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hw6 - CS 373 Combinatorial Algorithms Fall 2000 Homework...

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CS 373: Combinatorial Algorithms, Fall 2000 Homework 6 (due December 7, 2000 at midnight) Name: Net ID: Alias: U 3 / 4 1 Name: Net ID: Alias: U 3 / 4 1 Name: Net ID: Alias: U 3 / 4 1 Starting with Homework 1, homeworks may be done in teams of up to three people. Each team turns in just one solution, and every member of a team gets the same grade. Since 1-unit graduate students are required to solve problems that are worth extra credit for other students, 1-unit grad students may not be on the same team as 3/4-unit grad students or undergraduates. Neatly print your name(s), NetID(s), and the alias(es) you used for Homework 0 in the boxes above. Please also tell us whether you are an undergraduate, 3/4-unit grad student, or 1-unit grad student by circling U, 3 / 4 , or 1, respectively. Staple this sheet to the top of your homework. Required Problems 1. (a) Prove that P co-NP. (b) Show that if NP negationslash = co-NP, then no NP-complete problem is a member of co-NP. 2. 2 SAT is a special case of the formula satisfiability problem, where the input formula is in conjunctive normal form and every clause has at most two literals. Prove that 2 SAT is in P. 3. Describe an algorithm that solves the following problem, called 3 SUM , as quickly as possible: Given a set of n numbers, does it contain three elements whose sum is zero? For example, your algorithm should answer T RUE for the set {− 5 , 17 , 7 , 4 , 3 , 2 , 4 } , since 5+7+( 2) = 0 , and F ALSE for the set {− 6 , 7 , 4 , 13 , 2 , 5 , 13 } .
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CS 373 Homework 6 (due 12/7/00) Fall 2000 4.
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