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Series‐parallel reduction for difficult measures of network reliability
Author(s) -
Rosenthal Ar
Publication year - 1981
Publication title -
networks
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.977
H-Index - 64
eISSN - 1097-0037
pISSN - 0028-3045
DOI - 10.1002/net.3230110402
Subject(s) - variance reduction , reliability (semiconductor) , estimator , monte carlo method , series (stratigraphy) , variance (accounting) , computer science , reduction (mathematics) , importance sampling , sampling (signal processing) , mathematics , mathematical optimization , algorithm , statistics , paleontology , power (physics) , physics , geometry , accounting , filter (signal processing) , quantum mechanics , business , computer vision , biology
Formulas for series and parallel reductions are obtained for difficult measures of network reliability. Examples considered include “traffic to center,” “total traffic carried,” “minimum cut,” and “all demanding vertices communicate.” We find general properties of “distribution‐preserving” and “average‐preserving” replacements, and present several examples. For systems analyzed by Monte‐Carlo sampling, we find that the estimator variance is reduced by the replacement.