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How to prove that a problem is NPC

How to prove that a problem is NPC. Cook. Cook showed the first NPC problem: SAT Cook received Turing Award in 1982. Karp. R. Karp showed several NPC problems, such as 3-STA, node (vertex) cover, and Hamiltonian cycle, etc. Karp received Turing Award in 1985.

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How to prove that a problem is NPC