Related papers: Competitively Consistent Clustering
We study the consistent k-center clustering problem. In this problem, the goal is to maintain a constant factor approximate $k$-center solution during a sequence of $n$ point insertions and deletions while minimizing the recourse, i.e., the…
In metric $k$-clustering, we are given as input a set of $n$ points in a general metric space, and we have to pick $k$ centers and cluster the input points around these chosen centers, so as to minimize an appropriate objective function. In…
Given points from an arbitrary metric space and a sequence of point updates sent by an adversary, what is the minimum recourse per update (i.e., the minimum number of changes needed to the set of centers after an update), in order to…
This paper presents universal algorithms for clustering problems, including the widely studied $k$-median, $k$-means, and $k$-center objectives. The input is a metric space containing all potential client locations. The algorithm must…
In the dynamic metric $k$-median problem, we wish to maintain a set of $k$ centers $S \subseteq V$ in an input metric space $(V, d)$ that gets updated via point insertions/deletions, so as to minimize the objective $\sum_{x \in V} \min_{y…
We consider the approximability of center-based clustering problems where the points to be clustered lie in a metric space, and no candidate centers are specified. We call such problems "continuous", to distinguish from "discrete"…
In this paper, we consider the \emph{metric $k$-center} problem in the fully dynamic setting, where we are given a metric space $(V,d)$ evolving via a sequence of point insertions and deletions and our task is to maintain a subset $S…
Clustering is one of the most fundamental problems in unsupervised learning with a large number of applications. However, classical clustering algorithms assume that the data is static, thus failing to capture many real-world applications…
In fully dynamic clustering problems, a clustering of a given data set in a metric space must be maintained while it is modified through insertions and deletions of individual points. In this paper, we resolve the complexity of fully…
Given a sequence of adversarial point insertions and point deletions, is it possible to simultaneously optimize the approximation ratio, update time, and recourse for a $k$-clustering problem? If so, can this be achieved with worst-case…
We study two generalizations of classic clustering problems called dynamic ordered $k$-median and dynamic $k$-supplier, where the points that need clustering evolve over time, and we are allowed to move the cluster centers between…
We present approximation algorithms for some variants of center-based clustering and related problems in the fully dynamic setting, where the pointset evolves through an arbitrary sequence of insertions and deletions. Specifically, we…
We present the first algorithm for fully dynamic $k$-centers clustering in an arbitrary metric space that maintains an optimal $2+\epsilon$ approximation in $O(k \cdot \operatorname{polylog}(n,\Delta))$ amortized update time. Here, $n$ is…
We study in this paper the problem of maintaining a solution to $k$-median and $k$-means clustering in a fully dynamic setting. To do so, we present an algorithm to efficiently maintain a coreset, a compressed version of the dataset, that…
Given a stream of points in a metric space, is it possible to maintain a constant approximate clustering by changing the cluster centers only a small number of times during the entire execution of the algorithm? This question received…
The problem of constrained clustering has attracted significant attention in the past decades. In this paper, we study the balanced $k$-center, $k$-median, and $k$-means clustering problems where the size of each cluster is constrained by…
Recently, there has been substantial interest in clustering research that takes a beyond worst-case approach to the analysis of algorithms. The typical idea is to design a clustering algorithm that outputs a near-optimal solution, provided…
The $k$-center problem is a fundamental clustering variant with applications in learning systems and data summarization. In several real-world scenarios, the dataset to be clustered is not static, but evolves over time, as new data points…
Center-based clustering has attracted significant research interest from both theory and practice. In many practical applications, input data often contain background knowledge that can be used to improve clustering results. In this work,…
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…