[{"volume":146,"date_created":"2019-10-08T12:41:38Z","author":[{"full_name":"Nowak, Thomas","last_name":"Nowak","first_name":"Thomas"},{"first_name":"Joel","orcid":"0000-0002-6432-6646","full_name":"Rybicki, Joel","id":"334EFD2E-F248-11E8-B48F-1D18A9856A87","last_name":"Rybicki"}],"scopus_import":1,"oa_version":"Published Version","title":"Byzantine approximate agreement on graphs","publication_identifier":{"eisbn":["978-3-95977-126-9"]},"publication_status":"published","file_date_updated":"2020-07-14T12:47:44Z","has_accepted_license":"1","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","short":"CC BY (4.0)"},"abstract":[{"lang":"eng","text":"Consider a distributed system with n processors out of which f can be Byzantine faulty. In the\r\napproximate agreement task, each processor i receives an input value xi and has to decide on an\r\noutput value yi such that\r\n1. the output values are in the convex hull of the non-faulty processors’ input values,\r\n2. the output values are within distance d of each other.\r\n\r\n\r\nClassically, the values are assumed to be from an m-dimensional Euclidean space, where m ≥ 1.\r\nIn this work, we study the task in a discrete setting, where input values with some structure\r\nexpressible as a graph. Namely, the input values are vertices of a finite graph G and the goal is to\r\noutput vertices that are within distance d of each other in G, but still remain in the graph-induced\r\nconvex hull of the input values. For d = 0, the task reduces to consensus and cannot be solved with\r\na deterministic algorithm in an asynchronous system even with a single crash fault. For any d ≥ 1,\r\nwe show that the task is solvable in asynchronous systems when G is chordal and n > (ω + 1)f,\r\nwhere ω is the clique number of G. In addition, we give the first Byzantine-tolerant algorithm for a\r\nvariant of lattice agreement. For synchronous systems, we show tight resilience bounds for the exact\r\nvariants of these and related tasks over a large class of combinatorial structures."}],"intvolume":"       146","department":[{"_id":"DaAl"}],"file":[{"checksum":"2d2202f90c6ac991e50876451627c4b5","relation":"main_file","access_level":"open_access","content_type":"application/pdf","file_name":"LIPIcs-DISC-2019-29.pdf","file_id":"6934","creator":"jrybicki","date_updated":"2020-07-14T12:47:44Z","date_created":"2019-10-08T12:47:19Z","file_size":639378}],"arxiv":1,"citation":{"short":"T. Nowak, J. Rybicki, in:, 33rd International Symposium on Distributed Computing, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2019, p. 29:1--29:17.","ieee":"T. Nowak and J. Rybicki, “Byzantine approximate agreement on graphs,” in <i>33rd International Symposium on Distributed Computing</i>, Budapest, Hungary, 2019, vol. 146, p. 29:1--29:17.","ama":"Nowak T, Rybicki J. Byzantine approximate agreement on graphs. In: <i>33rd International Symposium on Distributed Computing</i>. Vol 146. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2019:29:1--29:17. doi:<a href=\"https://doi.org/10.4230/LIPICS.DISC.2019.29\">10.4230/LIPICS.DISC.2019.29</a>","mla":"Nowak, Thomas, and Joel Rybicki. “Byzantine Approximate Agreement on Graphs.” <i>33rd International Symposium on Distributed Computing</i>, vol. 146, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2019, p. 29:1--29:17, doi:<a href=\"https://doi.org/10.4230/LIPICS.DISC.2019.29\">10.4230/LIPICS.DISC.2019.29</a>.","apa":"Nowak, T., &#38; Rybicki, J. (2019). Byzantine approximate agreement on graphs. In <i>33rd International Symposium on Distributed Computing</i> (Vol. 146, p. 29:1--29:17). Budapest, Hungary: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. <a href=\"https://doi.org/10.4230/LIPICS.DISC.2019.29\">https://doi.org/10.4230/LIPICS.DISC.2019.29</a>","ista":"Nowak T, Rybicki J. 2019. Byzantine approximate agreement on graphs. 33rd International Symposium on Distributed Computing. DISC: International Symposium on Distributed Computing, LIPIcs, vol. 146, 29:1--29:17.","chicago":"Nowak, Thomas, and Joel Rybicki. “Byzantine Approximate Agreement on Graphs.” In <i>33rd International Symposium on Distributed Computing</i>, 146:29:1--29:17. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2019. <a href=\"https://doi.org/10.4230/LIPICS.DISC.2019.29\">https://doi.org/10.4230/LIPICS.DISC.2019.29</a>."},"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","oa":1,"language":[{"iso":"eng"}],"date_updated":"2021-01-12T08:09:38Z","_id":"6931","type":"conference","doi":"10.4230/LIPICS.DISC.2019.29","article_processing_charge":"No","alternative_title":["LIPIcs"],"publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","quality_controlled":"1","page":"29:1--29:17","ddc":["004"],"keyword":["consensus","approximate agreement","Byzantine faults","chordal graphs","lattice agreement"],"year":"2019","external_id":{"arxiv":["1908.02743"]},"ec_funded":1,"date_published":"2019-01-01T00:00:00Z","conference":{"location":"Budapest, Hungary","start_date":"2019-10-14","end_date":"2019-10-18","name":"DISC: International Symposium on Distributed Computing"},"project":[{"grant_number":"754411","name":"ISTplus - Postdoctoral Fellowships","call_identifier":"H2020","_id":"260C2330-B435-11E9-9278-68D0E5697425"}],"status":"public","publication":"33rd International Symposium on Distributed Computing"}]