Fair Colorful k-Center Clustering

Jia, Xinrui; Sheth, Kshiteej; Svensson, Ola

doi:10.1007/978-3-030-45771-6_17

Cited by 24 publications

(21 citation statements)

References 10 publications

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“…The k-Center problem [10,11] is a well-studied formulation of clustering, where one wants to cover points in a metric space with balls of minimum radius around k of them. This problem has been investigated under multiple generalizations such as with outliers [9] and multiple color classes [2,3,12]. From the viewpoint of k-Center being a location and routing problem, classic k-Center represents minimizing the maximum service time, assuming the speed of service is uniform at all locations.…”

Section: Introductionmentioning

confidence: 99%

Towards Non-Uniform k-Center with Constant Types of Radii

Jia¹,

Rohwedder²,

Sheth³

et al. 2021

Preprint

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In the Non-Uniform k-Center problem we need to cover a finite metric space using k balls of different radii that can be scaled uniformly. The goal is to minimize the scaling factor. If the number of different radii is unbounded, the problem does not admit a constant-factor approximation algorithm but it has been conjectured that such an algorithm exists if the number of radii is constant. Yet, this is known only for the case of two radii. Our first contribution is a simple black box reduction which shows that if one can handle the variant of t − 1 radii with outliers, then one can also handle t radii. Together with an algorithm by Chakrabarty and Negahbani for two radii with outliers, this immediately implies a constant-factor approximation algorithm for three radii; thus making further progress on the conjecture. Furthermore, using algorithms for the k-center with outliers problem, that is the one radii with outliers case, we also get a simple algorithm for two radii.The algorithm by Chakrabarty and Negahbani uses a top-down approach, starting with the larger radius and then proceeding to the smaller one. Our reduction, on the other hand, looks only at the smallest radius and eliminates it, which suggests that a bottom-up approach is promising. In this spirit, we devise a modification of the Chakrabarty and Negahbani algorithm which runs in a bottom-up fashion, and in this way we recover their result with the advantage of having a simpler analysis.

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Section: Introductionmentioning

confidence: 99%

Towards Non-Uniform k-Center with Constant Types of Radii

Jia¹,

Rohwedder²,

Sheth³

et al. 2021

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…Many variations of k-Center have been studied, most of which are based on generalizations along one of the following two main axes: A preliminary version of this work was presented at the 21st Conference on Integer Programming and Combinatorial Optimization (IPCO 2020). An independent work of Jia, Sheth, and Svensson [22], presented at the same venue, gave a 3-approximation for Colorful k-Center with constantly many colors using different techniques.…”

Section: Introductionmentioning

confidence: 99%

A Technique for Obtaining True Approximations for k-Center with Covering Constraints

Anegg

Angelidakis

Kurpisz

et al. 2020

Integer Programming and Combinatorial Optimization

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There has been a recent surge of interest in incorporating fairness aspects into classical clustering problems. Two recently introduced variants of the k-Center problem in this spirit are Colorful k-Center, introduced by Bandyapadhyay, Inamdar, Pai, and Varadarajan, and lottery models, such as the Fair Robust k-Center problem introduced by Harris, Pensyl, Srinivasan, and Trinh. To address fairness aspects, these models, compared to traditional k-Center, include additional covering constraints. Prior approximation results for these models require to relax some of the normally hard constraints, like the number of centers to be opened or the involved covering constraints, and therefore, only obtain constant-factor pseudo-approximations. In this paper, we introduce a new approach to deal with such covering constraints that leads to (true) approximations, including a 4-approximation for Colorful k-Center with constantly many colorssettling an open question raised by Bandyapadhyay, Inamdar, Pai, and Varadarajan-and a 4-approximation for Fair Robust k-Center, for which the existence of a (true) constant-factor approximation was also open. We complement our results by showing that if one allows an unbounded number of colors, then Colorful k-Center admits no approximation algorithm with finite approximation guarantee, assuming that P = NP. Moreover, under the Exponential Time Hypothesis, the problem is inapproximable if the number of colors grows faster than logarithmic in the size of the ground set.

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“…Harb and Shan [123] improved upon these fair k-center results of [85] by developing a faster 5-approximation algorithm for the non-exemplar case, and a better 3-approximation algorithm for the case with centers as exemplars. Jia et al [120] proposed a 3-approximation algorithm for the k-center objective that allowed for multiple groups or colors. Esmaeili et al [118] proposed approximation algorithms in the general setting where points are allowed to have uncertain protected group membership (that is, protected group memberships are provided as a distribution), and a sample in the dataset is assumed to only belong to one protected group at a time.…”

Section: A Clustering Objective 1) Center-based Clusteringmentioning

confidence: 99%

An Overview of Fairness in Clustering

Chhabra¹,

Masalkovaite

Mohapatra

2021

IEEE Access

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Clustering algorithms are a class of unsupervised machine learning (ML) algorithms that feature ubiquitously in modern data science, and play a key role in many learning-based application pipelines. Recently, research in the ML community has pivoted to analyzing the fairness of learning models, including clustering algorithms. Furthermore, research on fair clustering varies widely depending on the choice of clustering algorithm, fairness definitions employed, and other assumptions made regarding models. Despite this, a comprehensive survey of the field does not exist. In this paper, we seek to bridge this gap by categorizing existing research on fair clustering, and discussing possible avenues for future work. Through this survey, we aim to provide researchers with an organized overview of the field, and motivate new and unexplored lines of research regarding fairness in clustering.

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Fair Colorful k-Center Clustering

Cited by 24 publications

References 10 publications

Towards Non-Uniform k-Center with Constant Types of Radii

Towards Non-Uniform k-Center with Constant Types of Radii

A Technique for Obtaining True Approximations for k-Center with Covering Constraints

An Overview of Fairness in Clustering

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