An Introduction to Randomized algorithms - School of Technology ...
An Introduction to Randomized algorithms - School of Technology ...
An Introduction to Randomized algorithms - School of Technology ...
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Boosting success probability - IIA is a randomized algorithm <strong>to</strong> approximate #I .A runs in time poly(n, 1/ɛ) and outputs ans :Pr((1 − ɛ)(#I ) ≤ ans ≤ (1 + ɛ)(#I )) ≥ 1/2 + δ.Run m independent trials <strong>of</strong> A(I , ɛ).Take ans <strong>to</strong> be the median <strong>of</strong> {ans 1 , . . . , ans m }.Pr ((1 − ɛ)(#I ) ≤ ans ≤ (1 + ɛ)(#I )) ≥ 1 − e −δ2m/2 .Pr(success) = 1 − o(n −1 ) provided m ≥ 4(log n)/(δ 2 ).a good approximation efficiently computable.