The Complexity of Multiterminal Cuts
SIAM Journal on Computing
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ISLPED '97 Proceedings of the 1997 international symposium on Low power electronics and design
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Self-stabilization
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SIAM Journal on Computing
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Average Binary Long-Lived Consensus: Quantifying the Stabilizing Role Played by Memory
SIROCCO '08 Proceedings of the 15th international colloquium on Structural Information and Communication Complexity
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DISC'07 Proceedings of the 21st international conference on Distributed Computing
The optimal strategy for the average long-lived consensus
CSR'11 Proceedings of the 6th international conference on Computer science: theory and applications
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We study strategies that minimize the instability of a fault-tolerant consensus system. More precisely, we find the strategy than minimizes the number of output changes over a random walk sequence of input vectors (where each component of the vector corresponds to a particular sensor reading). We analyze the case where each sensor can read three possible inputs. The proof of this result appears to be much more complex than the proof of the binary case (previous work). In the binary case the problem can be reduced to a minimal cut in a graph. We succeed in three dimensions by using the fact that an auxiliary graph (projected graph) is planar. For four and higher dimensions this auxiliary graph is not planar anymore and the problem remains open.