
Back to the Coordinated Attack Problem
We consider the well known Coordinated Attack Problem, where two general...
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Joining Local Knowledge to Communicate Reliably (Extended Abstract)
A fundamental primitive in distributed computing is Reliable Message Tra...
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On the complexity of faulttolerant consensus
The paper studies the problem of reaching agreement in a distributed mes...
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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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An Asynchronous Computability Theorem for Fair Adversaries
This paper proposes a simple topological characterization of a large cla...
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Diffusion and consensus on weakly connected directed graphs
Let G be a weakly connected directed graph with asymmetric graph Laplaci...
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The Communication Cost of Information Spreading in Dynamic Networks
This paper investigates the message complexity of distributed informatio...
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Topological Characterization of Consensus under General Message Adversaries
In this paper, we provide a rigorous characterization of consensus solvability in synchronous directed dynamic networks controlled by an arbitrary message adversary using pointset topology: We extend the approach introduced by Alpern and Schneider in 1985 by introducing two novel topologies on the space of infinite executions: the processview topology, induced by a distance function that relies on the local view of a given process in an execution, and the minimum topology, which is induced by a distance function that focuses on the local view of the process that is the last to distinguish two executions. We establish some simple but powerful topological results, which not only lead to a topological explanation of bivalence arguments, but also provide necessary and sufficient topological conditions on the admissible graph sequences of a message adversary for solving consensus. In particular, we characterize consensus solvability in terms of connectivity of the set of admissible graph sequences. For noncompact message adversaries, which are not limitclosed in the sense that there is a convergent sequence of graph sequences whose limit is not permitted, this requires the exclusion of all "fair" and "unfair" limit sequences that coincide with the forever bivalent runs constructed in bivalence proofs. For both compact and noncompact message adversaries, we also provide tailored characterizations of consensus solvability, i.e., tight conditions for impossibility and existence of algorithms, based on the broadcastability of the connected components of the set of admissible graph sequences.
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