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 $k\left({{k+l}\choose{l}}-1\right)$ on uniform metrics. In the randomized online setting on uniform metrics, we give an algorithm which achieves a competitive ratio $\mathcal{O}(k^3\log l)$, beating the deterministic lower bound of ${{k+l}\choose{l}}-1$. 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.