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- Nitin H. Vaidya, Lewis Tseng, Guanfeng Liang
- PODC
- 2012

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)

- Lewis Tseng, Nitin H. Vaidya
- PODC
- 2015

Consider a point-to-point network in which nodes are connected by directed links. This paper proves tight necessary and sufficient conditions on the underlying communication graphs for solving the following fault-tolerant consensus problems: Exact crash-tolerant consensus in synchronous systems, Approximate crash-tolerant consensus in asynchronous systems,… (More)

- Nitin H. Vaidya, Lewis Tseng, Guanfeng Liang
- ArXiv
- 2012

Any opinions, findings, and conclusions or recommendations expressed here are those of the authors and do not necessarily reflect the views of the funding agencies or the U.S. government.

- Lewis Tseng, Nitin H. Vaidya
- ICDCN
- 2013

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)

- Lewis Tseng, Nitin H. Vaidya, Vartika Bhandari
- Inf. Process. Lett.
- 2015

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)

- Lewis Tseng, Nitin H. Vaidya
- NETYS
- 2014

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)

- Lewis Tseng, Nitin H. Vaidya
- PODC
- 2014

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)

- Lewis Tseng, Nitin H. Vaidya
- ArXiv
- 2013

Much of the past work on asynchronous approximate Byzantine consensus has assumed scalar inputs at the nodes [4, 8]. Recent work has yielded approximate Byzantine consensus algorithms for the case when the input at each node is a d-dimensional vector, and the nodes must reach consensus on a vector in the convex hull of the input vectors at the fault-free… (More)

- Lewis Tseng, Nitin H. Vaidya
- ArXiv
- 2012

For synchronous point-to-point n-node networks of undirected links, it has been previously shown that, to achieve consensus in presence of up to f Byzantine faults, the following two conditions are together necessary and sufficient: (i) n ≥ 3f + 1 and (ii) network connectivity greater than 2f. The first condition, that is, n ≥ 3f + 1, is known to be… (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)