral relaxation is close to an integral solution, is it possible to find this integral solution even though they might be in completely different…

This paper considers the well-studied algorithmic regime of designing a $(1+\epsilon)$-approximation algorithm for a $k$-clustering problem that runs in time $f(k,\epsilon)poly(n)$ (sometimes called an efficient parameterized approximation…

In the past few years powerful generalizations to the Euclidean k-means problem have been made, such as Bregman clustering [7], co-clustering (i.e., simultaneous clustering of rows and columns of an input matrix) [9,18], and tensor…

The classical center based clustering problems such as $k$-means/median/center assume that the optimal clusters satisfy the locality property that the points in the same cluster are close to each other. A number of clustering problems arise…

Given their widespread usage in the real world, the fairness of clustering methods has become of major interest. Theoretical results on fair clustering show that fairness enjoys transitivity: given a set of small and fair clusters, a…

We revisit the simultaneous approximation model for the correlation clustering problem introduced by Davies, Moseley, and Newman[DMN24]. The objective is to find a clustering that minimizes given norms of the disagreement vector over all…

We establish Multilayer Correlation Clustering, a novel generalization of Correlation Clustering to the multilayer setting. In this model, we are given a series of inputs of Correlation Clustering (called layers) over the common set $V$ of…

$k$-Clustering in $\mathbb{R}^d$ (e.g., $k$-median and $k$-means) is a fundamental machine learning problem. While near-linear time approximation algorithms were known in the classical setting for a dataset with cardinality $n$, it remains…

Metric clustering is fundamental in areas ranging from Combinatorial Optimization and Data Mining, to Machine Learning and Operations Research. However, in a variety of situations we may have additional requirements or knowledge, distinct…

We propose the first \emph{local search} algorithm for Euclidean clustering that attains an $O(1)$-approximation in almost-linear time. Specifically, for Euclidean $k$-Means, our algorithm achieves an $O(c)$-approximation in $\tilde{O}(n^{1…

The $k$-center problem is a classical clustering problem in which one is asked to find a partitioning of a point set $P$ into $k$ clusters such that the maximum radius of any cluster is minimized. It is well-studied. But what if we add up…

In this paper, we study parallel algorithms for the correlation clustering problem, where every pair of two different entities is labeled with similar or dissimilar. The goal is to partition the entities into clusters to minimize the number…

The subspace approximation problem Subspace($k$,$p$) asks for a $k$-dimensional linear subspace that fits a given set of points optimally, where the error for fitting is a generalization of the least squares fit and uses the $\ell_{p}$ norm…

The goal of clustering is to group similar objects into meaningful partitions. This process is well understood when an explicit similarity measure between the objects is given. However, far less is known when this information is not readily…

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…

We propose a novel clustering model encompassing two well-known clustering models: k-center clustering and k-median clustering. In the Hybrid k-Clusetring problem, given a set P of points in R^d, an integer k, and a non-negative real r, our…

We present a unified framework that yields EPASes for constrained $(k,z)$-clustering in metric spaces of bounded (algorithmic) scatter dimension, a notion introduced by Abbasi et al. (FOCS 2023). They showed that several well known metric…

Fair clustering is the process of grouping similar entities together, while satisfying a mathematically well-defined fairness metric as a constraint. Due to the practical challenges in precise model specification, the prescribed fairness…

Clustering is a fundamental problem in unsupervised learning, and has been studied widely both as a problem of learning mixture models and as an optimization problem. In this paper, we study clustering with respect the emph{k-median}…

In many submodular optimization applications, datasets are naturally partitioned into disjoint subsets. These scenarios give rise to submodular optimization problems with partition-based constraints, where the desired solution set should be…