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

Authors Reginald Frank , Jennifer L. Welch

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

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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)


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.

Subject Classification

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


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