IEOR 6614, Spring 2016 : Homework 3

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. Problem 4.52. Bidirectional shortest paths. This algorithm was mentioned in the slides, here you prove its correctness.
2. Problem 5.51, 5.52, Bit scaling for shortest paths
3. Problem 5.55. This is the question we discussed in class. Try to see how to use as little information as possible beyond what you compute in running the original algorithm.
4. On pg. 94, there is a linear program for computing single source-shortest paths. Suppose that you have solved this linear program optimally and have a solution where the variables all take on integral values.
   1. Explain how to use the solution to the linear program to output a shortest path tree.
   2. Take the dual of the linear program. Give an explanation of what the dual solution represents.

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• Homework 2
• Homework 4