Related papers: Complexity of Local Search for Euclidean Clusterin…

Connected clustering denotes a family of constrained clustering problems in which we are given a distance metric and an undirected connectivity graph $G$ that can be completely unrelated to the metric. The aim is to partition the $n$…

Hierarchical clustering is a critical task in numerous domains. Many approaches are based on heuristics and the properties of the resulting clusterings are studied post hoc. However, in several applications, there is a natural cost function…

Local learning of sparse image models has proven to be very effective to solve inverse problems in many computer vision applications. To learn such models, the data samples are often clustered using the K-means algorithm with the Euclidean…

The minimum sum-of-squares clustering (MSSC), or k-means type clustering, is traditionally considered an unsupervised learning task. In recent years, the use of background knowledge to improve the cluster quality and promote…

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 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 study the \LowerBoundedCenter (\lbc) problem, which is a clustering problem that can be viewed as a variant of the \kCenter problem. In the \lbc problem, we are given a set of points P in a metric space and a lower bound \lambda, and the…

Nearest Neighbor Search (NNS) over generalized weighted distances is fundamental to a wide range of applications. The problem of NNS over the generalized weighted square Euclidean distance has been studied in previous work. However,…

The Euclidean Steiner Minimal Tree problem takes as input a set $\mathcal P$ of points in the Euclidean plane and finds the minimum length network interconnecting all the points of $\mathcal P$. In this paper, in continuation to the works…

Clustering is a basic task in data analysis and machine learning, and the optimization of clustering objectives are well-studied optimization problems; amongst these, the $k$-Means objective is arguably the most well known. Given a…

The seminal paper by Mazumdar and Saha \cite{MS17a} introduced an extensive line of work on clustering with noisy queries. Yet, despite significant progress on the problem, the proposed methods depend crucially on knowing the exact…

We give the first $2$-approximation algorithm for the cluster vertex deletion problem. This is tight, since approximating the problem within any constant factor smaller than $2$ is UGC-hard. Our algorithm combines the previous approaches,…

This paper develops an efficient algorithm for computing the Euclidean projection onto the top-k-sum constraint, a key operation in financial risk management and matrix optimization problems. Existing projection methods rely on sorting and…

We consider the problem of clustering in the learning-augmented setting, where we are given a data set in $d$-dimensional Euclidean space, and a label for each data point given by an oracle indicating what subsets of points should be…

This paper proposes a variant of the normalized cut algorithm for spectral clustering. Although the normalized cut algorithm applies the K-means algorithm to the eigenvectors of a normalized graph Laplacian for finding clusters, our…

The higher-order correlation clustering problem is an expressive model, and recently, local search heuristics have been proposed for several applications. Certifying optimality, however, is NP-hard and practically hampered already by the…

The 2-opt heuristic is a simple local search heuristic for the Travelling Salesperson Problem (TSP). Although it usually performs well in practice, its worst-case running time is poor. Attempts to reconcile this difference have used…

We develop data structures for dynamic closest pair problems with arbitrary distance functions, that do not necessarily come from any geometric structure on the objects. Based on a technique previously used by the author for Euclidean…

We consider the problem of encoding a set of vectors into a minimal number of bits while preserving information on their Euclidean geometry. We show that this task can be accomplished by applying a Johnson-Lindenstrauss embedding and…

We propose a nearest neighbor based clustering algorithm that results in a naturally defined hierarchy of clusters. In contrast to the agglomerative and divisive hierarchical clustering algorithms, our approach is not dependent on the…