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Brief Announcement: A Tight Lower Bound for Clock Synchronization in Odd-Ary M-Toroids

Authors Reginald Frank , Jennifer L. Welch

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Subject Classification

ACM Subject Classification
  • Theory of computation → Distributed algorithms
Keywords
  • Clock synchronization
  • Lower bound
  • k-ary m-toroid

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Abstract

In this paper we show a tight closed-form expression for the optimal clock synchronization in k-ary m-cubes with wraparound, where k is odd. This is done by proving a lower bound of 1/4um (k-1/k), where k is the (odd) number of processes in each of the m dimensions, and u is the uncertainty in delay on every link. Our lower bound matches the previously known upper bound.

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Reginald Frank and Jennifer L. Welch. Brief Announcement: A Tight Lower Bound for Clock Synchronization in Odd-Ary M-Toroids. In 32nd International Symposium on Distributed Computing (DISC 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 121, pp. 47:1-47:3, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018) https://doi.org/10.4230/LIPIcs.DISC.2018.47

Author Details

Reginald Frank
  • Texas A&M University, College Station, TX, USA
Jennifer L. Welch
  • Texas A&M University, College Station, TX, USA

Funding

  • Frank, Reginald: Supported in part by CRA-W and CDC’s DREU program and NSF grant CNS-0540631.
  • Welch, Jennifer L.: Supported in part by NSF grant 1526725.

References

  1. Hagit Attiya, Amir Herzberg, and Sergio Rajsbaum. Optimal clock synchronization under different delay assumptions. SIAM J. Comput., 25(2):369-389, 1996. Google Scholar
  2. Hagit Attiya and Jennifer L. Welch. Distributed Computing: Fundamentals, Simulations, and Advanced Topics, Second Edition. John Wiley &Sons, Hoboken, NJ, 2004. Google Scholar
  3. Saad Biaz and Jennifer L. Welch. Closed form bounds for clock synchronization under simple uncertainty assumptions. Inf. Process. Lett., 80(3):151-157, 2001. Google Scholar
  4. Joseph Y. Halpern, Nimrod Megiddo, and Ashfaq A. Munshi. Optimal precision in the presence of uncertainty. J. Complexity, 1(2):170-196, 1985. Google Scholar
  5. Jennifer Lundelius and Nancy Lynch. An upper and lower bound for clock synchronization. Inform. Control, 62(2/3):190-204, 1984. Google Scholar
  6. Boaz Patt-Shamir and Sergio Rajsbaum. A theory of clock synchronization (extended abstract). In Proc. 26th Annual ACM Symp. Theory of Comput., pages 810-819, 1994. Google Scholar
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