Introduction to Algorithms, Second Edition

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The University of Texas at Austin Lecture 5 Department of Computer Sciences Professor Vijaya Ramachandran Randomized algorithms; random permutation CS357: ALGORITHMS, Spring 2006 Randomized algorithms Definition : A randomized algorithm is an algorithm that can make calls to a random number generator during the execution of the algorithm. These calls will be of the form x := Random ( a, b ) , where a, b are integers, a b . A call to Random ( a, b ) returns an integer in [ a, b ], with every integer in the range being equally likely to occur. Successive calls to Random ( * , * ) are assumed to be mutually independent. Definition : The expected running time of a randomized algorithm on a given input is the average running time of the algorithm over all outcomes of calls to the random number generator. The expected running time of a randomized algorithm for inputs of length n is the maximum expected running time of the algorithm over all inputs of length n . A randomized algorithm terminates in time t ( n ) with probability at least p if, for every input of length n , the probability that the algorithm terminates in time t ( n ) is at least p .
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