Optimally Selecting Representative Agents from a Metric Space
This paper studies the problem of proportionally fair clustering, where the goal is to select $k$ ``centers'' from a metric space that fairly represent a set of agents who also lie in the metric space. Specifically, we focus on finding a clustering satisfying a fairness property known as the Droop core. In the practical special case in which the set of feasible center locations contains every agent location, the previous best-known result guaranteed a $(1 + \sqrt{2})$-approximation of the Droop core, while the best-known lower bound was $2$. In this paper, we show that this lower bound is tight and that a clustering in the $2$-Droop core always exists. Further, we show that such a cluster...
| Authors | Benjamin Cookson, Eva Deltl, Yeeseok Oh |
|---|---|
| Primary category | cs.GT |
| Published | 29 August 2026 |
| Last updated at source | 29 August 2026 |
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