  The $k$-center problem is a central optimization problem with numerous
applications for machine learning, data mining, and communication networks.
Despite extensive study in various scenarios, it surprisingly has not been
thoroughly explored in the traditional distributed setting, where the
communication graph of a network also defines the distance metric.
  We initiate the study of the $k$-center problem in a setting where the
underlying metric is the graph's shortest path metric in three canonical
distributed settings: the LOCAL, CONGEST, and CLIQUE models. Our results
encompass constant-factor approximation algorithms and lower bounds in these
models, as well as hardness results for the bi-criteria approximation setting.
