CSU390 04F: Homework 09

Created: Tue 30 Nov 2004
Last modified: 

Assigned: Tue 30 Nov 2004
Due: Tue 07 Dec 2004

General Instructions

  1. Please review the grading policy outlined in the course information page.

  2. On the first page of each part of your solution write-up, you must make explicit which problems are to be graded for "regular credit", which problems are to be graded for "extra credit", and which problems you did not attempt. Please use a table something like the following

    Problem01020304 0506070809...
    CreditRCRCRCECRC RCNARCRC...

    where "RC" is "regular credit", "EC" is "extra credit", and "NA" is "not applicable" (not attempted). Failure to do so will result in an arbitrary set of problems being graded for regular credit, no problems being graded for extra credit, and a five percent penalty assessment.

  3. You must also 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.

Specific Instructions

  1. NOTE: This assignment cannot be accepted late since solutions for this assignment will be handed out on the last day of classes.

  2. Since you are only required to submit four problems, it is possible for you to solve Problems 1 and 2 (which are not reductions) and then only two reductions. I would strongly suggest that you attempt and solve at least three reductions. You will see NP-completeness reductions on the final exam, and it is important for you to have some experience solving such problems before the exam.

  3. For those of you who wish to improve your homework and overall course averages, I would suggest that you solve as many of the problems on this assignment as possible. If you solve all of the problems on this assignment (correctly), it will be worth 300 total points---as much as three typical assignments.

Problems

Required: 4 of the following 8 problems
Points: 25 pts per problem

  1. Exercises 7.6 and 7.7

  2. Exercises 7.11 and 7.33

  3. Exercise 7.16 (b)

  4. Exercise 7.19. Hint: Reduce from SAT or 3SAT. You may do so by adding one extra clause to the given formula.

  5. Exercise 7.21. Hint: Reduce from CLIQUE. You may do so by adding extra vertices and edges to the given graph.

  6. Exercise 7.22

  7. Exercise 7.27. Hint: Reduce from NOT-EQUAL-3SAT, defined in Exercise 7.22. (You need not solve Exercise 7.22 to solve this problem.)

  8. Exercise 7.26. Hint: Reduce from 3SAT. Each card will correspond to a variable, and flipping the card will correspond to setting its truth value. Each row on a card will correspond to a clause, and the absence or presence of a hole will correspond to whether that clause is satisfied by the variable setting or not. You will need one additional specially designed card as well.

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