doi 10.1007/11561927_34 https://doi.org/10.1007/11561927_34 second contribution optimal algorithm false quorum sets cardinality algorithm data structure en chapter issues parameters 2022-05-20T07:48 implementation good properties 2005-01-01 set dynamic overlay networks fact dynamic data structures structure gossip protocol overlay network The Dynamic And-Or Quorum System excellent candidate network dynamic quorums same parameters properties complexity de Bruijn networks chapters knowledge We investigate issues related to the probe complexity of the And-Or quorum system and its implementation in a dynamic environment. Our contribution is twofold: We first analyze the algorithmic probe complexity of the And-Or quorum system, and present two optimal algorithms. The first is a non-adaptive algorithm with \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$O(\sqrt{n}log n)$\end{document} probe complexity, which matches a known lower bound. The second is an adaptive algorithm with a probe complexity that is linear in the cardinality of a quorum set (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$O(\sqrt{n})$\end{document}), and requires at most O(loglogn) rounds. To the best of our knowledge, all other adaptive algorithms with same parameters (load and probe complexity) require \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\theta(\sqrt{n})$\end{document} rounds.Our second contribution is presenting the ‘dynamic And-Or’ quorum system – an adaptation of the above quorum system to a dynamic environment, where processors join and leave the network. It is based on a dynamic overlay network that emulates the De-Bruijn network and maintains the good properties of the quorum system(e.g.,load and availability). The algorithms suggested for the maintenance of these dynamic data structures are strongly coupled with the dynamic overlay network. This fact enables the use of gossip protocols which saves in message complexity and keeps the protocols simple and local. All these qualities make the ‘dynamic And-Or’ an excellent candidate for an implementation of dynamic quorums. adaptation adaptive algorithm maintenance quality probe complexity contribution https://scigraph.springernature.com/explorer/license/ twofold 472-486 environment quorum systems dynamics dynamic environment 2005 system candidates processors non-adaptive algorithms use protocol message complexity quorum Computation Theory and Mathematics Springer Nature - SN SciGraph project Distributed Computing 978-3-540-29163-3 978-3-540-32075-3 Uri Nadav dimensions_id pub.1030120041 Dept. of Computer Science, Tel-Aviv University Dept. of Computer Science, Tel-Aviv University Pierre Fraigniaud Dept. of Computer Science and Applied Mathematics, The Weizmann Institute Dept. of Computer Science and Applied Mathematics, The Weizmann Institute Information and Computing Sciences Naor Moni Springer Nature