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Serving Clients Fairly: On Facility Location and k-Median with Fair Outliers

Authors Rajni Dabas , Samir Khuller , Emilie Rivkin

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Subject Classification

ACM Subject Classification
  • Theory of computation → Facility location and clustering
Keywords
  • Approximation algorithms
  • fairness

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Abstract

Classical clustering problems such as Facility Location and k-Median aim to efficiently serve a set of clients from a subset of facilities - minimizing the total cost of facility openings and client assignments in Facility Location, and minimizing assignment (service) cost under a facility count constraint in k-Median. These problems are highly sensitive to outliers, and therefore researchers have studied variants that allow excluding a small number of clients as outliers to reduce cost. However, in many real-world settings, clients belong to different demographic or functional groups, and unconstrained outlier removal can disproportionately exclude certain groups, raising fairness concerns, especially when the facilities correspond to critically needed facilities for emergencies such as fire stations, hospitals and other emergency services.
We study Facility Location with Fair Outliers, where each group is allowed a specified number of outliers, and the objective is to minimize total cost while respecting group-wise fairness constraints. We present a bicriteria approximation with a O(1/ε) approximation factor and (1+ 2ε) factor violation in outliers per group. For k-Median with Fair Outliers, we design a bicriteria approximation with a 4(1+ω/ε) approximation factor and (ω + ε) violation in outliers per group improving on prior work by avoiding dependence on k in outlier violations. We also prove that the problems are W[1]-hard parameterized by ω. 
We complement our algorithmic contributions with a detailed empirical analysis, demonstrating that fairness can be achieved with negligible increase in cost and that the integrality gap of the standard LP is small in practice.

Cite As Get BibTex

Rajni Dabas, Samir Khuller, and Emilie Rivkin. Serving Clients Fairly: On Facility Location and k-Median with Fair Outliers. In 7th Symposium on Foundations of Responsible Computing (FORC 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 368, pp. 9:1-9:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.FORC.2026.9

Author Details

Rajni Dabas
  • Northwestern University, Evanston, IL, USA
Samir Khuller
  • Northwestern University, Evanston, IL, USA
Emilie Rivkin
  • Northwestern University, Evanston, IL, USA

Funding

Supported by NSF 2216970 (IDEAL) as well as a gift from Adobe Labs.

Supplementary Materials

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