--- _id: '6931' 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." alternative_title: - LIPIcs article_processing_charge: No author: - first_name: Thomas full_name: Nowak, Thomas last_name: Nowak - first_name: Joel full_name: Rybicki, Joel id: 334EFD2E-F248-11E8-B48F-1D18A9856A87 last_name: Rybicki orcid: 0000-0002-6432-6646 citation: ama: 'Nowak T, Rybicki J. Byzantine approximate agreement on graphs. In: 33rd International Symposium on Distributed Computing. Vol 146. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2019:29:1--29:17. doi:10.4230/LIPICS.DISC.2019.29' apa: 'Nowak, T., & Rybicki, J. (2019). Byzantine approximate agreement on graphs. In 33rd International Symposium on Distributed Computing (Vol. 146, p. 29:1--29:17). Budapest, Hungary: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPICS.DISC.2019.29' chicago: Nowak, Thomas, and Joel Rybicki. “Byzantine Approximate Agreement on Graphs.” In 33rd International Symposium on Distributed Computing, 146:29:1--29:17. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2019. https://doi.org/10.4230/LIPICS.DISC.2019.29. ieee: T. Nowak and J. Rybicki, “Byzantine approximate agreement on graphs,” in 33rd International Symposium on Distributed Computing, Budapest, Hungary, 2019, vol. 146, p. 29:1--29:17. 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.' mla: Nowak, Thomas, and Joel Rybicki. “Byzantine Approximate Agreement on Graphs.” 33rd International Symposium on Distributed Computing, vol. 146, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2019, p. 29:1--29:17, doi:10.4230/LIPICS.DISC.2019.29. short: T. Nowak, J. Rybicki, in:, 33rd International Symposium on Distributed Computing, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2019, p. 29:1--29:17. conference: end_date: 2019-10-18 location: Budapest, Hungary name: 'DISC: International Symposium on Distributed Computing' start_date: 2019-10-14 date_created: 2019-10-08T12:41:38Z date_published: 2019-01-01T00:00:00Z date_updated: 2021-01-12T08:09:38Z ddc: - '004' department: - _id: DaAl doi: 10.4230/LIPICS.DISC.2019.29 ec_funded: 1 external_id: arxiv: - '1908.02743' file: - access_level: open_access checksum: 2d2202f90c6ac991e50876451627c4b5 content_type: application/pdf creator: jrybicki date_created: 2019-10-08T12:47:19Z date_updated: 2020-07-14T12:47:44Z file_id: '6934' file_name: LIPIcs-DISC-2019-29.pdf file_size: 639378 relation: main_file file_date_updated: 2020-07-14T12:47:44Z has_accepted_license: '1' intvolume: ' 146' keyword: - consensus - approximate agreement - Byzantine faults - chordal graphs - lattice agreement language: - iso: eng license: https://creativecommons.org/licenses/by/4.0/ oa: 1 oa_version: Published Version page: 29:1--29:17 project: - _id: 260C2330-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '754411' name: ISTplus - Postdoctoral Fellowships publication: 33rd International Symposium on Distributed Computing publication_identifier: eisbn: - 978-3-95977-126-9 publication_status: published publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik quality_controlled: '1' scopus_import: 1 status: public title: Byzantine approximate agreement on graphs tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: conference user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87 volume: 146 year: '2019' ...