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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Las Vegas vs Monte-Carlo :Las Vegas → Monte-CarloA - Las Vegas algo with E[T A (I )] ≤ poly(n) for every I .By incorporating a counter which counts every elementarystep in<strong>to</strong> A and s<strong>to</strong>pping after, say, 4poly(n) steps, one gets apoly time Monte-Carlo algorithm B with a guaranteedconfidence <strong>of</strong> at least 3/4.Monte-Carlo → Las VegasA - Monte-Carlo alg with poly(n) time and 1/poly(n) successprobability. Suppose correctness <strong>of</strong> output can be verified inpoly(n) time.By running the alg A repeatedly (with independent coin<strong>to</strong>sses) until one gets a correct solution, we get a Las Vegasalgo with poly expected time.
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