Unformatted text preview: NP . We reduce 3 âˆ’ SAT to 0 âˆ’ 1 integer programming. Suppose we have m clauses (with three literals each) over variables u 1 , Â·Â·Â· , u n . Â±or each clause, construct an inequality by replacing âˆ¨ with +, u i with x i , and Â¯ u i by 1 âˆ’ x i , and requiring the sum to be at least 1. This gives m inequalities over n variables x 1 , Â·Â·Â· , x n . Â±or example, the clause u 2 âˆ¨ Â¯ u 4 âˆ¨ u 5 becomes x 2 + 1 âˆ’ x 4 + x 5 â‰¥ 1, with x i âˆˆ { , 1 } For each i . Clearly the original set oF clauses is satisfable iF and only iF the set oF m inequalities constructed has a solution. 1...
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 Spring '09
 ALEX
 Algorithms, C Programming, Berlin UBahn, dynamic programming solution, Jim Calvin Homework, Jim Calvin

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