eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2021-07-02
21:1
21:20
10.4230/LIPIcs.ICALP.2021.21
article
Revisiting Priority k-Center: Fairness and Outliers
Bajpai, Tanvi
1
Chakrabarty, Deeparnab
2
Chekuri, Chandra
1
Negahbani, Maryam
2
University of Illinois, Urbana-Champaign, Urbana, IL, USA
Dartmouth College, Hanover, NH, USA
In the Priority k-Center problem, the input consists of a metric space (X,d), an integer k and for each point v ∈ X a priority radius r(v). The goal is to choose k-centers S ⊆ X to minimize max_{v ∈ X} 1/(r(v)) d(v,S). If all r(v)’s were uniform, one obtains the classical k-center problem. Plesník [Ján Plesník, 1987] introduced this problem and gave a 2-approximation algorithm matching the best possible algorithm for vanilla k-center. We show how the Priority k-Center problem is related to two different notions of fair clustering [Harris et al., 2019; Christopher Jung et al., 2020]. Motivated by these developments we revisit the problem and, in our main technical contribution, develop a framework that yields constant factor approximation algorithms for Priority k-Center with outliers. Our framework extends to generalizations of Priority k-Center to matroid and knapsack constraints, and as a corollary, also yields algorithms with fairness guarantees in the lottery model of Harris et al.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol198-icalp2021/LIPIcs.ICALP.2021.21/LIPIcs.ICALP.2021.21.pdf
Fairness
Clustering
Approximation
Outliers