CMPSCI 611: Advanced Algorithms Micah Adler Summary: CMPSCI 611: Advanced Algorithms Micah Adler Problem Set 3 Out: October 31, 2002 Due: November 7, 2002 1. [CLRS] Problem 26-3: Space shuttle experiments. 2. Recall Karger's min-cut algorithm: While number of vertices > 2: Select edge e = (u; v) uniformly at random. Merge u and v into a single vertex. Return remaining edges. We proved that this returns a minimum cut in the original graph with probability at least 1 n 2 , where n = jV j. (a) Describe a data structure that allows each iteration of the while loop to be performed in O(n) time, and justify this bound. Describe how this allows us to nd a minimum cut with probability at least 1  in time O(n 4 log  1 ). We next consider how to improve on this run time. The idea behind this improvement is that the probability of the min-cut algorithm hitting an edge in the minimum cut is fairly small for the rst few edges that are chosen, but increases with each merge that is performed. Thus, we should be repeating Collections: Computer Technologies and Information Sciences