IEOR 6614, Spring 2016 : Homework 10

General Instructions

1. Please review the course information.
2. 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.
3. Numbered problems are all from the textbook Network Flows .

Problems

1. 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?
2. Show that the number of distinct minimum cuts in an n node multigraph G cannot exceed n(n-1)/2.
3. 17.22. 2 commodity flow.
4. 17.26. Concurrent flow problem.

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