Metrical service systems with multiple servers

Abstract

The problem of metrical service systems with multiple servers ((k,l)-MSSMS) proposed by Feuerstein [16] is to service requests, each of which is an l-point subset of a metric space, using k servers in an online manner, minimizing the distance traveled by the servers. We prove that Feuerstein's deterministic algorithm 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 Ω(logkl)-competitive. On arbitrary metric spaces, we have deterministic lower bounds which are significantly larger than the bound for uniform metrics [8]. For the offline (k,l)-MSSMS, we give a factor l pseudo-approximation algorithm using kl servers on any metric space, and prove a matching hardness result, that a pseudo-approximation using less than kl servers is unlikely, even on uniform metrics. © 2013 Springer-Verlag Berlin Heidelberg.