It is well-known that consensus (one-set agreement) and total order broadcast are equivalent in asynchronous systems prone to process crash failures. Considering wait-free systems, this article addresses and answers the following question: which is the communication abstraction that "captures" k-set agreement? To this end, it introduces a new broadcast communication abstraction, called k-BO-Broadcast, which restricts the disagreement on the local deliveries of the messages that have been broadcast (1-BO-Broadcast boils down to total order broadcast). Hence, in this context, k=1 is not a special number, but only the first integer in an increasing integer sequence. This establishes a new "correspondence" between distributed agreement problems and communication abstractions, which enriches our understanding of the relations linking fundamental issues of fault-tolerant distributed computing.
@InProceedings{imbs_et_al:LIPIcs.DISC.2017.27, author = {Imbs, Damien and Most\'{e}faoui, Achour and Perrin, Matthieu and Raynal, Michel}, title = {{Which Broadcast Abstraction Captures k-Set Agreement?}}, booktitle = {31st International Symposium on Distributed Computing (DISC 2017)}, pages = {27:1--27:16}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-053-8}, ISSN = {1868-8969}, year = {2017}, volume = {91}, editor = {Richa, Andr\'{e}a}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2017.27}, URN = {urn:nbn:de:0030-drops-79943}, doi = {10.4230/LIPIcs.DISC.2017.27}, annote = {Keywords: Agreement problem, Antichain, Asynchronous system, Communication abstraction, Consensus, Message-passing system, Partially ordered set, Process crash} }
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