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

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Unformatted text preview: 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. 2SAT 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 2SAT is in P. 3. Describe an algorithm that solves the following problem, called 3SUM, 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 TRUE for the set { 5 , 17 , 7 , 4 , 3 , 2 , 4 } , since 5+7+( 2) = , and FALSE for the set { 6 , 7 , 4 , 13 , 2 , 5 , 13 } . CS 373...
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This note was uploaded on 12/15/2009 for the course 942 cs taught by Professor A during the Spring '09 term at University of Illinois at Urbana–Champaign.

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

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