Fault-tolerant consensus in directed graphs and convex hull consensus

Consensus;Byzantine fault;Crash fault;Directed network;fault-tolerance;convex hull consensus

Tseng, Lewis

关键词: Consensus;    Byzantine fault;    Crash fault;    Directed network;    fault-tolerance;    convex hull consensus;   

Others  :  https://www.ideals.illinois.edu/bitstream/handle/2142/90567/TSENG-DISSERTATION-2016.pdf?sequence=1&isAllowed=y

美国|英语

来源: The Illinois Digital Environment for Access to Learning and Scholarship

【 摘 要 】

As distributed systems nowadays scale to thousands or more of nodes, fault-tolerance becomes one of the most important topics. This dissertation studies the fault-tolerance aspect of the consensus algorithm, which is a fundamental building block for the distributed systems. Particularly, the dissertation has the following two main contributions on fault-tolerant consensus in message-passing networks:• We explore various fault-tolerant consensus problems under different fault models in communication networks that are modeled as arbitrary directed graphs, i.e., two pairs of nodes may not share a bi- directional communication channel, and not every pair of nodes may be able to communicate with each other directly or indirectly. We prove the tight condition of the underlying communication graphs for solving each of the consensus problem, i.e., the necessary condition is equal to the sufficient condition.• We propose a new consensus problem – convex hull consensus – in which the input is a vector of reals in the d-dimensional space, and the output is a convex polytope contained within the convex hull of all inputs at fault-free nodes. For asynchronous systems, we present an approximate convex hull consensus algorithm with optimal fault tolerance that reaches consensus on optimal output polytope under crash fault model. Convex hull consensus may be used to solve related problems, such as vector consensus and function optimization with the initial convex hull as the domain.