Approximating Fair Clustering with Cascaded Norm Objectives

Eden Chlamtác, Yury Makarychev, Ali Vakilian

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

1 Scopus citations

Abstract

We introduce the (p, q)-Fair Clustering problem. In this problem, we are given a set of points P and a collection of different weight functions W. We would like to find a clustering which minimizes the ℓq-norm of the vector over W of the ℓp-norms of the weighted distances of points in P from the centers. This generalizes various clustering problems, including Socially Fair k-Median and k-Means, and is closely connected to other problems such as Densest k-Subgraph and Min k-Union. We utilize convex programming techniques to approximate the (p, q)-Fair Clustering problem for different values of p and q. When p ≥ q, we get an O(k(p-q)/(2pq)), which nearly matches a kΩ((p-q)/(pq)) lower bound based on conjectured hardness of Min k-Union and other problems. When q ≥ p, we get an approximation which is independent of the size of the input for bounded p,q, and also matches the recent O((log n/(log log n))1/p)-approximation for (p, ∞)-Fair Clustering by Makarychev and Vakilian (COLT 2021)

Original languageEnglish
Title of host publicationACM-SIAM Symposium on Discrete Algorithms, SODA 2022
PublisherAssociation for Computing Machinery
Pages2664-2683
Number of pages20
ISBN (Electronic)9781611977073
StatePublished - 1 Jan 2022
Event33rd Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2022 - Alexander, United States
Duration: 9 Jan 202212 Jan 2022

Publication series

NameProceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms
Volume2022-January

Conference

Conference33rd Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2022
Country/TerritoryUnited States
CityAlexander
Period9/01/2212/01/22

ASJC Scopus subject areas

  • Software
  • Mathematics (all)

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