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.
@InProceedings{frank_et_al:LIPIcs.DISC.2018.47, author = {Frank, Reginald and Welch, Jennifer L.}, title = {{Brief Announcement: A Tight Lower Bound for Clock Synchronization in Odd-Ary M-Toroids}}, booktitle = {32nd International Symposium on Distributed Computing (DISC 2018)}, pages = {47:1--47:3}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-092-7}, ISSN = {1868-8969}, year = {2018}, volume = {121}, editor = {Schmid, Ulrich and Widder, Josef}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2018.47}, URN = {urn:nbn:de:0030-drops-98360}, doi = {10.4230/LIPIcs.DISC.2018.47}, annote = {Keywords: Clock synchronization, Lower bound, k-ary m-toroid} }
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