Related papers: Fully Dynamic Consistent $k$-Center Clustering

Offline k-means clustering was studied extensively, and algorithms with a constant approximation are available. However, online clustering is still uncharted. New factors come into play: the ordering of the dataset and whether the number of…

We explore clustering problems in the streaming sliding window model in both general metric spaces and Euclidean space. We present the first polylogarithmic space $O(1)$-approximation to the metric $k$-median and metric $k$-means problems…

Many real-world applications pose challenges in incorporating fairness constraints into the $k$-center clustering problem, where the dataset consists of $m$ demographic groups, each with a specified upper bound on the number of centers to…

Clustering is a hard discrete optimization problem. Nonconvex approaches such as low-rank semidefinite programming (SDP) have recently demonstrated promising statistical and local algorithmic guarantees for cluster recovery. Due to the…

Clustering aims to group unlabeled objects based on similarity inherent among them into clusters. It is important for many tasks such as anomaly detection, database sharding, record linkage, and others. Some clustering methods are taken as…

We consider clustering in the perturbation resilience model that has been studied since the work of Bilu and Linial [ICS, 2010] and Awasthi, Blum and Sheffet [Inf. Proc. Lett., 2012]. A clustering instance $I$ is said to be…

We study $k$-clustering problems with lower bounds, including $k$-median and $k$-means clustering with lower bounds. In addition to the point set $P$ and the number of centers $k$, a $k$-clustering problem with (uniform) lower bounds gets a…

The $k$-center problem for a point set~$P$ asks for a collection of $k$ congruent balls (that is, balls of equal radius) that together cover all the points in $P$ and whose radius is minimized. The $k$-center problem with outliers is…

In the Euclidean $k$-center problem in sliding window model, input points are given in a data stream and the goal is to find the $k$ smallest congruent balls whose union covers the $N$ most recent points of the stream. In this model, input…

The $k$-center problem is a classic facility location problem, where given an edge-weighted graph $G = (V,E)$ one is to find a subset of $k$ vertices $S$, such that each vertex in $V$ is "close" to some vertex in $S$. The approximation…

We study approximation algorithms for the socially fair $(\ell_p, k)$-clustering problem with $m$ groups, whose special cases include the socially fair $k$-median ($p=1$) and socially fair $k$-means ($p=2$) problems. We present (1) a…

We study the fair variant of the classic $k$-median problem introduced by Chierichetti et al. [2017]. In the standard $k$-median problem, given an input pointset $P$, the goal is to find $k$ centers $C$ and assign each input point to one of…

Fueled by massive data, important decision making is being automated with the help of algorithms, therefore, fairness in algorithms has become an especially important research topic. In this work, we design new streaming and distributed…

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…

In addition to finding meaningful clusters, centroid-based clustering algorithms such as K-means or mean-shift should ideally find centroids that are valid patterns in the input space, representative of data in their cluster. This is…

We study the problem of fair $k$-median where each cluster is required to have a fair representation of individuals from different groups. In the fair representation $k$-median problem, we are given a set of points $X$ in a metric space.…

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 initiate the study of the following general clustering problem. We seek to partition a given set $P$ of data points into $k$ clusters by finding a set $X$ of $k$ centers and assigning each data point to one of the centers. The cost of a…

This paper proposes a centroid-based clustering algorithm which is capable of clustering data-points with n-features, without having to specify the number of clusters to be formed. The core logic behind the algorithm is a similarity…

We consider the online $k$-median clustering problem in which $n$ points arrive online and must be irrevocably assigned to a cluster on arrival. As there are lower bound instances that show that an online algorithm cannot achieve a…