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Metrical Service Systems with Multiple Servers

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Abstract

The problem of metrical service systems with multiple servers (\((k,l)\)-MSSMS), proposed by Feuerstein (LATIN’98: Theoretical Informatics, Third Latin American Symposium, 1998), 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 for \((k,l)\)-MSSMS actually achieves an improved competitive ratio of \(k\left( {{k+l}\atopwithdelims (){l}}-1\right) \) 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 \({{k+l}\atopwithdelims (){l}}-1\). We prove that any randomized algorithm for \((k,l)\)-MSSMS on uniform metrics must be \(\varOmega (\log kl)\)-competitive. 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.

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Notes

  1. Feuerstein used ‘\(w\)’ for the width parameter, while we use ‘\(l\)’.

  2. For instance, when \(k=\Theta (l)\), Feuerstein’s bound is \(\varOmega (l^l)\), whereas ours is \(\mathcal {O}(c^l)\) for some constant \(c\).

  3. An oblivious adversary is an adversary who does not have access to the random bits used by the algorithm.

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Correspondence to Ashish Chiplunkar.

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Chiplunkar, A., Vishwanathan, S. Metrical Service Systems with Multiple Servers. Algorithmica 71, 219–231 (2015). https://doi.org/10.1007/s00453-014-9903-7

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