Finding the minimum cut of an undirected graph

Question Detail: 

Here's a question from a past exam I'm trying to solve:

For an undirected graph $G$ with positive weights $w(e) \geq 0$, I'm trying to find the minimum cut. I don't know other ways of doing that besides using the max-flow min-cut theorem. But the graph is undirected, so how should I direct it? I thought of directing edges on both ends, but then which vertex would be the source and which vertex would be the sink? Or is there another way to find the minimum cut?

Asked By : Jozef

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Question Source : http://cs.stackexchange.com/questions/3399

Answered By : Juho

There are plenty of algorithms for finding the min-cut of an undirected graph. Karger's algorithm is a simple yet effective randomized algorithm.

In short, the algorithm works by selecting edges uniformly at random and contracting them with self-loops removed. The process halts when there are two nodes remaining, and the two nodes represent a cut. To increase the probability of success, the randomized algorithm is ran several times. While doing the runs, one keeps track of the smallest cut found so far.

See the Wikipedia entry for more details. For perhaps a better introduction, check out the first chapter of Probability and Computing: Randomized Algorithms and Probabilistic Analysis by Michael Mitzenmacher and Eli Upfal.