IEOR 6605, Fall 2001: Homework 05

General Instructions

1. 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.
2. Please do not express an algorithm using only pseudocode. Additional explanation is required!
3. Numbered problems are all from the textbook Network Flows .

Problems

1. Problem 7.15. Bad example for FIFO.
2. Problem 7.22. You only need to do 2 of the parts.
3. This problem asks you to prove that the gap heuristic, described in class, is correct. Suppose that at some point in the execution of a push-relabel algorithm, there exists an integer k, 0 < k < n for which no vertex has d(v) = k. Prove that all vertices with d(v) > k are on the source side of a minimum cut. If such a k exists, the gap heuristic updates every vertex v (except for t and s) for which d(v) > k to max(d(v), n+1). Prove that the resulting distance labelling is valid (see p. 209 for the definition of valid).

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