Revisiting Priority k-Center: Fairness and Outliers
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.
Fairness
Clustering
Approximation
Outliers
Theory of computation~Facility location and clustering
21:1-21:20
Track A: Algorithms, Complexity and Games
https://arxiv.org/abs/2103.03337
Tanvi
Bajpai
Tanvi Bajpai
University of Illinois, Urbana-Champaign, Urbana, IL, USA
Supported in part by NSF grant CCF-1910149.
Deeparnab
Chakrabarty
Deeparnab Chakrabarty
Dartmouth College, Hanover, NH, USA
Supported by NSF grants CCF-1813053 and CCF-2041920.
Chandra
Chekuri
Chandra Chekuri
University of Illinois, Urbana-Champaign, Urbana, IL, USA
Supported by NSF grants CCF-1910149 and CCF-1907939.
Maryam
Negahbani
Maryam Negahbani
Dartmouth College, Hanover, NH, USA
10.4230/LIPIcs.ICALP.2021.21
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Tanvi Bajpai, Deeparnab Chakrabarty, Chandra Chekuri, and Maryam Negahbani. Revisiting priority k-center: Fairness and outliers, 2021. URL: http://arxiv.org/abs/2103.03337.
http://arxiv.org/abs/2103.03337
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Tanvi Bajpai, Deeparnab Chakrabarty, Chandra Chekuri, and Maryam Negahbani
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