Metrical Service Systems with Multiple Servers

The problem of metrical service systems with multiple servers (-MSSMS), proposed by Feuerstein (LATIN'98: Theoretical Informatics, Third Latin American Symposium, 1998), is to service requests, each of which is an -point subset of a metric space, using servers in an online manner, minimizing the distance traveled by the servers. We prove that Feuerstein's deterministic algorithm for -MSSMS actually achieves an improved competitive ratio of on uniform metrics. In the randomized online setting on uniform metrics, we give an algorithm which achieves a competitive ratio , beating the deterministic lower bound of . We prove that any randomized algorithm for -MSSMS on uniform metrics must be -competitive. For the offline -MSSMS, we give a factor pseudo-approximation algorithm using servers on any metric space, and prove a matching hardness result, that a pseudo-approximation using less than servers is unlikely, even on uniform metrics.