Accession Number : ADA580186


Title :   Byzantine Vector Consensus in Complete Graphs


Corporate Author : ILLINOIS UNIV AT URBANA DEPT OF ELECTRICAL AND COMPUTER ENGINEERING


Personal Author(s) : Vaidya, Nitin H ; Garg, Vijay K


Full Text : http://www.dtic.mil/get-tr-doc/pdf?AD=ADA580186


Report Date : 11 Feb 2013


Pagination or Media Count : 21


Abstract : Consider a network of n processes each of which has a d-dimensional vector of reals as its input. Each process can communicate directly with all the processes in the system thus the communication network is a complete graph. All the communication channels are reliable and FIFO (first-in-first-out). The problem of Byzantine vector consensus (BVC) requires agreement on a d-dimensional vector that is in the convex hull of the d-dimensional input vectors at the non-faulty processes. We obtain the following results for Byzantine vector consensus in complete graphs while tolerating up to f Byzantine failures: * We prove that in a synchronous system, n or = max(3f+1; (d+1)f+1) is necessary and sufficient for achieving Byzantine vector consensus. * In an asynchronous system, it is known that exact consensus is impossible in presence of faulty processes. For an asynchronous system, we prove that n or = (d+2)f+1 is necessary and sufficient to achieve approximate Byzantine vector consensus. Our sufficiency proofs are constructive. We show sufficiency by providing explicit algorithms that solve exact BVC in synchronous systems, and approximate BVC in asynchronous systems. We also obtain tight bounds on the number of processes for achieving BVC using algorithms that are restricted to a simpler communication pattern.


Descriptors :   *DISTRIBUTED COMPUTING , GRAPHS , NETWORKS , VECTOR ANALYSIS


Subject Categories : Computer Systems


Distribution Statement : APPROVED FOR PUBLIC RELEASE