How did Karp establish NP-completeness for so many problems?
My approach centered on the idea of polynomial-time reductions. I showed that if you could solve one problem efficiently, you could use that ability to solve another problem efficiently as well, by transforming an instance of the second problem into an instance of the first. By establishing a chain of such reductions, starting from a known NP-complete problem (like the Satisfiability problem), I demonstrated that many other important combinatorial problems shared the same computationally hard characteristic.
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