2014/03/13 by Lewis Tseng, Tseng, Lewis, Nitin H. Vaidya +2
Computer Science · #Distributed #Distributed Control Multi-Agent Systems #Distributed systems and fault tolerance #FOS: Computer and information sciences #Optimization and Search Problems #Parallel #and Cluster Computing (cs.DC) #cs.DC
paper · pdf · doi:10.48550/arxiv.1403.3455
A version of this work is published in PODC 2014
openalex publication_date 2014/03/13 · arxiv created 2015/08/31 · arxiv updated 2015/09/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper defines a new consensus problem, convex consensus. Similar to vector consensus [13, 20, 19], the input at each process is a d-dimensional vector of reals (or, equivalently, a point in the d-dimensional Euclidean space). However, for convex consensus, the output at each process is a convex polytope contained within the convex hull of the inputs at the fault-free processes. We explore the convex consensus problem under crash faults with incorrect inputs, and present an asynchronous approximate convex consensus algorithm with optimal fault tolerance that reaches consensus on an optimal output polytope. Convex consensus can be used to solve other related problems. For instance, a solution for convex consensus trivially yields a solution for vector consensus. More importantly, convex consensus can potentially be used to solve other more interesting problems, such as convex function optimization [5, 4].