The randomized version of this algorithm is also fun: repeatedly find an edge that is not yet covered, select one of the two end points at random, and add it to S.
It's a nice exercise to show that the randomized algorithm is also a 2-approximate algorithm, i.e., the size of S is at most twice the size of S_{OPT}, in expectation.
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The randomized version of this algorithm is also fun: repeatedly find an edge that is not yet covered, select one of the two end points at random, and add it to S.
It's a nice exercise to show that the randomized algorithm is also a 2-approximate algorithm, i.e., the size of S is at most twice the size of S_{OPT}, in expectation.
I refer you to Bogosort. [1] One of the simplest interesting randomized algorithms.
https://en.wikipedia.org/wiki/Bogosort