OPTIMAL TENTMATE ASSIGNMENT

In this homework, you will continue to consider the basic optimization problem posed in the August 1998 Dr. Dobb's Journal article entitled Mates, in Dennis Shasha's regular Dr. Ecco's Omniheurist Corner column. This time, however, you will be concerned with the tractability properties of the problem.

1. Give a generalization of the DDJ problem, in the problem description style of [Garey-Johnson]. For uniformity's sake, name it OPTIMAL TENTMATE ASSIGNMENT.
   1. How hard would it be to modify your code from assignment 1a to accept arbitrary instances of the problem you pose?
   2. How natural is the generalization you give?
2. Prove that your generalization of OPTIMAL TENTMATE ASSIGNMENT is NP-complete, or give a polytime algorithm for it. If your generalization is NP-complete, you might try to show this by reducing one of these 4 problems from [Garey-Johnson] to it: [ND17] MINIMUM CUT INTO BOUNDED SETS, [GT19] CLIQUE, [GT11] PARTITION INTO TRIANGLES, [SP18] EXPECTED COMPONENT SUM. (Assume that those 4 particular caught your eye when browsing the appendix...) My reformatted versions are available on-line [PS] [PDF], but of course all typos are mine. :-) Feel free to use any other known NP-complete problem as well.

Homework should be submitted by e-mail to <bart@cs.pdx.edu>. The words "CS410/510CS HW1b" should appear somewhere in the subject line. Remember:

• If I can't understand your submission, I can't give you credit for it.
• Everything I asked for is for a reason. Please follow the assignment instructions.
• If you need help, or have any question whatsoever, just ask!