Key Concepts

Maxflow, mincut, and Ford-Fulkerson basics

Ford-Fulkerson details

Residual network

Recommended Problems

C level

  1. Fall 2011, #11
  2. Spring 2012, #11
  3. Fall 2012, #6

B level

  1. Textbook 6.36
  2. Textbook 6.38

A level

  1. The instructors plan to grade the final, May 20. They have scheduled 8 hours for it. Each instructor prefers to grade only a certain subset of the 11 problems. They have represented their preferences in a graph in which a grader is connected to a problem if they are willing to grade it.

    Each grader has a grading speed, and each problem has a grading difficulty. If a problem with difficulty d is graded by an instructor with speed s, it will take d/s minutes to grade. There are N problems and M instructors; S students took the exam.

    Design an algorithm to determine if the instructors will be able to finish grading within the scheduled 8 hours, respecting their grading preferences.

    What is the order-of-growth worst-case running time of your algorithm as a function of both M and N? Assume that the speeds and difficulties are integers between 1 and 10. Also, assume that the work for a problem can be divided among different graders.

    Hint: formulate it as a maxflow problem and invoke a known algorithm for solving maxflow. Draw the resulting flow network to illustrate your construction. Answers

  2. Textbook 6.37