OCD: obsessive consensus disorder (or repetitive consensus)
Proceedings of the twenty-seventh ACM symposium on Principles of distributed computing
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
Self-stabilizing Numerical Iterative Computation
SSS '08 Proceedings of the 10th International Symposium on Stabilization, Safety, and Security of Distributed Systems
Average long-lived binary consensus: Quantifying the stabilizing role played by memory
Theoretical Computer Science
The optimal strategy for the average long-lived consensus
CSR'11 Proceedings of the 6th international conference on Computer science: theory and applications
Average long-lived memoryless consensus: the three-value case
SIROCCO'10 Proceedings of the 17th international conference on Structural Information and Communication Complexity
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Multivalued consensus functions defined from a vector of inputs over the set $V$ of possible input values (and possibly from the previous input and output values) to a single output are investigated. The consensus functions are designed to tolerate $t$ faulty inputs. Two classes of multivalued consensus functions are defined, the exact value and the range value, which require the output to be one of the nonfaulty inputs or in the range of the nonfaulty inputs, respectively. The instability of consensus functions is examined, counting the maximal number of output changes along a geodesic path of input changes, a path in which each input is changed at most once. Lower and upper bounds for the instability of multivalued consensus functions as a function of $n$, the number of sensors, $t$, and $|V|$ are presented. A new technique for obtaining such lower bounds, using edgewise simplex subdivision, is presented.