IEOR 6614, Spring 2006 : Homework 7

Assigned: Thursday, March 23, 2006
Due: Wednesday, March 29, 2006

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 .


  1. Problem 7.15. FIFO algorithm.
  2. Problem 7.14. Generic preflow-push.
  3. Problem 7.18. Note that the capacity scaling algorithm is slightly different, but related to the bit scaling algorithm and the maximum capacity path algorithm covered in class.
  4. Another variant of the prelfow-push algorithms is called "relabel-to-front". This algorithm works like the FIFO algorithm, except that we maintain the list of active vertices in a different way. Here the rule is that whenever we relabel a vertex it moves to the front of the list. We always choose the vertex at the front of the list for a discharge operation. Note that this means that if you are performing a discharge operation from node v, and v is relabeled, v then goes on the front of the list, and you call discharge on v again. Show that the relabel-to-front algorithm runs in O(V3) time.
  5. Problem 7.29. Parametric maximum flow.

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