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Service in Your Neighborhood: Fairness in Center Location

Authors Christopher Jung, Sampath Kannan, Neil Lutz

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  • Theory of computation → Theory and algorithms for application domains
Keywords
  • Fairness
  • Clustering
  • Facility Location

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Abstract

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.

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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) https://doi.org/10.4230/LIPIcs.FORC.2020.5

Author Details

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

Funding

  • Jung, Christopher: Research supported by a grant from the Quattrone Center, University of Pennsylvania.
  • Kannan, Sampath: Research supported in part by NSF Grants CCF-1733794 and CCF-1763307.

Acknowledgements

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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