Paper Info
Title
Stability of Multivalued Continuous Consensus
Abstract
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.
Year
DOI
Venue
2007
10.1137/S0097539704446335
SIAM J. Comput.
Keywords
Field
DocType
multivalued consensus function,multivalued continuous consensus,possible input value,previous input,output change,output value,input change,nonfaulty input,single output,faulty input,consensus function,consensus,stability
Discrete mathematics,Combinatorics,Upper and lower bounds,Instability,Simplex,Input/output,Subdivision,Geodesic,Mathematics,Numerical stability,Multivalued function
Journal
Volume
Issue
ISSN
37
4
0097-5397
Citations 
PageRank 
References 
8
0.67
0
Authors
3
Name
Order
Citations
PageRank
Lior Davidovitch1202.97
Shlomi Dolev22962260.61
Sergio Rajsbaum31367115.89