Reduction

What is reduction?

Reduction is the single most common technique used in designing algorithms. Reducing one problem $X$ to another problem $Y$ means to write an algorithm for $X$ that uses an algorithm for $Y$ as a black box or subroutine. Crucially, the correctness of the resulting algorithm for $X$ can’t depend in any way on how the algorithm for $Y$ works. The only thing we can assume is that the black box solves $Y$ correctly. The inner workings of the black box are simply none of our business; they’re somebody else’s problem. It’s often best to literally think of the black box as functioning purely by magic.