--- res: bibo_abstract: - "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.@eng" bibo_authorlist: - foaf_Person: foaf_givenName: Thomas foaf_name: Nowak, Thomas foaf_surname: Nowak - foaf_Person: foaf_givenName: Joel foaf_name: Rybicki, Joel foaf_surname: Rybicki foaf_workInfoHomepage: http://www.librecat.org/personId=334EFD2E-F248-11E8-B48F-1D18A9856A87 orcid: 0000-0002-6432-6646 bibo_doi: 10.4230/LIPICS.DISC.2019.29 bibo_volume: 146 dct_date: 2019^xs_gYear dct_language: eng dct_publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik@ dct_subject: - consensus - approximate agreement - Byzantine faults - chordal graphs - lattice agreement dct_title: Byzantine approximate agreement on graphs@ ...