We present a distributed minimum spanning tree algorithm with near-optimal round complexity of O~(D+sqrt{n}) and message complexity O~(min{n^{3/2}, m}). This is the first algorithm with sublinear message complexity and near-optimal round complexity and it improves over the recent algorithms of Elkin [PODC'17] and Pandurangan et al. [STOC'17], which have the same round complexity but message complexity O~(m). Our method also gives the first broadcast algorithm with o(n) time complexity - when that is possible at all, i.e., when D=o(n) - and o(m) messages. Moreover, our method leads to an O~(sqrt{nD})-round GOSSIP algorithm with bounded-size messages. This is the first such algorithm with a sublinear round complexity.
@InProceedings{ghaffari_et_al:LIPIcs.DISC.2018.30, author = {Ghaffari, Mohsen and Kuhn, Fabian}, title = {{Distributed MST and Broadcast with Fewer Messages, and Faster Gossiping}}, booktitle = {32nd International Symposium on Distributed Computing (DISC 2018)}, pages = {30:1--30:12}, 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.2018.30}, URN = {urn:nbn:de:0030-drops-98194}, doi = {10.4230/LIPIcs.DISC.2018.30}, annote = {Keywords: Distributed Algorithms, Minimum Spanning Tree, Round Complexity, Message Complexity, Gossiping, Broadcast} }
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