Karp's reductions are a specific type of polynomial-time many-one reduction used in computational complexity theory to show that one problem is at least as hard as another. These reductions allow us to transform instances of one decision problem into instances of another in such a way that the answer is preserved, which is essential for establishing the NP-completeness of problems. The importance of Karp's reductions lies in their ability to demonstrate the relationships among NP-complete problems and the implications of their complexity.
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