B. Charron-Bost,M Függer, T. Nowak:

"Fast, Robust, Quantizable Approximate Consensus";

Talk: International Colloquium on Automata, Languages and Programming (ICALP), Rome, Italy; 2016-07-12 - 2016-07-15; in: "Proceedings 43rd International Colloquium on Automata, Languages, and Programming (ICALP'16)", Leibniz International Proceedings in Informatics (LIPIcs), (2016), ISBN: 978-3-95977-013-2; 1 - 14.

We introduce a new class of distributed algorithms for the approximate consensus problem in dynamic rooted networks, which we call amortized averaging algorithms. They are deduced from ordinary averaging algorithms by adding a value-gathering phase before each value update. This results in a drastic drop in decision times, from being exponential in the number n of processes to being polynomial under the assumption that each process knows n. In particular, the amortized midpoint algorithm is the first algorithm that achieves a linear decision time in dynamic rooted networks with an optimal contraction rate of 1/2 at each update step. We then show robustness of the amortized midpoint algorithm under violation of network assumptions: it gracefully degrades if communication graphs from time to time are non rooted, or under a wrong estimate of the number of processes. Finally, we prove that the amortized midpoint algorithm behaves well if processes can store and send only quantized values, rendering it well-suited for the design of dynamic networked systems. As a corollary we obtain that the 2-set consensus problem is solvable in linear time in any dynamic rooted network model.

approximate consensus, dynamic networks, averaging algorithms

http://dx.doi.org/10.4230/LIPIcs.ICALP.2016.137

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