Properties of randomized algorithms (Monte Carlo, Las Vegas) -

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Now I am learning Las Vegas and Monte Carlo algorithms, and two questions can be simple but I can not answer them. If someone can help me ... thanks in advance

  1. Consider Monte Carlo Algorithm A for a Problem P, whose expected running time is the highest T (N) Let's suppose that N is producing the right solution with probability y (n) A has a solution, we can verify its Shita (n) time. How to get Las Vegas algorithm, which always gives the correct answer for P and runs in maximum time (T) (T) (N) / Y (N).

  2. Let 0 < Ε2 & lt; Ε1 & lt; Consider 1 Monte Carlo algorithm, which provides the correct solution to a problem with the possibility of at least 1-ε 1 regardless of input. How many independent hangings of this algorithm are enough to increase the probability of obtaining at least 1-ε2 enough input, regardless of input?

    1. repeat your algorithm to run And do not get the right answer until the result is tested. Each run and check takes (T) + T (N) is a geometric random variable with the units of time, and the run number 1 / y (n).

    2. What is the probability of failure for one run? For two runs? Not run? Determine the probability of failure for N, solve e2 and solve for n.


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