Faster (and Still Pretty Simple) Unbiased Estimators for Network (Un)reliability
2017 IEEE 58th Annual Symposium on Foundations of Computer Science (FOCS)(2017)
摘要
Consider the problem of estimating the (un)reliability of an n-vertex graph when edges fail with probability p. We show that the Recursive Contraction Algorithms for minimum cuts, essentially unchanged and running in n
2+o(1)
time, yields an unbiased estimator of constant relative variance (and thus an FPRAS with the same time bound) whenever p
c
<; n
-2
. For larger p, we show that reliable graphs-where failures are rare so seemingly harder to find-effectively act like small graphs and can thus be analyzed quickly. Combining these ideas gives us an unbiased estimator for unreliability running in Õ(n
2.78
) time, an improvement on the previous Õ(n
3
) time bound.
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关键词
recursive contraction algorithms,constant relative variance,n-vertex graph,networkreliability,unreliability running,unbiased estimator
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