文章基本信息

标题：Fast Multidimensional Asymptotic and Approximate Consensus
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作者：Matthias F{\"u}gger ; Thomas Nowak
期刊名称：LIPIcs : Leibniz International Proceedings in Informatics
电子版ISSN：1868-8969
出版年度：2018
卷号：121
页码：1-16
DOI：10.4230/LIPIcs.DISC.2018.27
出版社：Schloss Dagstuhl -- Leibniz-Zentrum fuer Informatik
摘要：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.
关键词：asymptotic consensus; approximate consensus; multidimensional data; dynamic networks; Byzantine processes