hw1(7) - CS 473G Graduate Algorithms Spring 2007 Homework 1...

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Unformatted text preview: CS 473G: Graduate Algorithms, Spring 2007 Homework 1 Due February 6, 2007 Remember to submit separate, individually stapled solutions to each of the problems. 1. Jeff tries to make his students happy. At the beginning of class, he passes out a questionnaire to students which lists a number of possible course policies in areas where he is flexible. Every student is asked to respond to each possible course policy with one of “strongly favor”, “mostly neutral”, or “strongly oppose”. Each student may respond with “strongly favor” or “strongly oppose” to at most five questions. Because Jeff’s students are very understanding, each student is happy if he or she prevails in just one of his or her strong policy preferences. Either describe a polynomial time algorithm for setting course policy to maximize the number of happy students or show that the problem is NP-hard. 2. Consider a variant 3SAT of 3SAT which asks, given a formula φ in conjunctive normal form in which each clause contains at most 3 literals and each variable appears in at most 3 clauses,...
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