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

07/13/2018

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by   Reginald Frank, et al.

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Synchronizing clocks in a distributed system in which processes communicate through messages with uncertain delays is subject to inherent errors. Prior work has shown upper and lower bounds on the best synchronization achievable in a variety of network topologies and assumptions about the uncertainty on the message delays. However, until now there has not been a tight closed-form expression for the optimal synchronization in k-ary m-cubes with wraparound, where k is odd. In this paper, we prove a lower bound of 1/4um(k-1/k), where k is the (odd) number of processes in the each of the m dimensions, and u is the uncertainty in delay on every link. Our lower bound matches the previously known upper bound.