Abstract
We study the fundamental problem of achieving consensus in a synchronous dynamic network, where an omniscient adversary controls the unidirectional communication links. Its behavior is modeled as a sequence of directed graphs representing the active (i.e. timely) communication links per round. We prove that consensus is impossible under some natural weak connectivity assumptions, and introduce vertex-stable root components as a—practical and not overly strong—means for circumventing this impossibility. Essentially, we assume that there is a short period of time during which an arbitrary part of the network remains strongly connected, while its interconnect topology keeps changing continuously. We present a consensus algorithm that works under this assumption, and prove its correctness. Our algorithm maintains a local estimate of the communication graphs, and applies techniques for detecting stable network properties and univalent system configurations. Our possibility results are complemented by several impossibility results and lower bounds, which reveal that our algorithm is asymptotically optimal.
This work has been supported by the Austrian Science Foundation (FWF) project P20529 and S11405. Peter Robinson has also been supported in part by Nanyang Technological University grant M58110000 and Singapore Ministry of Education (MOE) Academic Research Fund (AcRF) Tier 2 grant MOE2010-T2-2-082.
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Biely, M., Robinson, P., Schmid, U. (2012). Agreement in Directed Dynamic Networks. In: Even, G., Halldórsson, M.M. (eds) Structural Information and Communication Complexity. SIROCCO 2012. Lecture Notes in Computer Science, vol 7355. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31104-8_7
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DOI: https://doi.org/10.1007/978-3-642-31104-8_7
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