TY - GEN

T1 - Tight bounds on online checkpointing algorithms

AU - Bar-On, Achiya

AU - Dinur, Itai

AU - Hod, Rani

AU - Dunkelman, Orr

AU - Keller, Nathan

AU - Ronen, Eyal

AU - Shamir, Adi

N1 - Publisher Copyright:
© Achiya Bar-On, Itai Dinur, Orr Dunkelman, Rani Hod, Nathan Keller.

PY - 2018/7/1

Y1 - 2018/7/1

N2 - 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/o ine 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 ln 4−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 ln 4 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.

AB - 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/o ine 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 ln 4−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 ln 4 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.

KW - Checkpoint

KW - Checkpointing algorithm

KW - Discrepancy

KW - Online algorithm

KW - Uniform distribution

UR - http://www.scopus.com/inward/record.url?scp=85049803274&partnerID=8YFLogxK

U2 - 10.4230/LIPIcs.ICALP.2018.13

DO - 10.4230/LIPIcs.ICALP.2018.13

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AN - SCOPUS:85049803274

T3 - Leibniz International Proceedings in Informatics, LIPIcs

BT - 45th International Colloquium on Automata, Languages, and Programming, ICALP 2018

A2 - Kaklamanis, Christos

A2 - Marx, Daniel

A2 - Chatzigiannakis, Ioannis

A2 - Sannella, Donald

PB - Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing

T2 - 45th International Colloquium on Automata, Languages, and Programming, ICALP 2018

Y2 - 9 July 2018 through 13 July 2018

ER -