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DOI: 10.4230/LIPIcs.ICALP.2018.13
Tight Bounds on Online Checkpointing Algorithms

Authors: Achiya Bar-On, Itai Dinur, Orr Dunkelman, Rani Hod, Nathan Keller, Eyal Ronen, and Adi Shamir

Published in: LIPIcs, Volume 107, 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)

Abstract
The problem of online checkpointing is a classical problem with numerous applications which had been studied in various forms for almost 50 years. In the simplest version of this problem, a user has to maintain k memorized checkpoints during a long computation, where the only allowed operation is to move one of the checkpoints from its old time to the current time, and his goal is to keep the checkpoints as evenly spread out as possible at all times. At ICALP'13 Bringmann et al. studied this problem as a special case of an online/offline optimization problem in which the deviation from uniformity is measured by the natural discrepancy metric of the worst case ratio between real and ideal segment lengths. They showed this discrepancy is smaller than 1.59-o(1) for all k, and smaller than ln4-o(1)~~1.39 for the sparse subset of k's which are powers of 2. In addition, they obtained upper bounds on the achievable discrepancy for some small values of k. In this paper we solve the main problems left open in the ICALP'13 paper by proving that ln4 is a tight upper and lower bound on the asymptotic discrepancy for all large k, and by providing tight upper and lower bounds (in the form of provably optimal checkpointing algorithms, some of which are in fact better than those of Bringmann et al.) for all the small values of k <= 10.
Cite as

Achiya Bar-On, Itai Dinur, Orr Dunkelman, Rani Hod, Nathan Keller, Eyal Ronen, and Adi Shamir. Tight Bounds on Online Checkpointing Algorithms. In 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 107, pp. 13:1-13:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{baron_et_al:LIPIcs.ICALP.2018.13,
  author =	{Bar-On, Achiya and Dinur, Itai and Dunkelman, Orr and Hod, Rani and Keller, Nathan and Ronen, Eyal and Shamir, Adi},
  title =	{{Tight Bounds on Online Checkpointing Algorithms}},
  booktitle =	{45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)},
  pages =	{13:1--13:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-076-7},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{107},
  editor =	{Chatzigiannakis, Ioannis and Kaklamanis, Christos and Marx, D\'{a}niel and Sannella, Donald},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2018.13},
  URN =		{urn:nbn:de:0030-drops-90179},
  doi =		{10.4230/LIPIcs.ICALP.2018.13},
  annote =	{Keywords: checkpoint, checkpointing algorithm, online algorithm, uniform distribution, discrepancy}
}
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