Related papers: New Approximation Algorithms for Fair $k$-median P…

Due to the growing concern about unsavory behaviors of machine learning models toward certain demographic groups, the notion of 'fairness' has recently drawn much attention from the community, thereby motivating the study of fairness in…

Fair top-$k$ selection, which ensures appropriate proportional representation of members from minority or historically disadvantaged groups among the top-$k$ selected candidates, has drawn significant attention. We study the problem of…

Sorting is one of the most basic primitives in many algorithms and data analysis tasks. Comparison-based sorting algorithms, like quick-sort and merge-sort, are known to be optimal when the outcome of each comparison is error-free. However,…

An instance of colorful k-center consists of points in a metric space that are colored red or blue, along with an integer k and a coverage requirement for each color. The goal is to find the smallest radius \r{ho} such that there exist…

In this paper, we study the fault-tolerant matroid median and fault-tolerant knapsack median problems. These two problems generalize many fundamental clustering and facility location problems, such as uniform fault-tolerant $k$-median,…

Constrained clustering problems generalize classical clustering formulations, e.g., $k$-median, $k$-means, by imposing additional constraints on the feasibility of clustering. There has been significant recent progress in obtaining…

We present a study on how to effectively reduce the dimensions of the $k$-means clustering problem, so that provably accurate approximations are obtained. Four algorithms are presented, two \textit{feature selection} and two \textit{feature…

We consider a recently introduced fair repetitive scheduling problem involving a set of clients, each asking for their associated job to be daily scheduled on a single machine across a finite planning horizon. The goal is to determine a job…

In this paper, we study k-means++ and k-means++ parallel, the two most popular algorithms for the classic k-means clustering problem. We provide novel analyses and show improved approximation and bi-criteria approximation guarantees for…

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 restricted max-min fair allocation problem seeks an allocation of resources to players that maximizes the minimum total value obtained by any player. It is NP-hard to approximate the problem to a ratio less than 2. Comparing the current…

$k$-center is one of the most popular clustering models. While it admits a simple 2-approximation in polynomial time in general metrics, the Euclidean version is NP-hard to approximate within a factor of 1.93, even in the plane, if one…

This paper investigates the following natural greedy procedure for clustering in the bi-criterion setting: iteratively grow a set of centers, in each round adding the center from a candidate set that maximally decreases clustering cost. In…

We study the notion of perturbation resilience introduced by Bilu and Linial (2010) and Awasthi, Blum, and Sheffet (2012). A clustering problem is $\alpha$-perturbation resilient if the optimal clustering does not change when we perturb all…

The $k$-means method is an iterative clustering algorithm which associates each observation with one of $k$ clusters. It traditionally employs cluster centers in the same space as the observed data. By relaxing this requirement, it is…

Fair resource allocation is a fundamental optimization problem with applications in operations research, networking, and economic and game theory. Research in these areas has led to the general acceptance of a class of $\alpha$-fair utility…

In 2015, Driemel, Krivo\v{s}ija and Sohler introduced the $(k,\ell)$-median problem for clustering polygonal curves under the Fr\'echet distance. Given a set of input curves, the problem asks to find $k$ median curves of at most $\ell$…

In this paper we study constrained subspace approximation problem. Given a set of $n$ points $\{a_1,\ldots,a_n\}$ in $\mathbb{R}^d$, the goal of the {\em subspace approximation} problem is to find a $k$ dimensional subspace that best…

This paper provides a general mathematical optimization based framework to incorporate fairness measures from the facilities' perspective to Discrete and Continuous Maximal Covering Location Problems. The main ingredients to construct a…

$k$-means clustering is a well-studied problem due to its wide applicability. Unfortunately, there exist strong theoretical limits on the performance of any algorithm for the $k$-means problem on worst-case inputs. To overcome this barrier,…