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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

  

Source: Adler, Micah - Department of Computer Science, University of Massachusetts at Amherst

 

Collections: Computer Technologies and Information Sciences