TY - GEN

T1 - Iterative Byzantine vector consensus in incomplete graphs

AU - Vaidya, Nitin H.

PY - 2014

Y1 - 2014

N2 - This work addresses Byzantine vector consensus, wherein the input at each process is a d-dimensional vector of reals, and each process is required to decide on a decision vector that is in the convex hull of the input vectors at the fault-free processes [9,12]. The input vector at each process may also be viewed as a point in the d-dimensional Euclidean space Rd, where d > 0 is a finite integer. Recent work [9,12] has addressed Byzantine vector consensus, and presented algorithms with optimal fault tolerance in complete graphs. This paper considers Byzantine vector consensus in incomplete graphs using a restricted class of iterative algorithms that maintain only a small amount of memory across iterations. For such algorithms, we prove a necessary condition, and a sufficient condition, for the graphs to be able to solve the vector consensus problem iteratively. We present an iterative Byzantine vector consensus algorithm, and prove it correct under the sufficient condition. The necessary condition presented in this paper for vector consensus does not match with the sufficient condition for d > 1; thus, a weaker condition may potentially suffice for Byzantine vector consensus.

AB - This work addresses Byzantine vector consensus, wherein the input at each process is a d-dimensional vector of reals, and each process is required to decide on a decision vector that is in the convex hull of the input vectors at the fault-free processes [9,12]. The input vector at each process may also be viewed as a point in the d-dimensional Euclidean space Rd, where d > 0 is a finite integer. Recent work [9,12] has addressed Byzantine vector consensus, and presented algorithms with optimal fault tolerance in complete graphs. This paper considers Byzantine vector consensus in incomplete graphs using a restricted class of iterative algorithms that maintain only a small amount of memory across iterations. For such algorithms, we prove a necessary condition, and a sufficient condition, for the graphs to be able to solve the vector consensus problem iteratively. We present an iterative Byzantine vector consensus algorithm, and prove it correct under the sufficient condition. The necessary condition presented in this paper for vector consensus does not match with the sufficient condition for d > 1; thus, a weaker condition may potentially suffice for Byzantine vector consensus.

UR - http://www.scopus.com/inward/record.url?scp=84893088254&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84893088254&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-45249-9_2

DO - 10.1007/978-3-642-45249-9_2

M3 - Conference contribution

AN - SCOPUS:84893088254

SN - 9783642452482

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 14

EP - 28

BT - Distributed Computing and Networking - 15th International Conference, ICDCN 2014, Proceedings

T2 - 15th International Conference on Distributed Computing and Networking, ICDCN 2014

Y2 - 4 January 2014 through 7 January 2014

ER -