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On the Smoothness of Paging Algorithms

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Book cover Approximation and Online Algorithms (WAOA 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9499))

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Abstract

We study the smoothness of paging algorithms. How much can the number of page faults increase due to a perturbation of the request sequence? We call a paging algorithm smooth if the maximal increase in page faults is proportional to the number of changes in the request sequence. We also introduce quantitative smoothness notions that measure the smoothness of an algorithm.

We derive lower and upper bounds on the smoothness of deterministic and randomized demand-paging and competitive algorithms. Among strongly-competitive deterministic algorithms LRU matches the lower bound, while FIFO matches the upper bound.

Well-known randomized algorithms like Partition, Equitable, or Mark are shown not to be smooth. We introduce two new randomized algorithms, called Smoothed-LRU and LRU-Random. Smoothed-LRU allows to sacrifice competitiveness for smoothness, where the trade-off is controlled by a parameter. LRU-Random is at least as competitive as any deterministic algorithm while smoother.

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Acknowledgments

This work was partially supported by the DFG as part of the SFB/TR 14 AVACS.

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Authors and Affiliations

  1. Department of Computer Science, Saarland University, Saarbrücken, Germany

    Jan Reineke & Alejandro Salinger

Authors
  1. Jan Reineke
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  2. Alejandro Salinger
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Corresponding author

Correspondence to Jan Reineke .

Editor information

Editors and Affiliations

  1. University of Waterloo, Waterloo, Canada

    Laura Sanità

  2. Technische Universität Berlin, Berlin, Berlin, Germany

    Martin Skutella

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Reineke, J., Salinger, A. (2015). On the Smoothness of Paging Algorithms. In: Sanità, L., Skutella, M. (eds) Approximation and Online Algorithms. WAOA 2015. Lecture Notes in Computer Science(), vol 9499. Springer, Cham. https://doi.org/10.1007/978-3-319-28684-6_15

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  • DOI: https://doi.org/10.1007/978-3-319-28684-6_15

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-28683-9

  • Online ISBN: 978-3-319-28684-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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