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On the Competitive Ratio for Online Facility Location

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Abstract

We consider the problem of Online Facility Location, where the demand points arrive online and must be assigned irrevocably to an open facility upon arrival. The objective is to minimize the sum of facility and assignment costs. We prove that the competitive ratio for Online Facility Location is Θ \((\frac{\log n}{\log\log n})\) . On the negative side, we show that no randomized algorithm can achieve a competitive ratio better than Ω \((\frac{\log n}{\log\log n})\) against an oblivious adversary even if the demands lie on a line segment. On the positive side, we present a deterministic algorithm which achieves a competitive ratio of \(\mathrm{O}(\frac{\log n}{\log\log n})\) in every metric space.

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Authors and Affiliations

  1. Department of Information and Communication Systems Engineering, University of the Aegean, 83200, Karlovasi, Samos, Greece

    Dimitris Fotakis

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  1. Dimitris Fotakis
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Correspondence to Dimitris Fotakis.

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A preliminary version of this work appeared in the Proceedings of the 30th International Colloquium on Automata, Languages and Programming (ICALP 2003), Lecture Notes in Computer Science 2719. This work was done while the author was at the Max-Planck-Institut für Informatik, Saarbrücken, Germany, and was partially supported by the Future and Emerging Technologies programme of the EU under contract number IST-1999-14186 (ALCOM–FT).

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Fotakis, D. On the Competitive Ratio for Online Facility Location. Algorithmica 50, 1–57 (2008). https://doi.org/10.1007/s00453-007-9049-y

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  • DOI: https://doi.org/10.1007/s00453-007-9049-y

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