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oai:drops-oai.dagstuhl.de:9816 2024-03-06T10:45:00Z ddc:004 open_access

Fast Multidimensional Asymptotic and Approximate Consensus Függer, Matthias Nowak, Thomas asymptotic consensus approximate consensus multidimensional data dynamic networks Byzantine processes We study the problems of asymptotic and approximate consensus in which agents have to get their values arbitrarily close to each others' inside the convex hull of initial values, either without or with an explicit decision by the agents. In particular, we are concerned with the case of multidimensional data, i.e., the agents' values are d-dimensional vectors. We introduce two new algorithms for dynamic networks, subsuming classical failure models like asynchronous message passing systems with Byzantine agents. The algorithms are the first to have a contraction rate and time complexity independent of the dimension d. In particular, we improve the time complexity from the previously fastest approximate consensus algorithm in asynchronous message passing systems with Byzantine faults by Mendes et al. [Distrib. Comput. 28] from Omega(d log (d Delta)/epsilon) to O(log Delta/epsilon), where Delta is the initial and epsilon is the terminal diameter of the set of vectors of correct agents. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Matthias Függer and Thomas Nowak 2018 Is Part Of LIPIcs, Volume 121, 32nd International Symposium on Distributed Computing (DISC 2018) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.DISC.2018.27 urn:nbn:de:0030-drops-98167 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2018.27 eng https://creativecommons.org/licenses/by/3.0/legalcode