10. Randomized Algorithms: color coding and monotone local search - COMP6741: Parameterized and Exact Computation
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چکیده
Monte Carlo algorithms Definition 1. • A Monte Carlo algorithm is an algorithm whose output is incorrect with probability at most p. • A one sided error means that an algorithm’s input is incorrect only on true outputs, or false outputs but not both. • A false negative Monte Carlo algorithm is always correct when it returns false. Suppose we have an algorithm A for a decision problem which: • If no-instance: returns “no”. • If yes-instance: returns “yes” with probability p. Algorithm A is a one-sided Monte Carlo algorithm with false negatives. Problem Suppose A is a one-sided Monte Carlo algorithm with false negatives, that with probability p returns “yes” when the input is a yes-instance. How can we use A and design an a new algorithm which ensures a new success probability of a constant C? Let t = − ln(1−C) p and repeat t times. Failure probability is (1− p) ≤ (e−p)t = 1 ept = 1− C via the inequality 1− x ≤ e−x.
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تاریخ انتشار 2017