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Revisiting Priority k-Center: Fairness and Outliers

Authors Tanvi Bajpai, Deeparnab Chakrabarty, Chandra Chekuri, Maryam Negahbani

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  • Theory of computation → Facility location and clustering
Keywords
  • Fairness
  • Clustering
  • Approximation
  • Outliers

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Abstract

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.

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Tanvi Bajpai, Deeparnab Chakrabarty, Chandra Chekuri, and Maryam Negahbani. Revisiting Priority k-Center: Fairness and Outliers. In 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 198, pp. 21:1-21:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021) https://doi.org/10.4230/LIPIcs.ICALP.2021.21

Author Details

Tanvi Bajpai
  • University of Illinois, Urbana-Champaign, Urbana, IL, USA
Deeparnab Chakrabarty
  • Dartmouth College, Hanover, NH, USA
Chandra Chekuri
  • University of Illinois, Urbana-Champaign, Urbana, IL, USA
Maryam Negahbani
  • Dartmouth College, Hanover, NH, USA

Funding

  • Bajpai, Tanvi: Supported in part by NSF grant CCF-1910149.
  • Chakrabarty, Deeparnab: Supported by NSF grants CCF-1813053 and CCF-2041920.
  • Chekuri, Chandra: Supported by NSF grants CCF-1910149 and CCF-1907939.

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