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OnlineMin: A Fast Strongly Competitive Randomized Paging Algorithm

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Abstract

In the field of online algorithms paging is one of the most studied problems. For randomized paging algorithms a tight bound of H k on the competitive ratio has been known for decades, yet existing algorithms matching this bound have high running times. We present a new randomized paging algorithm OnlineMin that has optimal competitiveness and allows fast implementations. In fact, if k pages fit in internal memory the best previous solution required O(k 2) time per request and O(k) space. We present two implementations of OnlineMin which use O(k) space, but only O(logk) worst case time and O(logk/loglogk) worst case time per page request respectively.

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Notes

  1. In [6] Equitable2 is denoted A k . Due to its similarity to Equitable we use its original name of Equitable2.

  2. Since no explicit implementation of Equitable2 is provided, due to their similarity we assume it to be the same as for Equitable.

  3. We use a slightly modified, yet equivalent, version of the layer representation in [16].

  4. For easiness of exposition we refer by ω to both the offset function and its corresponding layer representation.

  5. Theorem 1 does not explicitly take into account the forgiveness step. According to Definition 1, if p∈L 0 and forgiveness is applied we treat p as if it was requested in L 1.

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Acknowledgements

We would like to thank previous anonymous reviewers for very insightful comments and suggestions. Also, we would like to thank Annamária Kovács for useful advice on improving the presentation of the paper.

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Authors and Affiliations

  1. MADALGO (Center for Massive Data Algorithmics, a Center of the Danish National Research Foundation), Department of Computer Science, Aarhus University, Åbogade 34, 8200, Aarhus N, Denmark

    Gerth Stølting Brodal

  2. Institut für Informatik, Goethe-Universität Frankfurt am Main, Robert-Mayer-Str. 11-15, 60325, Frankfurt am Main, Germany

    Gabriel Moruz & Andrei Negoescu

Authors
  1. Gerth Stølting Brodal
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  2. Gabriel Moruz
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  3. Andrei Negoescu
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Corresponding author

Correspondence to Gabriel Moruz.

Additional information

G. Moruz was partially supported by the DFG grants ME 3250/1-3 and MO 2057/1-1, and by MADALGO.

A. Negoescu was partially supported by DFG grant ME 3250/1-3 and by MADALGO.

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Brodal, G.S., Moruz, G. & Negoescu, A. OnlineMin: A Fast Strongly Competitive Randomized Paging Algorithm. Theory Comput Syst 56, 22–40 (2015). https://doi.org/10.1007/s00224-012-9427-y

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