The online $$k$$ k -server problem with max-distance objective

Abstract

This paper studies the online $$k$$ k -server problem with max-distance objective, i.e. minimizing the maximum distance moved among all the servers. For this objective, we prove that no deterministic online algorithm has a competitive ratio better than $$k$$ k . We also analyze several classical algorithms for two special cases and show that some algorithms do have a competitive ratio of $$k$$ k and hence optimal. Consequently, we conjecture that any metric space allows for a deterministic $$k$$ k -competitive $$k$$ k -server algorithm with max-distance objective.