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2-SAT — Forcing variable to be true
By tom, history, 9 years ago, In English

Hello,

I'm solving problem with 2-SAT algorithm and I need to be sure that some xi will be 1 (or 0). How can I make this happen with 2SAT algorithm? When I add "xi or xi", I put xi and not xi into one SCC and 2-SAT returns me that there is no solution. Is it possible?

Thanks

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9 years ago, # |
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when you add x or x you shouldn't put them in one SCC. because you are adding 2 same sdges.

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9 years ago, # |
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If you want to force x_i to be true just add implication !x_i -> x_i.

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9 years ago, # |
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It's simple: BFS over the 2-SAT graph (the skew-symmetric one) from the fixed variables while checking for contradictions. When it finishes, there will be no edge from a known variable to an unknown one. The skew-symmetricity makes sure that there's no unfixed variable from which a fixed variable can be reached afterwards, so any solution of the unfixed part of the graph + the variables you fixed this way is a solution of the original problem.

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