A Fast and Simple Unbiased Estimator for Network (Un)reliability
2016 IEEE 57th Annual Symposium on Foundations of Computer Science (FOCS)(2016)
摘要
The following procedure yields an unbiased estimator for the disconnection probability of an n-vertex graph with minimum cut c if every edge fails independently with probability p: (i) contract every edge independently with probability 1- n
-2/c
, then (ii) recursively compute the disconnection probability of the resulting tiny graph if each edge fails with probability n
2/c
p. We give a short, simple, self-contained proof that this estimator can be computed in linear time and has relative variance O(n
2
). Combining these two facts with a standard sparsification argument yields an O(n
3
log n)-time algorithm for estimating the (un)reliability of a network. We also show how the technique can be used to create unbiased samples of disconnected networks.
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关键词
fast unbiased estimator,network reliability,network unreliability,disconnection probability,n-vertex graph,graph edge,linear time computation,standard sparsification argument
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