example-reductions - Example Reductions 1. SAT p 3SAT...

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Unformatted text preview: Example Reductions 1. SAT p 3SAT Transformation uses local replacement technique Identify any clause with n > 3 literals: Example: (l1 l2 l3 l4 l5 . . . ln ) Create n - 2 new clauses using n - 3 new variables zj as follows: (l1 l2 z1 ), (z1 l3 z2 ), (z2 l4 z3 ), . . . , (zn-3 ln-1 ln ) Key idea: New n - 3 variables can satisfy exactly n - 3 of the n - 2 clauses, so at least one of the new clauses must be satisfied by an old literal. Somewhat similar to what we did with Chomsky Normal Form 1 2. Hamiltonian Path p Hamiltonian Circuit Transformation R Input to R (graph G = (V, E), an input to HP) Output of R (graph G = (V , E ), an input to HC) V = V {x V )} E = E {(x, v) | v V ) Argument that output of R, namely G , has polynomial size What is the size of G relative to G? Yes to Yes argument (if G has a HP, then G has a HC) Let (v1 , v2 , . . . , vV ) be the HP in G Then is a HC in G Briefly argue why Yes from yes argument (or No to No argument) (If G' has a HC, then G has a HP) Let (x, v1 , v2 , . . . , vV , x) be the HC in G Then is a HP in G Briefly argue why 2 ...
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example-reductions - Example Reductions 1. SAT p 3SAT...

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