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This paper proves a necessary and sufficient condition for the existence of <i>iterative</i>, algorithms that achieve <i>approximate Byzantine consensus</i> in arbitrary directed graphs, where each directed edge represents a communication channel between a pair of nodes. The class of iterative algorithms considered in this paper ensures that, after each(More)
In this work, we consider a generalized fault model that can be used to represent a wide range of failure scenarios, including correlated failures and non-uniform node reliabilities. This fault model is general in the sense that fault models studied in prior related work, such as f-total and f-local models, are special cases of the generalized fault model.(More)
We explore the correctness of the Certified Propagation Algorithm (CPA) [5, 1, 7, 4] in solving broadcast with locally bounded Byzantine faults. CPA allows the nodes to use only local information regarding the network topology. We provide a tight necessary and sufficient condition on the network topology for the correctness of CPA. We also present some(More)
This paper explores the problem of reaching approximate consensus in synchronous point-to-point networks, where each directed link of the underlying communication graph represents a communication channel between a pair of nodes. We adopt the transient Byzantine link failure model [15, 16], where an omniscient adversary controls a subset of the directed(More)
This paper defines a new consensus problem, <i>convex hull consensus</i>. The input at each process is a d-dimensional vector of reals (or, equivalently, a point in the d-dimensional Euclidean space), and the output at each process is a <i>convex polytope</i> contained within the convex hull of the inputs at the fault-free processes. We explore the convex(More)
The CAP theorem is a fundamental result that applies to distributed storage systems. In this article, we first present and prove two CAP-like impossibility theorems. To state these theorems, we present probabilistic models to characterize the three important elements of the CAP theorem: consistency (C), availability or latency (A), and partition tolerance(More)