Service in Your Neighborhood: Fairness in Center Location

Authors Christopher Jung, Sampath Kannan, Neil Lutz

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Christopher Jung
  • University of Pennsylvania, Philadelphia, PA, USA
Sampath Kannan
  • University of Pennsylvania, Philadelphia, PA, USA
Neil Lutz
  • Iowa State University, Ames, IA, USA


We thank Moni Naor and Omer Reingold for helpful discussions, and we thank Anupam Gupta for alerting us to the similarities between our Theorem 2 and Lemma 1 of Chan, Dinitz, and Gupta [Chan et al., 2006].

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Christopher Jung, Sampath Kannan, and Neil Lutz. Service in Your Neighborhood: Fairness in Center Location. In 1st Symposium on Foundations of Responsible Computing (FORC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 156, pp. 5:1-5:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


When selecting locations for a set of centers, standard clustering algorithms may place unfair burden on some individuals and neighborhoods. We formulate a fairness concept that takes local population densities into account. In particular, given k centers to locate and a population of size n, we define the "neighborhood radius" of an individual i as the minimum radius of a ball centered at i that contains at least n/k individuals. Our objective is to ensure that each individual has a center that is within at most a small constant factor of her neighborhood radius. We present several theoretical results: We show that optimizing this factor is NP-hard; we give an approximation algorithm that guarantees a factor of at most 2 in all metric spaces; and we prove matching lower bounds in some metric spaces. We apply a variant of this algorithm to real-world address data, showing that it is quite different from standard clustering algorithms and outperforms them on our objective function and balances the load between centers more evenly.

Subject Classification

ACM Subject Classification
  • Theory of computation → Theory and algorithms for application domains
  • Fairness
  • Clustering
  • Facility Location


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