Revisiting Priority $k$-Center: Fairness and Outliers

• URL: http://arxiv.org/abs/2103.03337v1
• Date: Thu, 4 Mar 2021 21:15:37 GMT
• Title: Revisiting Priority $k$-Center: Fairness and Outliers
• Authors: Tanvi Bajpai, Deeparnab Chakrabarty, Chandra Chekuri, Maryam Negahbani
• Abstract summary: We 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.
• Score: 5.3898004059026325
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In the Priority $k$-Center problem, the input consists of a metric space $(X,d)$, an integer $k$ and for each point $v \in X$ a priority radius $r(v)$. The goal is to choose $k$-centers $S \subseteq X$ to minimize $\max_{v \in X} \frac{1}{r(v)} d(v,S)$. If all $r(v)$'s were uniform, one obtains the classical $k$-center problem. Plesn\'ik [Plesn\'ik, Disc. Appl. Math. 1987] introduced this problem and gave a $2$-approximation algorithm matching the best possible algorithm for vanilla $k$-center. We show how the problem is related to two different notions of fair clustering [Harris et al., NeurIPS 2018; Jung et al., FORC 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.

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