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# Lecture28 - CSE 421 Algorithms Richard Anderson Lecture 28...

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CSE 421 Algorithms Richard Anderson Lecture 28 NP-Completeness

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Populating the NP-Completeness Universe Circuit Sat < P 3-SAT 3-SAT < P Independent Set 3-SAT < P Vertex Cover Independent Set < P Clique 3-SAT < P Hamiltonian Circuit Hamiltonian Circuit < P Traveling Salesman 3-SAT < P Integer Linear Programming 3-SAT < P Graph Coloring 3-SAT < P Subset Sum Subset Sum < P Scheduling with Release times and deadlines
Cook’s Theorem The Circuit Satisfiability Problem is NP- Complete Circuit Satisfiability Given a boolean circuit, determine if there is an assignment of boolean values to the input to make the output true

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Circuit SAT AND OR AND AND OR OR AND NOT OR NOT x 1 x 2 x 3 x 4 x 5 AND AND NOT NOT AND OR NOT AND OR AND Satisfying assignment x 1 = T, x 2 = F, x 3 = F x 4 = T, x 5 = T Find a satisfying assignment
Proof of Cook’s Theorem Reduce an arbitrary problem Y in NP to X Let A be a non-deterministic polynomial time algorithm for Y Convert A to a circuit, so that Y is a Yes instance iff and only if the circuit is satisfiable

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• Fall '06
• RichardAnderson
• Algorithms, Computational complexity theory, vertex cover, NP-complete problems, NP-complete, Boolean satisfiability problem, Hamiltonian Circuit Hamiltonian Circuit

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