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def-dec - CS648 Randomized Algorithms Lecture...

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CS648 Randomized Algorithms Lecture notes :Principle of deferred decision II Expected distance between two vertices in a complete graph with random edge weights Principle of deferred decision : Let f be a function of n random variables and there is an underlying algorithm that computes the value of f . These n random variables may be initially chosen to be independent and assumed to have certain probability distribution in the beginning. Sometimes there is an algorithm which computes f . In such scenario, the naive and usual way of calculating the expected value of f will be to compute value of f for each possible input (assigning all possible values to the random variables), and then taking an average of these values. This approach is a very cumbersome approach to compute expected value of f . On the contrary, there is a lazy way of exposing the random variables during the execution where we defer revealing the exact value of a random variable unless it is absolutely needed. Taking this approach turns out to be very effective in calculating the expected value of f . The reason why it is sometimes helpful is that the this approach imposes the least dependency on the values of the unexposed random variables in terms of the values taken by the already exposed random variables. As a result, it is much easier to analyze a particular step of the algorithm for calculating the final value taken by f . We shall highlight the usefulness of this approach with the following problem : Problem : Given a complete graph G = ( V, E ) on n

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