3-SAT as integer program

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Presentation transcript:

3-SAT as integer program x ¬x y ¬y z ¬z 1 1 1 >= 1 ¬x ∨ y ∨ ¬z 1 1 1 >= 1 x ∨ ¬ y ∨ z x ∨ y ∨ z 1 1 1 >= 1 ¬ x ∨ ¬ y 1 1 >= 1 Exactly one of x, ¬ x 1 1 = 1 1 1 = 1 1 1 = 1 1

3-SAT -> SubSet Sum: separate digits Exactly one of x, ¬ x ¬x ∨ y ∨ ¬z x ∨ ¬ y ∨ z x ∨ y ∨ z ¬ x ∨ ¬ y x 1 1 1 1 ¬x 1 1 1 y 1 1 ¬y 1 1 1 1 z 1 1 1 ¬z 1 W >= 1 >= 1 >= 1 1 1 1 >= 1 2

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Approximation <u <u <u u u u `Loss’ in price: < u per item, Total loss: < nu 4

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