
Byzantine Consensus under Local Broadcast Model: Tight Sufficient Condition
In this work we consider Byzantine Consensus on undirected communication...
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Exact Byzantine Consensus on Arbitrary Directed Graphs under Local Broadcast Model
We consider Byzantine consensus in a synchronous system where nodes are ...
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Exact Byzantine Consensus on Undirected Graphs under Local Broadcast Model
This paper considers the Byzantine consensus problem for nodes with bina...
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Asynchronous CrashTolerant Consensus in Directed Graphs: Randomization and Topology Knowledge
Consider a directed pointtopoint network. We are interested in the asy...
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Asynchronous Byzantine Approximate Consensus in Directed Networks
In this work, we study the approximate consensus problem in asynchronous...
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Myerson value of directed hypergraphs
In this paper, we consider a directed hypergraph as cooperative network,...
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Decentralized Langevin Dynamics over a Directed Graph
The prevalence of technologies in the space of the Internet of Things an...
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Byzantine Consensus in Directed Hypergraphs
Byzantine consensus is a classical problem in distributed computing. Each node in a synchronous system starts with a binary input. The goal is to reach agreement in the presence of Byzantine faulty nodes. We consider the setting where communication between nodes is modelled via a directed hypergraph. In the classical pointtopoint communication model, the communication between nodes is modelled as a simple graph where all messages sent on an edge are private between the two endpoints of the edge. This allows a faulty node to equivocate, i.e., lie differently to its different neighbors. Different models have been proposed in the literature that weaken equivocation. In the local broadcast model, every message transmitted by a node is received identically and correctly by all of its neighbors. In the hypergraph model, every message transmitted by a node on a hyperedge is received identically and correctly by all nodes on the hyperedge. Tight network conditions are known for each of the three cases for undirected (hyper)graphs. For the directed models, tight conditions are known for the pointtopoint and local broadcast models. In this work, we consider the directed hypergraph model that encompasses all the models above. Each directed hyperedge consists of a single head (sender) and at least one tail (receiver), This models a local multicast channel where messages transmitted by the sender are received identically by all the receivers in the hyperedge. For this model, we identify tight network conditions for consensus. We observe how the directed hypergraph model reduces to each of the three models above under specific conditions. In each case, we relate our network condition to the corresponding known tight conditions. The directed hypergraph model also encompasses other practical network models of interest that have not been explored previously, as elaborated in the paper.
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