Assigned:
Thursday, April 7, 2016
Due:
Thursday, April 14, 2016
General Instructions
- Please review the
course information.
- You must write down with whom you worked on the assignment. If this
changes from problem to problem, then you should write down this
information separately with each problem.
- Numbered problems are all from the textbook Network Flows .
Problems
- Consider running the contraction algorithm until the number of vertices is reduced to some value t, and then
using a deterministic O(t3) algorithm to find the minimum cut in the remaining t node graph. What is the running time
of this procedure as a function of n and t, and what is the probability that it finds the minimum cut? Now suppose that you repeat this
algorithms enough times so that the probability of finding the minimum cut is at least 1-n-a for some constant a. What is
the running time of this algorithm?
- Show that the number of distinct minimum cuts in an n node multigraph G cannot exceed n(n-1)/2.
- 17.22. 2 commodity flow.
- 17.26. Concurrent flow problem.
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